Alas, we also only found the shorter paper in English.
Given that you tried google translate, I can’t stop myself from auto-completing; did you try an LLM? If you do get a write-up of the proofs in English, I think some people at Dovetail would like to take a look at it, so please ping me!
Silly question, but… where is the delete button for posts?
(This would have been a good setup for an April fool’s post where you introduce a new notation, which you call “Feynman diagrams”.)
Ah sorry, I was using LW’s feature of highlighting something in the text and then making a comment about it. This is the part that says;
Theorem 2 (Coding Theorem). There is a constant
…
0
Should be 1?
I’m sure you’ve had lots of discussion about this; why the label “AI alignment”?
I think “alignment” refers to the somewhat specific task of aligning an AIs values to human values. But my understanding of your actual scope is more like “theoretical AI safety”. A lot of foundational work is done with the intention that it will eventually help with alignment, but which definitely isn’t about alignment, and a lot of theoretical AI safety work isn’t about alignment per se at all. For example, some of my research problems are trying to understand which types of AI systems are not dangerous, not because their values are aligned with ours, but because they’re not unrestrained consequentialists.
I mean, I just think the post isn’t very good. It’s kinda funny, but it’s not THAT funny, and also it’s not the kind of funny that is appropriate for curation. Overall I think curating it wasted a bunch of people’s time and somewhat eroded the commons.
But, I also don’t expect to convince you personally? Because you are a trickster archetype. Trickster archetypes have a valuable place in society but that place is not in choosing curated posts for LW. So the people I am petitioning to un-curate this are the other LW mods.
Hi all! I’m a long-time LWer, but I’m making a comment thread here so that my research fellows can introduce themselves under it!
For the past year or so I’ve been running the Dovetail research fellowship in agent foundations with @Alfred Harwood. We like to have our fellows make LW posts about what they worked on during the fellowship, and everyone needs a bit of karma to get started. Here’s a place to do that!
I think your title “The Axiom of Choice is Not Controversial” is literally false, because “controversial” is a social property referring to how much disageement there is, and not whether something is true. Rejecting the AoC is a minorinty view but it is not that minority. It’s also a respected alternative view, and texts often go out of their way to mention when they are acceping the AoC. It may if anything be the most controversial thing in math.
I basically agree with all of this. I had this thought in part because I have the fairly strong sense that (current, US) society has a belief that there is a healthy state we should be aiming for, and does a lot of question substitution like “does this feel good/acceptable”. There are much better and worse ways to orient to x-risk, but it may be that all of them feel “bad/unacceptable” and it’s hard for me to see how they could be accurately labeled “healthy”.
I’ve been worried that the Solstice isn’t really set up to handle “actually looking at human extinction in nearmode” in a psychologically healthy way
A thought I had when I read this sentence was, “what makes you think there is a healthy way?” It kinda feels to me like, just as there’s no way to get in a car accident that’s healthy for your body, there’s no way to actually believe the world is going to end that’s “healthy” for your mind. There could be better or worse ways it could impact you, but you’re gonna get some impact trauma.
Is there any polyamorous fanfiction of The Incredibles?
I think something like “accountability” is a much more accurate term for this generalization than “dominance”. Parents, teachers, bosses etc. are roughly as motivated by their accountability to their children, students and employees.
Finite Factored Sets
Nitpick; I thought “finite factored sets” were being rebranded as factored space models, because the finiteness was inessential. I think this name is better and would like to see the switch-over happen before the framework gets more popularity. But maybe I’m wrong about this intention?
As I learn mathematics I try to deeply question everything, and pay attention to which assumptions are really necessary for the results that we care about. Over time I have accumulated a bunch of “hot takes” or opinions about how conventional math should be done differently. I essentially never have time to fully work out whether these takes end up with consistent alternative theories, but I keep them around.
In this quick-takes post, I’m just going to really quickly write out my thoughts about one of these hot takes. That’s because I’m doing Inkhaven and am very tired and wish to go to sleep. Please point out all of my mistakes politely.
The classic methods of defining numbers (naturals, integers, rationals, algebraic, reals, complex) are “wrong” in the sense that it doesn’t match how people actually think about numbers (correctly) in their heads. That is to say, it doesn’t match the epistemically most natural conceptualization of them: the one that carves nature at its joints.
For example, addition and multiplication are not two equally basic operations that just so happen to be related through the distributivity property, forming a ring. Instead, multiplication is repeated addition. It’s a theorem that repeated addition is commutative. Similarly, exponentiation is repeated multiplication. You can keep defining repeated operations, resulting in the hyperoperator. I think this is natural, but I’ve never taken a math class or read a textbook that talked about the hyperoperators. (If they do, it will be via the much less natural version that is the Ackermann function.)
This actually goes backwards one more step; addition is repeated “add 1”. Associativity is an axiom, and commutativity of addition is a theorem. You start with 1 as the only number. Zero is not a natural number, and comes from the next step.
The negative numbers are not the “additive inverse”. You get the negatives (epistemically) by deciding you want to work with solutions to all equations of the form for naturals and . The fact that declaring these objects to exist is consistent should be a theorem, as should the fact that some of the solutions to different equations are equal (e.g. that the solution to is the same as the solution to ).
This idea is also iterated up through the hyperoperations. The rational numbers are (again, epistemically) the set of all solutions to the equations where and are integers. The fact that this set is not consistent when is should also be a theorem.
Since the third-degree hyperoperation is not commutative, you can demand two new types of solutions, those of and those of . This gives you roots and logs. The fact that roots require you to define the imaginary numbers, and therefore lose the total ordering over the numbers, should be a theorem.
Some of the solutions to these equations are numbers we already had, and some of them are new numbers that we didn’t have This setup leads to the natural question of whether we will keep on producing new types of numbers or not. The complex numbers are special in part because they are closed under all these inverse operations. But do we need new types of numbers if we demand solutions to the fourth-order hyperoperator? What happens if we go all the way up? I have no idea.
Yeah, I agree. An earlier deadline would cut out procrastination time, or more accurately, it would just make people write more efficiently per unit time. I’d honestly be pretty excited to try having a deadline even as early as 6pm.
Some subtle signals perhaps?
(I have no idea what y’all are using KL-divergence for, so I have no opinion about whether you should have been using it in this theorem.)
a metric, a feature sorely lacking from
I have a pet peeve around this, which is hopefully a useful comment for someone to read; KL-divergence should not be symmetric, because of the whole thing that it is. If you’re using KL-divergence and thinking to yourself “I wish this was symmetric”, then that should be a red flag that you’re using the wrong tool!
I think it’s easy for people to think, “hm, I’d like a way to quantify the how different two probability distributions are from each other” and then they grab the nearest hammer, which happens to be KL-divergence. But mathematical definitions are not for things, instead they mean things.
You should use KL-divergence when you want to measure the cost of modelling a true distribution using a false distribution. The asymmetry comes from the fact that one of them is the true one (and therefore the one that you take the expected value with respect to).
Positive feedback, I put this doc on the recommended reading list for the newest Dovetail fellowship, and people really liked it!