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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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 @Meaningness
What would bother me: if mathematicians were (1) routinely publishing proofs of theorems that later turned out to be false; and (2) those theorems were important enough that they caused large quantities of followon work to be done, based on those results. I know of...
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Replying to @michael_nielsen @Meaningness
plenty of minor instances of this. But no really major instance.
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Yes, as I said at the beginning of the thread, I don’t think there’s a lot of false theorems, and the analogy with science is imperfect. The harm of non-replicability would not be wrong results but reduced productivity, relevance, and enjoyment.
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