i really think it's quite a shame that there aren't more people who are both "mathematically mature", and also try to teach young kids "real math", and collaborate to figure out what works. like, keeping eyes on the ball of real math, here.
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Replying to @argletargle
i think a lot of your arguments make sense if you want your child to be a mathematician but i don't see how any of these will be material if they just need to learn calculus/linear algebra and move on to other things (which i think won't be affected by learning math)
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Replying to @alexeyguzey
hm.. this isn't coming from gearing toward them being a mathematician, but it is coming from gearing toward them being able to "theorize seriously" in some general sense, like be able to see deeper into things than the intuitions we develop naturally. maybe we differ in that goal
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Replying to @argletargle
why do you believe that learning math would help to theorize in some general sense better than playing Civilization or Europa Universalis?
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Replying to @alexeyguzey
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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Replying to @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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Replying to @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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Replying to @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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Replying to @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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Replying to @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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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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Replying to @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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Replying to @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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