it's really bizarre how often students are like "help i'm stuck on this problem" and when you ask what they're stuck on they reveal that they don't even know the meaning of one or more of the words in it
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like... of course you're stuck on the problem, you don't even know what it's asking! but for some reason it doesn't occur to them to ask "help what does this even mean"
maybe they don't feel like they're allowed to?
cursed school system
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i have a half-baked rant in the works about this and it's not all the way done yet but there's something really fucked up and gaslight-y about how school teaches you to orient towards knowledge
knowledge as what authorities say rather than knowledge as derived from perception
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okay yeah here it is: school teaches you that being gaslit is the *fundamental source of knowledge*
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remembering that story about a teacher who told their students that 1/3 was irrational
one of the best things about being too smart for your own good as a kid, at least, is being disabused of the idea that teachers had any kind of special access to knowledge that i didn't
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(i am thinking about all of this in the context of e.g. how poorly the vaccine rollout is going, how unwilling people are to disobey guidelines and vaccinate people who aren't "supposed" to be vaccinated, the bad situation around covid epistemics generally, etc.)
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Its decimal expansion goes on forever! Surely it must be irrational, and also since the decimal expansion is infinitely long it must contain every possible sequence of digits as a substring
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this reminds me of when my middle school teacher got furious when I kept insisting that he explain why pi is irrational
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Gotta share my story about a physical science teacher that didn't understand inertia:
lesswrong.com/posts/48WeP7oT
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We taught for centuries that knowledge stems naturally and exclusively from authority and when that inevitably failed many people lost their epistemic compass and we have flat earth and anti vaxxers.