Someone, somewhere, trying to improve at some things.
Pawn
Karma: 26
My worry (gut-worry?) is that cabal vs externally-opaque meritocracy is a false dilemma and cabal (for the given examples) is a strawman (ergo, opaque meritocracy).
I’m (for now, as I explicitly stated) not judging people for upvoting, I’m judging the votes! I generally can’t interpret them pretty well (especially on a small scale, where I can’t tell how many put how much), but I’ll certainly take note if you say they’re unreliable.
Thank you for the reasonable take on scientific consensus.
The way I read Seth’s initial comment is that arguing that (for example) string theorists aren’t an externally-opaque meritocracy, only illustrates the point that they are. That would take the claim to be unfalsifiable. I.e you’d reject concrete counter-evidence because it actually confirms the claim using this abstract argument.
Let me say outright: That’s crazy. I don’t think you agree with that. And if I understand Seth’s reply just below, I now believe Seth also disagrees with that (phew!).
I’d still appreciate an answer to “if the string theory example were false, how would you be able to find out” by Seth. Just as a sanity check, for me. It’s a routine question in SE and it shouldn’t be hard to answer. I reiterate that isn’t about whether string theory is true or false or whatever (which is what Seth now addressed a little further below), but about the experts dynamic illustrated (hypothesized?) here.
Disclaimer: I think the string theory example is wrong and have what I believe to be reasonable counter-evidence to back that up (again, not evidence that String Theory is wrong!).
I honestly haven’t read the analytic philosophy example because the string theory one already raised quite a bit of red flags for me. I think I’m slightly less worried, but the trees and forest analogy down below is a new red flag! A forest of rotten trees isn’t one where I want to be. You wouldn’t get away with rotten trees in academia. I’d prefer if LW plainly rejected rotten trees and frowned upon possibly/possibly not rotten trees.
Disclaimer 2: I’m currently operating on gut feelings, because the whole thing rubbed me off. I’ll probably take it slow soonish.
Okay, now I am extremely surprised.
I genuinely and sincerely did not believe that the previous statement was said in a positive light.
Are you getting behind an unfalsifiable claim? If the string theory example were false, how would you be able to find out?
This is very important to answer, unless you’re renouncing yourselves as a meritocracy of critical thinkers (slightly ambiguous statement. I don’t mean to say that Seth represents the community).
Were you just reading the essay, thinking about AI alignement the whole time, not particularly caring about the veracity of the specific examples?
Sure, but pretty much all of applied model theory is about developing ‘decision procedures’ for certain classes of structures. That’s as central to mathematical logic as prime numbers are to arithmetic.
Establishing the decidability of a first order theory and/or quantifier-elimination are the bread an butter of the discipline. Sometimes it works, sometimes it doesn’t and sometimes it’s still an open problem.
Maybe look up Tarski’s proof of Hilberth’s 17th problem? Or the model-theoretic proof of the Nullstellensatz? These are the prototypical examples of how it goes when it goes well.
Classical propositional logic is also decidable, but it’s not very useful in mainstream math because it’s not very expressive (which doesn’t mean not useful at all. I’m aware of at least one application in graph theory).
And with all my respect to Zeilberger, he doesn’t do very “classical” mathematical logic. Which is not bad at all! But you can’t rely on someone going against the grain to make an opinion on the general direction of a field (which, on an unrelated note, is what I suspect this essay basically is).
If you want stuff about irrationality, there’s deep work connecting Schanuel’s conjecture to logic. I don’t know if that body of knowledge can currently produce concrete irrationality proofs, but really only because of my lack of expertise.
Modal logics are just fragments of classical first order logic (there are clever ways of doing this, illustrated in modal logics textbooks but there is also a dumb systematic way of doing it, if you’re comfortable with many-sorted logic).
As such, I don’t expect it to be particularly innovative in deep novel ways mathematical logicians haven’t considered.
But I know of some uses of modal logic in constructive math which simplifies (the presentation of) some forcing arguments for example.
I also personally use modal logic to more easily remember Tarski-Vaught’s test, which actually is the converse Barcan formula in disguise.
Are you saying this as criticism of the essay or in its favor? (This is not entirely a rhetorical question, unfortunately)
My gut instinct is that the whole thing reeks of a false dilemma on top of a strawman and the author isn’t really acknowledging how strong of a prior scientific consensus is. Are we supposed to be convinced of this idea because if it were true, that would explain a lot?
I genuinely don’t understand how this has so many upvotes (106 at the moment of writing the comment) and I’m not happy with what it would say about this community.
I’m reserving judgment, but man am I confused!
In the (classical) King’s Indian defense, the center is locked, black is attacking on the kingside and white on the queenside. If one responds too much to what the other is doing, they lose the initiative and from there, usually the game too.
Race situations aren’t uncommon in chess!
I can’t speak much of multiplayer board games. I do tend to win by minding my own business and hoping nobody notices what resources I’m collecting but I haven’t played enough of those to experience situations where I’m competing for resources with other players for instance. That could turn into a fight. Or maybe not, maybe we’d just gradually and peacefully shift interests. I don’t know.
