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[silverspawn]

obviously clear clarifying oblation, clearly obfuscating orderly clarity, overly clouding cleared mind

[Awaclus]

I don't really get it. Isn't it obviously 4+2 since that's the only thing that doesn't equal 5, making it obviously distinct from the rest?

It's obviously distinct, by virtue of being the least fivey thing on the list. If the prompt was "good platform for a secret private conversation" instead of "5" and the options were three pretty good platforms and one obviously terrible platform, would you pick the obviously terrible option or try to figure out a reason why one of the three good ones was better than the rest?

[Awaclus]

Also it isn't super clear if the poll is asking for the Schelling point out of the four options, or the Schelling point out of any number of arbitrary options (with the correct answer being one of the four options).

[silverspawn]

I don't really get it. Isn't it obviously 4+2 since that's the only thing that doesn't equal 5, making it obviously distinct from the rest?

It's obviously distinct, by virtue of being the least fivey thing on the list. If the prompt was "good platform for a secret private conversation" instead of "5" and the options were three pretty good platforms and one obviously terrible platform, would you pick the obviously terrible option or try to figure out a reason why one of the three good ones was better than the rest?

the latter, but that analogy has the property that you have to use the thing you pick

[Awaclus]

I don't really get it. Isn't it obviously 4+2 since that's the only thing that doesn't equal 5, making it obviously distinct from the rest?

It's obviously distinct, by virtue of being the least fivey thing on the list. If the prompt was "good platform for a secret private conversation" instead of "5" and the options were three pretty good platforms and one obviously terrible platform, would you pick the obviously terrible option or try to figure out a reason why one of the three good ones was better than the rest?

the latter, but that analogy has the property that you have to use the thing you pick

I would assume that the "pick something useful" convention would carry over to situations where being useful is just an arbitrary property among others. Like when you're playing Hanabi and the convention of what to do with new cards in your hand vs. old cards in your hand, which forms naturally due to the cards having been in your hand for a different amount of time, carries over to the order in which you drew your starting hand just for the sake of convention.

[silverspawn]

I don't really get it. Isn't it obviously 4+2 since that's the only thing that doesn't equal 5, making it obviously distinct from the rest?

It's obviously distinct, by virtue of being the least fivey thing on the list. If the prompt was "good platform for a secret private conversation" instead of "5" and the options were three pretty good platforms and one obviously terrible platform, would you pick the obviously terrible option or try to figure out a reason why one of the three good ones was better than the rest?

the latter, but that analogy has the property that you have to use the thing you pick

I would assume that the "pick something useful" convention would carry over to situations where being useful is just an arbitrary property among others. Like when you're playing Hanabi and the convention of what to do with new cards in your hand vs. old cards in your hand, which forms naturally due to the cards having been in your hand for a different amount of time, carries over to the order in which you drew your starting hand just for the sake of convention.

Can you rephrase this? Like, are you saying that being useful ≙ being correct?

[silverspawn]

I wonder how much better my grades in university would have been if I had done an annealing session every evening before writing an exam

[Awaclus]

I would assume that the "pick something useful" convention would carry over to situations where being useful is just an arbitrary property among others. Like when you're playing Hanabi and the convention of what to do with new cards in your hand vs. old cards in your hand, which forms naturally due to the cards having been in your hand for a different amount of time, carries over to the order in which you drew your starting hand just for the sake of convention.

Can you rephrase this? Like, are you saying that being useful ≙ being correct?

I am saying that being incorrect ≙ being obviously not useful. 4+1 is probably not useful in most situations even though it's correct, but 5+0 and 2+3 could be. If we're, say, carrying five heavy things (that weigh like 10 kg each so it's reasonable to carry more than one per person, but each additional one makes it substantially less pleasant) somewhere and there's two of us, then obviously one of us taking four of the five things and the other taking two is not even possible, and 4+1 or 5+0 aren't very reasonable either, so 2+3 ends up being the convention. If we're carrying five sheets of paper instead, there's probably no point in doing anything other than 5+0, so that's what the convention is in that situation.

When it's a question where it doesn't matter in principle what you pick, you just have to figure out what convention to extrapolate from so that it covers that situation in addition to the situation where it formed for some reason that mattered in that context. Which is usually pretty easy, like in the Hanabi starting hand example. If the question is as abstract as "5", it's a lot more difficult, which is why I can see a case for both 2+3 and 5+0, but I don't know why there would be a convention of picking the only answer that doesn't work.

