jaydaigle

4 ms·

1.
by jaydaigle 5y ago
Interesting! My experience is that scooping is less of an issue in math than in any of the science fields I have friends in. Papers are lower-stakes, there's less money involved, and if two of you are working on the same project you
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by jaydaigle 5y ago
But what does "picking at random" mean? If you think it's obvious that you can just make infinitely many random choices at the same time, you're endorsing the axiom of choice. (If you think you can make one random choic
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by jaydaigle 5y ago
This is super cool and I wish I'd known about it before writing the piece; I'd have been comfortable being a lot more muscular in the conclusion. This seems like it makes precise my suggestion that the axiom of choice only matter
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by jaydaigle 5y ago
My take on this is that the axiom of choice allows you to produce infinite amounts of information, if and only if you start with infinite amounts of input. Think about how much information is involved in presenting an infinite collection of
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by jaydaigle 5y ago
I'd agree with this entirely, honestly. (Including the sleight-of-hand I'm engaging in to make things seem exactly the right amount of weird; see footnote 14.) Infinity is so weird that it's really hard to agree on what infi
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by jaydaigle 5y ago
ketralnis is right that this only terminates if an algorithm exists, so the claim that this terminates is equivalent to the axiom of choice. But I'd also add that you can have a choice function that isn't an "algorithm".
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by jaydaigle 6y ago
You're totally right, of course. And I even mention that in the post. If we assume that S ~ N then we get that exponential growth. But eventually (unfortunately) enough people will get sick that S is no longer close to N; that'
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by jaydaigle 6y ago
I'm a bit late to this, sorry; one of my students let me know this thread existed! I want to encourage you not to try to use this formula or anything like it to make concrete predictions. You are, unfortunately, right that the numbers