Comfortable folk theories of technical work do harm by filling the space where a better understanding could go, making its absence invisible. “Yes of course we know how to do science! We are scientists!” But clearly you didn’t, because you go so much of it wrong.
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Some sciences are upgrading their understanding, which I am optimistic will lead to better science.https://meaningness.com/metablog/upgrade-your-cargo-cult …
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Does the folk theory of mathematics also cause trouble? Here I am less confident, because math rarely has replication crises. However, this paper suggests to me that more and better math might get done if it were upgraded: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/XSbDWXhDpz
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"Of course we know how to do mathematics! We are mathematicians!" But there's good evidence you don't, and so you can't teach it clearly, and you can't reflect on whether you are doing it well or badly. https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/YsL16YdGVe
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Replying to @Meaningness
yeah, I suspect that for many students who find they're "no good at" a subject (even when they're good at other similarly difficult subjects), it's because they can't catch on to the pattern of which things that discipline includes in its models and which are "irrelevant details"
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Replying to @s_r_constantin @Meaningness
My copy of that Ideal Mathematician essay has this Wittgenstein story at the start. "If a child does not respond to the suggestive gesture, it is separated from the others and treated as a lunatic."pic.twitter.com/lFMVTXqAux
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(the book is Tymoczko's 'New Directions in the Philosophy of Mathematics: An Anthology')
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Replying to @drossbucket @s_r_constantin
Would you recommend it? ("This provocative book goes beyond foundationalist questions to offer what has been called a “postmodern” assessment of the philosophy of mathematics — one that addresses issues of theoretical importance in terms of mathematical experience.") —blurb
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Replying to @Meaningness @s_r_constantin
Yeah I would, though you've already read the best bits - The Ideal Mathematician and Thurston's Proof and Progress. There's also some of Lakatos Proofs and Refutations, and I liked Judith Grabiner on 18th c mathematical culture - emailed you notes on that a while back.
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It's an anthology so obviously patchy, and some of the rest is formal logic and computer proofs which I have zero interest in - ymmv. But the general theme of the book is great and I haven't really seen anything else like it.
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