[silverspawn]

Reasonable. But the thing is... well actually there are two things

If we're, say, carrying five heavy things (that weigh like 10 kg each so it's reasonable to carry more than one per person, but each additional one makes it substantially less pleasant) somewhere and there's two of us, then obviously one of us taking four of the five things and the other taking two is not even possible, and 4+1 or 5+0 aren't very reasonable either, so 2+3 ends up being the convention.

- In math formalized as set theory, 2+3 and 4+1 refer to *the same object*, as defined by the axiom of extensionality. I think this is a similar issue as when people say "one drop of water plus another drop is just one drop not two, math is wrong lol". You've computed something like human_description(merge(water_drop, water_drop)), not water_drop + water_drop. The + operator doesn't do all of your intuitive "and" things, it does something much more narrow. 2 objects in the left hand and 3 in the right aren't any more 2+3 than 4+1... under that extremely formal view.

I am saying that being incorrect ≙ being obviously not useful.

- I don't think saying "5" implies a normative thing. Like, there was another twitter poll that asked,

"Pick the shelling point and also don't pick c" with answers a, b, c, d.

In *that* case, I buy talking about correctness. (Hilariously, that poll has majority answers on c, ffs.) But if you just say "5", only "5", not even "5.", I don't think you are incorrect to say 4+2 since the poll didn't ask you to choose a number that's 5. You just have an abstract "truth" property.

( This difference between "just writing down an abstract element with a truth value" and "making a claim" really creates a knot in my brain. It's not the first time I've thought about it. )

[silverspawn]

How nice of ETH to go down right before my Goodheart-week-1$-per-karma-point-in-LW is paid out in ETH. Very forthcoming.

[Awaclus]

Reasonable. But the thing is... well actually there are two things

If we're, say, carrying five heavy things (that weigh like 10 kg each so it's reasonable to carry more than one per person, but each additional one makes it substantially less pleasant) somewhere and there's two of us, then obviously one of us taking four of the five things and the other taking two is not even possible, and 4+1 or 5+0 aren't very reasonable either, so 2+3 ends up being the convention.

- In math formalized as set theory, 2+3 and 4+1 refer to *the same object*, as defined by the axiom of extensionality. I think this is a similar issue as when people say "one drop of water plus another drop is just one drop not two, math is wrong lol". You've computed something like human_description(merge(water_drop, water_drop)), not water_drop + water_drop. The + operator doesn't do all of your intuitive "and" things, it does something much more narrow. 2 objects in the left hand and 3 in the right aren't any more 2+3 than 4+1... under that extremely formal view.

If you talk to the average person about the axiom of extensionality, they're definitely not going to know what that is, and while they might agree that 4+1 is a correct way to describe 2 objects in the left hand and 3 in the right, they are also definitely going to think that 2+3 is a better way.

I am saying that being incorrect ≙ being obviously not useful.

- I don't think saying "5" implies a normative thing. Like, there was another twitter poll that asked,

"Pick the shelling point and also don't pick c" with answers a, b, c, d.

In *that* case, I buy talking about correctness. (Hilariously, that poll has majority answers on c, ffs.) But if you just say "5", only "5", not even "5.", I don't think you are incorrect to say 4+2 since the poll didn't ask you to choose a number that's 5. You just have an abstract "truth" property.

( This difference between "just writing down an abstract element with a truth value" and "making a claim" really creates a knot in my brain. It's not the first time I've thought about it. )

I think the fact that we're picking a Schelling point inherently implies a normative thing. If one of the answers doesn't appear better than any other, there is no Schelling point.

[silverspawn]

right... but the respondent to this twitter poll aren't random people, and the author most likely knows set theory

[Awaclus]

right... but the respondent to this twitter poll aren't random people, and the author most likely knows set theory

It's very likely most of them aren't particularly exceptional either, although they might want to believe they are, which is probably why they're following someone who most likely knows set theory. And given that it's not clear from the poll that you're supposed to find the Schelling point among the responders and not the general population (i.e. even if it is really about the responders, some of the responders are going to respond assuming the general population), I would pretty much just answer as though it was the general population.

For what it's worth, I am not familiar with the term axiom of extensionality, and I feel like I know set theory (I'm at least reasonably comfortable with the basics).

[silverspawn]

Mh.

@Set theory: There's a big difference between rudimentary set theory where you do union, intersection, powerset, Cartesian product, et cetera, and axiomatic set theory, where you ground math in a formal language.

[silverspawn]

White to move. What's the move?

