Of the forms of exercise I cover, weight training has the most rigorous evidence separating what works and what doesn’t. This study (pdf warning) examines what sort of resistance training results in the most rapid improvements.
Link is now broken, but this one works (assuming that this is the article you were thinking of).
Perhaps it would be beneficial to make a game used for probability calibration in which players are asked questions and give answers along with their probability estimate of it being correct. The number of points gained or lost would be a function of the player’s probability estimate such that players would maximize their score by using an unbiased confidence estimate (i.e. they are wrong p proportion of the time when they say they think they are correct with probability p. I don’t know of such a function off hand, but they are used in machine learning, so they should be able to be found easily enough. This might already exist, but if not, it could be something CFAR could use.
One function that works for this is log scoring: the number of points you get is the log of the probability you place in the correct answer. The general thing to google to find other functions that work for this is "log scoring rules".
At the Australian mega-meetup, we played the standard 2-truths-1-lie icebreaker game, except participants had to give their probability for each statement being the lie, and were given log scores. I can't answer for everybody, but I thought it was quite fun.
Canberra HPMOR Wrap Party:
The amount of suffering introduced by factory-farming is entirely negligible compared to the amount of wild-animal suffering that's been taking place as long as life has existed, continues to take place, and will continue to take place unless we cause a wholesale extinction of the Earth's biosphere.
Unless you're prepared to eradicate animal life, no personal choice you ever make will have a meaningful impact on the amount of suffering in the universe.
Your second sentence doesn't follow from the first. Just because there is an enormous amount of suffering in the world doesn't mean that you can't alleviate a meaningful amount. The only way this is true is if by "meaningful" you mean as a proportion of the total amount of suffering, which doesn't really make sense - the fact that others are suffering doesn't make a good act any less good.
Ohhh, thanks. That explains it. I feel like there should exist things for which provable(not(p)), but I can't think of any offhand, so that'll do for now.
To answer the below: I'm not saying that provable(X or notX) implies provable (not X). I'm saying...I'll just put it in lemma form(P(x) means provable(x):
If P( if x then Q) AND P(if not x then Q)
Then P(not x or Q) and P(x or Q): by rules of if then
Then P( (X and not X) or Q): by rules of distribution
Then P(Q): Rules of or statements
So my proof structure is as follows: Prove that both Provable(P) and not Provable(P) imply provable(P). Then, by the above lemma, Provable(P). I don't need to prove Provable(not(Provable(P))), that's not required by the lemma. All I need to prove is that the logical operations that lead from Not(provable(P))) to Provable(P)) are truth and provability preserving
Breaking my no-comment commitment because I think I might know what you were thinking that I didn't realise that you were thinking (won't comment after this though): if you start with (provable(provable(P)) or provable(not(provable(P)))), then you can get your desired result, and indeed, provable(provable(P) or not(provable(P))). However, provable(Q or not(Q)) does not imply provable(Q) or provable(not(Q)), since there are undecideable questions in PA.
To answer the below: I'm not saying that provable(X or notX) implies provable (not X). I'm saying...I'll just put it in lemma form(P(x) means provable(x):
If P( if x then Q) AND P(if not x then Q)
Then P(not x or Q) and P(x or Q): by rules of if then
Then P( (X and not X) or Q): by rules of distribution
Then P(Q): Rules of or statements
So my proof structure is as follows: Prove that both Provable(P) and not Provable(P) imply provable(P). Then, by the above lemma, Provable(P). I don't need to prove Provable(not(Provable(P))), that's not required by the lemma. All I need to prove is that the logical operations that lead from Not(provable(P))) to Provable(P)) are truth and provability preserving
I agree that if you could prove that (if not(provable(P)) then provable(P)), then you could prove provable(P). That being said, I don't think that you can actually prove (if not(provable(P)) then provable(P)). A few times in this thread, I've shown what I think the problem is with your attempted proof - the second half of step 3 does not follow from the first half. You are assuming X, proving Y, then concluding provable(Y), which is false, because X itself might not have been provable. I am really tired of this thread, and will no longer comment.
is x or not x provable? Then use my proof structure again.
The whole point of this discussion is that I don't think that your proof structure is valid. To be honest, I'm not sure where your confusion lies here. Do you think that all statements that are true in PA are provable in PA? If not, how are you deriving provable(if x then q) from (if x then q)?
In regards to your above comment, just because you have provable(x or not(x)) doesn't mean you have provable(not(x)), which is what you need to deduce provable(if x then q).
So then here's a smaller lemma: for all x and all q:
If(not(x))
Then provable(if x then q): by definition of if-then
So replace x by Provable(P) and q by p.
Where's the flaw?
The flaw is that you are correctly noticing that provable(if(not(x) then (if x then q)), and incorrectly concluding if(not(x)) then provable(if x then q). It is true that if(not(x)) then (if x then q), but if(not(x)) is not necessarily provable, so (if x then q) is also not necessarily provable.
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