My response would be that this unfairly (and even absurdly) maligns “theory”!
I agree. However, the way I’ve had the two generals problem framed to me, it’s not a solution unless it guarantees successful coordination. Like, if I claim to solve the halting problem because in practice I can tell if a program halts, most of the time at least, I’m misunderstanding the problem statement. I think that conflating “approximately solves the 2GP” with “solves the 2GP” is roughly as malign as my claim that the approximate solution is not the realm of theory.
Some people (as I understand it, core LessWrong staff, although I didn’t go find a reference) justify some things in terms of common knowledge.
You either think that they were not intending this literally, or at least, that no one else should take them literally, and instead should understand “common knowledge” to mean something informal (which you yourself admit you’re somewhat unclear on the precise meaning of).
I think that the statement, taken literally, is false, and egregiously so. I don’t know how the LW staff meant it, but I don’t think they should mean it literally. I think that when encountering a statement that is literally false, one useful mental move is to see if you can salvage it, and that one useful way to do so is to reinterpret an absolute as a gradient (and usually to reduce the technical precision). Now that you have written this post, the commonality of the knowledge that the statement should not be taken literally and formally is increased; whether the LW staff responds by changing the statement they use, or by adding a disclaimer somewhere, or by ignoring all of us and expecting people to figure it out on their own, I did not specify.
My problem with this is that it creates a missing stair kind of issue. There’s the people “in the know” who understand how to walk carefully on the dark stairway, but there’s also a class of “newcomers” who are liable to fall. (Where “fall” here means, take all the talk of “common knowledge” literally.)
Yes, and I think as aspiring rationalists we should try to eventually do better in our communications, so I think that mentions of common knowledge should be one of:
explicitly informal, intended to gesture to some real world phenomenon that has the same flavor
explicitly contrived, like the blue islanders puzzle
explicitly something else, like p-common knowledge; but beware, that’s probably not meant either
This idea is illustrated with the electronic messaging example, which purports to show that any number of levels of finite iteration are as good as no communication at all.
I think (I haven’t read the SEP link) that this is correct—in the presence of uncertainty, iteration does not achieve the thing we are referring to precisely as “common knowledge”—but we don’t care, for the reasons mentioned in your post.
I think your post and my reply together actually point to two interesting lines of research:
formalize measures of “commonness” of knowledge and see how they respond to realistic scenarios such as “signal boosting”
see if there is an interesting “approximate common knowledge”, vaguely analogous to The Complexity of Agreement
I agree. However, the way I’ve had the two generals problem framed to me, it’s not a solution unless it guarantees successful coordination. Like, if I claim to solve the halting problem because in practice I can tell if a program halts, most of the time at least, I’m misunderstanding the problem statement. I think that conflating “approximately solves the 2GP” with “solves the 2GP” is roughly as malign as my claim that the approximate solution is not the realm of theory.
I think this is very fair (and I will think about editing my post in response).
I agree. However, the way I’ve had the two generals problem framed to me, it’s not a solution unless it guarantees successful coordination. Like, if I claim to solve the halting problem because in practice I can tell if a program halts, most of the time at least, I’m misunderstanding the problem statement. I think that conflating “approximately solves the 2GP” with “solves the 2GP” is roughly as malign as my claim that the approximate solution is not the realm of theory.
I think that the statement, taken literally, is false, and egregiously so. I don’t know how the LW staff meant it, but I don’t think they should mean it literally. I think that when encountering a statement that is literally false, one useful mental move is to see if you can salvage it, and that one useful way to do so is to reinterpret an absolute as a gradient (and usually to reduce the technical precision). Now that you have written this post, the commonality of the knowledge that the statement should not be taken literally and formally is increased; whether the LW staff responds by changing the statement they use, or by adding a disclaimer somewhere, or by ignoring all of us and expecting people to figure it out on their own, I did not specify.
Yes, and I think as aspiring rationalists we should try to eventually do better in our communications, so I think that mentions of common knowledge should be one of:
explicitly informal, intended to gesture to some real world phenomenon that has the same flavor
explicitly contrived, like the blue islanders puzzle
explicitly something else, like p-common knowledge; but beware, that’s probably not meant either
I think (I haven’t read the SEP link) that this is correct—in the presence of uncertainty, iteration does not achieve the thing we are referring to precisely as “common knowledge”—but we don’t care, for the reasons mentioned in your post.
I think your post and my reply together actually point to two interesting lines of research:
formalize measures of “commonness” of knowledge and see how they respond to realistic scenarios such as “signal boosting”
see if there is an interesting “approximate common knowledge”, vaguely analogous to The Complexity of Agreement
I think this is very fair (and I will think about editing my post in response).