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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A better understanding of what math is and how we do it might improve the rate at which mathematical understanding increases, its dissemination to other fields, and its relevance and usefulness.pic.twitter.com/POO3njXgfj
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OK, maybe mathematics DOES have a broad replicability problem! Seemingly strong evidence and arguments from
@XenaProject, whose post I tweeted yesterday. Great slides! (h/t@vonbladet,@aelkus) (“Seemingly”: I’m not qualified to have an opinion here) http://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf …pic.twitter.com/UDQLsKoph3
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What is the right one? Or is the point that they should not assume a theory at all?
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We don’t have a very good one yet, although there’s some understanding. Much meta-science research is needed!
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Have you written at length on this somewhere, to which you could give us a link?
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Not yet published, I’m afraid!
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Mathematicians and scientists have vague folk theories of what math and science are that both are blurred ancestral memories of pre-WWII logical positivism.
These theories are totally wrong, but do little *direct* harm because they are mainly ignored in practice.