Matt Schwartz

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Matt Schwartz

Matt Schwartz

@mattcschwartz

PhD student @PrincetonEcon

Katılım Ocak 2019
358 Takip Edilen71 Takipçiler
Matt Schwartz
Matt Schwartz@mattcschwartz·
@AlexTISYoung Yeah certainly towards 0, but that effect wouldn't explain a negative correlation. Agreed though, basically what's happening is that because of the effect there's very little correlation, and then in the small sample it happened to be negative
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Alex Strudwick Young
Alex Strudwick Young@AlexTISYoung·
@mattcschwartz It is from a small sample. But you'd expect some movement of the correlation down towards to zero/negative due to selection.
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@thomasfbloom I kind of disagree about the second claim? It seems like if you believe there's even a reasonable chance that AI gets much better at math, then the main importance of these results is how it affects our beliefs about future capabilities
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Thomas Bloom
Thomas Bloom@thomasfbloom·
I hope that, in all of the publicity around recent AI solutions of Erdos problems, at least a few people have actually read the maths and learned some of the theory behind e.g. primitive sets. The role of these problems as AI headlines is secondary to some beautiful mathematics!
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Matt Schwartz
Matt Schwartz@mattcschwartz·
This relates to a simpler question I've thought about a lot: if you're on an island with a perfect clone of yourself, should you cooperate in a prisoner's dilemma? Similar idea to Newcomb's paradox
Jeffrey Ladish@JeffLadish

You find yourself trapped on an island with 99 identical copies of yourself. If you press the red button, you will certainly die. If you press the blue button, you’ll die if and only if at least half of the clones presses blue. What do you do?

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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford Of course it’s hard to count this as serious evidence, but I asked my friend who’s the most pedantic person I know and does probability-theory-heavy work
Matt Schwartz tweet media
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Jesse Spafford
Jesse Spafford@jessespafford·
@mattcschwartz Well, no. They have deviated from standard academic convention without noticing because they are eliding a conceptual distinction. That's the whole problem!
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford But if 10% = 0.1, then it's in line with the conventional definition of a probability function to write P(X) = 10%. It might not be the way academics usually write it, but it's not a problem
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford I guess you should be reassured then that to those people, and I believe to most, the expression 10% is taken to be equivalent to 0.1, so that all tools are indeed being used properly
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Jesse Spafford
Jesse Spafford@jessespafford·
@mattcschwartz And I guess I'd be fine with "P(x)" language so long as it was being used in (what I take to be) the correct way. I actually favor people drawing on technical tools and have no real preference for "the chance of x" vs. "P(x)." but I do think using the latter requires more care.
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford Yeah this point I agree with. I find it pretty stupid how much they like saying P(X), orthogonal, etc. I just don't have a problem with referring to a probability by its percent representation
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Jesse Spafford
Jesse Spafford@jessespafford·
@mattcschwartz I think this gets at the heart of my complaint. It's not like saying "P(something)" is actually shorter or more efficient than saying "the chance of something." So, to use that language but imprecisely is just pseudo-technicality, which is a bad epistemic practice.
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford I really don't think it does. Different communities use slightly different conventions for standard notation all the time, and it's completely fine. Everyone knew what he meant by 10%
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Jesse Spafford
Jesse Spafford@jessespafford·
@mattcschwartz Okay, well, then setting it aside, the complaint I have is that there are these established things called probability functions that take states of affairs as inputs and produce decimal values as outputs—and it makes a mess of things when people help themselves to the language...
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford I find it very hard to imagine how this is defective. Like you accepted that it's fine to say the chance of something is 10%. But if we accept saying the probability of something is 10%, shorthanded by P(something) is 10%, then that's a problem?
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Jesse Spafford
Jesse Spafford@jessespafford·
@mattcschwartz Like, yes, I believe that this person was using language in the way that their community uses the language. But the community is doing something defective.
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford Yeah it is, I was just pointing out that if we want to be this pedantic we should use the most standard terminology. Not a serious point
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Jesse Spafford
Jesse Spafford@jessespafford·
@mattcschwartz Isn't a probability measure still a function? What do you take the difference to be here?
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford In this specific case, where they really are just using their own shorthand that's completely fine and very convenient. Especially for them because they talk so much about specific probabilities, and it's a lot easier to read 0.1% than 0.001
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford Yes I mean I do find them incredibly annoying, but I still don't think they're really violating convention x.com/mattcschwartz/…
Matt Schwartz@mattcschwartz

@jessespafford I'm not even sure we should think of the whole P() thing as a "probability function" (since we're being very pedantic I think you should call it a probability measure), it's just this short-hand for saying "what is your belief about X"

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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford Because like no one's defined what this function/measure P is, what the set of states and sigma algebra even are, etc. It's just a shorthand way of expressing an intuitive idea
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford I'm not even sure we should think of the whole P() thing as a "probability function" (since we're being very pedantic I think you should call it a probability measure), it's just this short-hand for saying "what is your belief about X"
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford And in that community (and I think the forecasting community more broadly), they are completely fine with saying the probability of something is 20%
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford They weren't following the convention that's used in journals because it wasn't a journal, it was a tweet. I mean I'd argue the whole "what's your P(X)" thing is actually a rationalist community phrase rather than an academic one
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Matt Schwartz
Matt Schwartz@mattcschwartz·
@jessespafford They also wouldn't write "my P(doom) is >0.1" but that doesn't make it a technical error
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