I don't get it, either. But it's not Rxg2, that's a Blunder.

[silverspawn]

Draw by stalemate, according to chess.com

[silverspawn]

chess.com also immediately crashed when I setup a game with kings and forked them. I question the solidity of the programming

[silverspawn]

The secret of "actually" is that it is sometimes useful. It's overused, but not every instance is wrong.

[faust]

Reasonable. But the thing is... well actually there are two things

If we're, say, carrying five heavy things (that weigh like 10 kg each so it's reasonable to carry more than one per person, but each additional one makes it substantially less pleasant) somewhere and there's two of us, then obviously one of us taking four of the five things and the other taking two is not even possible, and 4+1 or 5+0 aren't very reasonable either, so 2+3 ends up being the convention.

- In math formalized as set theory, 2+3 and 4+1 refer to *the same object*, as defined by the axiom of extensionality. I think this is a similar issue as when people say "one drop of water plus another drop is just one drop not two, math is wrong lol". You've computed something like human_description(merge(water_drop, water_drop)), not water_drop + water_drop. The + operator doesn't do all of your intuitive "and" things, it does something much more narrow. 2 objects in the left hand and 3 in the right aren't any more 2+3 than 4+1... under that extremely formal view.

This is a very narrow view on math. It is a fallacy to assume that + means the same thing in any context. Yes, if you define numbers using set theory and addition of numbers on the back of that, then sure these are the same object. But it is reasonable to think that this is not the intended meaning here. Instead it looks like an integer partition.

In the context of integer partitions, we can indeed write 2+3 and 4+1 and mean different objects.

[faust]

With regards to the question, I am inclined to pick 2+3 as the Schelling point because

• as Awaclus said, it is the most even distribution
• all the other sums lead with the bigger integer, which is unnatural when you write a sum
• I have to assume that the extra prompt "5" is there for a reason
• I am naturally inclined to associate 2+3 more strongly with 5 because my birthday is May 23.

[silverspawn]

Reasonable. But the thing is... well actually there are two things

If we're, say, carrying five heavy things (that weigh like 10 kg each so it's reasonable to carry more than one per person, but each additional one makes it substantially less pleasant) somewhere and there's two of us, then obviously one of us taking four of the five things and the other taking two is not even possible, and 4+1 or 5+0 aren't very reasonable either, so 2+3 ends up being the convention.

- In math formalized as set theory, 2+3 and 4+1 refer to *the same object*, as defined by the axiom of extensionality. I think this is a similar issue as when people say "one drop of water plus another drop is just one drop not two, math is wrong lol". You've computed something like human_description(merge(water_drop, water_drop)), not water_drop + water_drop. The + operator doesn't do all of your intuitive "and" things, it does something much more narrow. 2 objects in the left hand and 3 in the right aren't any more 2+3 than 4+1... under that extremely formal view.

This is a very narrow view on math. It is a fallacy to assume that + means the same thing in any context. Yes, if you define numbers using set theory and addition of numbers on the back of that, then sure these are the same object. But it is reasonable to think that this is not the intended meaning here. Instead it looks like an integer partition.

In the context of integer partitions, we can indeed write 2+3 and 4+1 and mean different objects.

totally grant that

[silverspawn]

I have to assume that the extra prompt "5" is there for a reason

Isn't this *the* argument for picking 4+2. If "5" wasn't included, I'd have picked 5+0 (with 2+3 a runner-up).

[silverspawn]

Like I agree with all the things you say, basically, but you don't address the reason for picking 4+2 which seems much simpler and stronger

[infangthief]

With regards to the question, I am inclined to pick 2+3 as the Schelling point because

• as Awaclus said, it is the most even distribution
• all the other sums lead with the bigger integer, which is unnatural when you write a sum
• I have to assume that the extra prompt "5" is there for a reason
• I am naturally inclined to associate 2+3 more strongly with 5 because my birthday is May 23.

I think I would also pick 2+3, mostly because of the even distribution. Also because it is first on the list.
However I feel it is more natural to lead with the bigger integer (i.e. if 3+2 were an option I would pick that ahead of 2+3).

I haven't read everything here, but doesn't Schelling Point depend a lot (or actually entirely?!) on the target audience. I see the logic in going for 4+2, but I don't think it is a logic that appeals to society in general.

[silverspawn]

the reason why I don't buy that is because of the "5". Without the "5" comment, you have the value of the sum as one property of many. But with the "5" comment, we are explicitly being told that the sum is the important property, and that property splits our data set 3:1.