I’m not disagreeing with the heuristic necessarily (races vs fights seems like an interesting distinction), but it’s oversimplifying the situation to reduce it to the number of players.
I don’t think it’s the ‘size of the world’ that matters but the distance induced by how easy it is to reach and have an impact on other individuals. And so ‘Big’ is meant in the sense of this metric, not necessarily physical reality.
For instance, I don’t think this heuristic applies very well to Go, despite the enormous size of the board, because players’ stones are pretty much at distance zero. In fact, because I know close to nothing about Go, the above statement is a prediction based on my mental model. I’d be interested if a competent Go player could confirm or deny it.
I feel like you’re saying that for two players chess because of how the evaluation bar looks like, but in a four players situation, you’d rather have four independent evaluation bars.
I.e you’re making two different claims on two different methods of evaluation.
The statement “increasing your score is as good as decreasing your opponent’s” is true by definition for the first method of evaluation in two players chess. And it has an equally banal generalization for multi-player board games (in which that evaluation method applies). That would be the correct multi-player version of the first statement.
The statement “increasing your score even if it increases your opponent’s” is not true by definition for the second method of evaluation (for any number of players) but isn’t even well-defined for the first method of evaluation.
So the second statement is not really a generalization of the first.
I think the chess example is inaccurate, but it doesn’t refute the main message (or how I choose to interpret it at the very least).
It’s very wrong to say that in chess, in the opening moves, both players do their own little thing and after some development, only then do the cordialities end.
In the opening phase, both players aim to achieve certain advantages and if you let your opponent get all the advantages they want, you won’t have a very pleasant middle game.
Openings have a ‘logic’. If white plays 1.e4 then black doesn’t want white to get the full center and thus plays a move that prevents that, while also grabbing for center. This is the logic of 1.e5. Now white can’t have the whole center and so focuses on developing their pieces. Maybe they could do it in a way that would let them keep the initiative and so plays 2.Nf3, getting the Knight out while attacking the e5 pawn and thus again forcing black to respond etc.
If you don’t understand your opening’s ‘logic’ and play against someone who does, it’s very easy to get disadvantaged early on, possibly several moves before even noticing you’re on the backfoot.
On the other hand, what is true, is the slow, gradual, incremental nature of ‘advantage’ in chess. Unless both opponents decide to go for a very sharp and complicated game (I’m assuming good players btw), then progress is going to be very slow and players won’t really be thinking about checkmate until much much later.
This is the nature of Strategy vs Tactics. Tactics are about identifying a short, exact sequence of moves that leads to an immediate concrete advantage.
Strategy is essentially about developing a situation that makes it easier/likelier for there to be tactics for you to execute.
Pawn’s Shortform
I just saw a post about mindreading tech. Has there been/is there going to be any interest among the LW community to consider the likelihood of such technology being within reach or if it’s even already here and well-developped through Manhattan style projects?
It’s a very murky subject and I’m curious how LWers would approach it.
If it’s just about remembering the formula, would it be helpful to point out that “the fractions on the right simplifies”? If I write P(B|A)=P(A|B)P(B)/P(A) and just look at the symbols (A|B)B/A you can see it as a fraction that reduces to 1.
The next step would be to replace B and A with T and D for Theory and Data (or H for Hypothesis if you want to be fancy).
From someone who cannot use Bayes theorem in real life… probably.
Examples one and two are normal situations and people should know how to respond to them. The general principle is that when given an open ended question, don’t aim to answer it in full, but make a small contribution and let the conversation flow.
Computational unkindness:
“What do you want to do? I’m completely fine with anything!”
“I’ve heard about X, I’d love to visit that place!”, or “I don’t know. What’s a good place to hang out?”
Responsibility Offloading 1:
B: “By the way—feel free to throw me out any time! I’ve got tomorrow off, so am flexible, but just let me know when you’ve had enough of me”
A: “Hmm… I usually go to bed at 11pm.”
Responsibility Offloading 2:
“Do you mind if I smoke?”
“Yes, I do mind people in a 10m radius of me smoking!”
Ok that was a joke. But you can still convey irritation and offoffload the responsibility at the same time. Say “Sure...” with discomfort in the intonation.
This is exactly what I’ve been doing when studying mathematics! From letting my mind wander down to just staring at a definition and be ‘genuinely curious’ about it. In fact one of my favourite activities is to ask “What motivated this definition? Assuming these motivations, what definitions would I’ve come up with? How do they relate with this one?”. It’s the sort of exercise that feels important and meaningful to me, but I don’t think I know anybody in my circle of friends who ever gives it a try. So I’m very happy to see it acknowledged!
Entirely coincidental. I haven’t gotten to the analytic philosophy part yet, even!
To make that example slightly less minor, because (in the appropriate modal logic etc.) the hypotheses of the Tarski-Vaught test as well as its conclusion are statements in that logic (and thus in first order logic), that result can be given a purely syntactic proof, which happens to be much nicer to visualize than the usual ugly inductive argument (in short, you just move the square/diamond for left to right in the formula).
The Barcan formula (in that specific modal logic) also happens to be a tautology, for what it’s worth.