“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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Replying to @michael_nielsen @XenaProject and
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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Replying to @Meaningness
Why is this a problem? Similar thing happened with Nash's proof of the (possibly more important?) embedding theorem: the proof had an error that wasn't discovered for ~50 years. But that made no difference at all, because the existing processes of mathematics worked just fine...
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Replying to @michael_nielsen
My hope would be that math could be more productive if its self-understanding and social processes worked better. I have little experience with those processes personally, so I am not in a position to do more than suggest the possibility.
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Replying to @Meaningness @michael_nielsen
Seems like at least some members of the math community have an understanding of the meta-problem of proof:https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ …
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Replying to @krowney @michael_nielsen
Yes, there’s about five things that we all cite whenever anything like this comes up, and that is one of them! That there are only five suggests there’s tons of low-hanging fruit ripe for the picking
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Replying to @Meaningness @michael_nielsen
If I’m not mistaken, Tao is working with other mathematicians on formalizing these notions of proof in much more formal detail as a new meta-mathematical framework on foundations.
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I didn’t know that; thank you!
As I said to @michael_nielsen, I’m not at all sure “more formal” is the best way forward, but it seems one sensible direction to pursue
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Replying to @Meaningness @michael_nielsen
There’s been a few foundational “crises” of a sort in past math history. Not sure if the completeness theorems really resolved them, but at least the increased use of formal treatment of these questions shed light on the nature of mathematical thought.
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