I’m having trouble following this step of the proof of Theorem 4: “Obviously, the first conditional probability is 1”. Since the COD isn’t necessarily reflective, couldn’t the conditional be anything?
The linchpin discovery is probably February 2016.
Ok. I think that’s the way I should have written it, then.
The definition involving the permutation is a generalization of the example earlier in the post: ϕ(T) is the identity and ϕ(H) swaps heads and tails. And X=ϕ(A)−1(C). In general, if you observe A=a and C=c, then the counterfactual statement is that if you had observed A=a′, then you would have also observed C=ϕ(a′)(ϕ(a)−1(c)).
I just learned about probability kernels thanks to user Diffractor. I might be using them wrong.
Oh, interesting. Would your interpretation be different if the guess occurred well after the coinflip (but before we get to see the coinflip)?
That sounds about right to me. I think people have taken stabs at looking for causality-like structure in logic, but they haven’t found anything useful.
What predictions can we get out of this model? If humans use counterfactual reasoning to initialize MCMC, does that imply that humans’ implicit world models don’t match their explicit counterfactual reasoning?
I agree exploration is a hack. I think exploration vs. other sources of non-dogmatism is orthogonal to the question of counterfactuals, so I’m happy to rely on exploration for now.
“Programmatically Interpretable Reinforcement Learning” (Verma et al.) seems related. It would be great to see modular, understandable glosses of neural networks.
I’d like to rescue/clarify Mitchell’s summary. The paper’s resolution of the Fermi paradox boils down to “(1) Some factors in the Drake equation are highly uncertain, and we don’t see any aliens, so (2) one or more of those factors must be small after all”.
(1) is enough to weaken the argument for aliens, to the point where there’s no paradox anymore. (2) is basically Section 5 from the paper (“Updating the factors”).
The point you raised, that “expected number of aliens is high vs. substantial probability of no aliens” is an explanation of why people were confused.
I’m making this comment because if I’m right it means that we only need to look for people (like me?) who were saying all along “there is no Fermi paradox because abiogenesis is cosmically rare”, and figure out why no one listened to them.
I heard a similar story about when Paul Sally visited a grade school classroom. He asked the students what they were learning, and they said “Adding fractions. It’s really hard, you have to find the greatest common denominator....” Sally said “Forget about that, just multiply the numerator of each fraction by the denominator of the other and add them, and that’s your numerator.” The students loved this, and called it the Sally method.
Cool, do you remember what the 5-minute explanation was?
I’d love to hear your thoughts on A Fable Of Politics And Science. Would you say that Barron’s attitude is better than Ferris’s, at least sometimes?
I like the resemblance to this scene from The Fall Of Doc Future.
Why is the scenario you describe the “real” argument for transitivity, rather than the sequential scenario? Or are you pointing to a class of scenarios that includes the sequential one?
This seems to belong to a family of personal narratives invented by people at CFAR (some combination of Andrew Critch and Valentine Smith?).
Here’s a post about a narrative that says that you’re immune to narratives.
There’s also the “Fully General Meta-Narrative” that says that you can get the benefits of any particular narrative without actually employing the narrative. (For example, if you’re tired, there’s probably a narrative that will give you a second wind. The Fully General Meta-Narrative says you can just get a second wind when you want to. I hope I’m remembering this correctly.)
In this language, you’re proposing a narrative that says that you can employ any object-level narrative you wish.
Regarding a couple of your concrete suggestions: I like the idea of using existing academic jargon where it exists. That way, reading LW would teach me search terms I could use elsewhere or to communicate with non-LW users. (Sometimes, though, it’s better to come up with a new term; I like “trigger-action plans” way better than “implementation intentions”.)
It would be nice if users did literature reviews occasionally, but I don’t think they’ll have time to do that often at all.