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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Replying to @Meaningness @XenaProject and
It's easy to find old, old examples of this. Consider Hilbert's published "proof" of the Continuum Hypothesis. Or any one of thousands of similar (though usually less spectacular) examples.
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Replying to @michael_nielsen @Meaningness and
So published proofs are sometimes wrong. So what? This doesn't seem especially notable. It is, of course, nice to have fairly reliable process for telling what's well established from what's wrong, but publication of a paper has never been more than a small part of that.
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Replying to @michael_nielsen @XenaProject and
Well the question would be whether that process could be improved. The slides provide examples of ways it seems not to work very well.
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Replying to @Meaningness @michael_nielsen and
“Replicability” here would mean “how can we find out whether this result is true, other than by opinion polling?”
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Replying to @Meaningness @XenaProject and
"Improved"? You can improve traffic safety by speed limiting all cars to 3 miles per hour. But it would have some other disadvantages. I'm not against formally checkable proofs, but it does seem like focusing on the 17th most significant bit.
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Oh, to be clear, I am not advocating for computer proof checking. I hope it can be made useful but that’s not what I had in mind in today’s tweets at all. Rather, an upgrade in social processes, as in the psychology re-credibilizing movement.
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Replying to @Meaningness @XenaProject and
It's not an upgrade. It's a change. Having more rigorous standards is an error in the earliest days of a field. I wince when I hear people say "X didn't replicate" and then imply therefore it's not true. Much of the time I suspect they're discarding important scientific insight.
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Replying to @michael_nielsen @XenaProject and
I agree with everything you say here; not sure what you disagree with? (Math isn’t a new field?) Assuming
@XenaProject’s statements here are correct, this seems like a problem. Presumably not that it’s false, but more like “we lost the data”pic.twitter.com/pTnSxvn59s
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