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ControlsFreak


				

				

				
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User ID: 1422

ControlsFreak


				
				
				

				
5 followers   follows 0 users   joined 2022 October 02 23:23:48 UTC

					

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User ID: 1422

This is quite exciting! Some scattered thoughts.

I definitely had the sense that we had hope for this type of thing, since math is (mostly) mechanically-verifiable. Lean is about to be getting even more attention than it had before, and it's important that these all come with Lean code attached. That said, my understanding is that it is still possible to do somewhat sketchy things in Lean. I'm expecting a lot more folks will see how important that concern is and really focus on either shoring it up or put together some set of principles like, "If you proof has X component in Lean, we're going to unfortunately simply discount it for now." But most results that come with Lean code will probably be just fine. (I certainly have no reasons to doubt any of these particular results, myself. Nor do have strong personal opinions about the edges of where possibly sketchy things can be done in Lean.)

On the use and human interpretability of results. This question is not new. Take, for example, the massive human-generated proof of Fermat's last theorem or the exhaustive computer-generated proof of the Four Color Theorem. Many many folks don't actually understand these proofs. Perhaps no one "understands" the proof of the Four Color Theorem, whereas at least the proof of Fermat's last theorem is understood well enough by an extremely small group of folks.

Using those results is easy. You don't have to understand them! If you're working on a problem, and you see that it would be useful for one of those things to be true, congrats! You can just use a pointer to the fact that it's true and move on. This is an unalloyed good.

Understanding those results is another matter. I was looking at a paper recently with some collaborators, and it was one of those situations where we were just failing to have much intuition about how to think about certain parts. (FYI, I think this paper was human-generated, but I don't know.) Multiple people in the group suggested that a few things could be, "They just tried a bunch of options, and found one where they could make the computation work out." And that's fine. I've done that before. Plenty of methods include, "You can just try stuff, and if one works, great!" I also happened to afterward figure out a different way to describe the same thing in a way that made intuitive sense out of it, which was extra neat. Maybe if we bang our head against their paper for long enough, we'll be able to find a way to make intuitive sense out of it, too. Maybe an LLM will help! Tao recently mentioned that he had a discussion with an LLM to help him grab some additional intuition around the counterexample to the jacobian conjecture.

At least in the near term, there will probably be a fair number of LLM-produced proofs that people look at and say, "How the hell does that work?" Plenty of time will be spent trying to understand them. Are there new concepts in there? Can you relate it to other math? Can you simplify it and make it more intuitive? Does something in the method raise new interesting questions?

Which leads me to the most hazy part; the somewhat longer term. Will LLMs be able to consistently make intuitive sense of their proofs for humans? Will they be able to help us understand the connections or identify new questions that we would understand as being interesting that are now relevant?

I certainly don't know how to prognosticate all that well, but I do think of some analogies to another domain that is (mostly) verifiable and where computers already significantly outperform humans - chess. Humans still try to understand something from the superhuman output of chess engines. Unfortunately, I can't find it immediately, but I very recently read (as in the last couple weeks, I believe) an argument that top human grandmaster play has barely improved outside of the opening phase, where folks are memorizing more and more of the output of engines. I'm not sure I believe this analysis (I didn't dig into the details of the methodology, and I can imagine plenty of methodological difficulties), but that's something somewhere in my mind. Another thing is that chess has one single extremely well-defined goal: win the game when you can, otherwise draw. This collapses neatly at any particular point in time to, "What is the objectively best move for this game state?" It is relatively easy to accept that the computer is just flatly going to estimate that far better than we are. It's harder to understand the reasons why that is the best move. It's harder (not necessarily impossible, but harder) to take a variety of examples like this from a computer and have a sense for how to built it into a broader understanding of the game. It's harder to make connections like, "The computer seems to value space in positions like X and Y, but not Z; why is that?"

We have plenty of mathematical "positions" teed up for this type of tool. We can hopefully just ask the LLM what the objective evaluation of these "positions" are. Where else it goes, how we understand the whole thing, and what we can do with it are open and exciting questions.

Posting separately and prior to the above, so it appears separately and below; this is much less important.

IMHO, this topic is a culture war topic (or at least, it can be, depending upon the presentation). Given that premise, the root comment is a nearly contentless bare link with a one liner snipe of the commenter's outgroup. For example questions, what is "it" and what does it mean for "it" to be "over"? It is plausible that these sorts of questions could have coherent answers that make the original comment benign, but they were not included in the original.

An alternative interpretation is that it is a "First"-post, though I would still probably characterize it at first impression as being paired with a one liner snipe of the commenter's outgroup.

Indeed, I think that the same sense that there even is such a thing as a commenter's "outgroup" on the topic in an indicator in favor of the premise that the topic (or at least a presentation of the topic such as this) is culture war.

EDIT: I should clarify that I am NOT asking for the comment to be modded. I am not entirely confident of my interpretation, and I'm not at all confident that the mods would think so, either. I did not report it because I don't have a strong opinion that it should be modded. I am merely expressing my opinion on some things that I did not like, and I am very open to contrary perspectives.

I don't know about medical, but for engineering, the competitiveness level for professorships is so high that there is quite a lot of talent distributed pretty widely. If one looks around for, I don't know, top quantum researchers, you might be surprised how widely you'll find them. There's still a lot of garbage being published, sure, but that's more a product of the incentive structure demanding more more more in terms of publications. Moreover, while academia hasn't been entirely immune to the general homogenization effects that happened to much of the rest of society, there are still somewhat distinctive flavors that can be seen. For example, (being a bit reductive here), one could say that there's something of a "Berkeley way" of approaching learning problems that is more distinctive on the west coast. Obviously, some of their successes filter over to other folks, but they have sort of a different mindset (purely technically speaking, not about their weird political bubble).

Ok, that is by far the more reasonable option, even if I find it less natural as a matter of language.

It is, of course, difficult to strictly evaluate the extent to which a third party is "increasing" in a sense of reliance/confidence/trust. That said, I would note that a couple days ago I referred to this recent blog post by Tao, where he presented some criteria that he says he uses to guide his usage. I don't necessarily agree with them all, but I do get the sense that he maintains a distrust of them, even while trying to get as much value out of them as possible. In the comments on that blog post, he re-endorses his comments on using "AI on the red team" from this paper, which also reads to me as having a sense of distrust and trying to describe ways of working with the thing that he has a sense of distrust in, while leveraging its strengths.

If Terence Tao is increasingly reliant on it

Do you mean "reliant" in the sense of "having or showing dependence" or in the sense of "confident; trustful"?

The topic of the use of LLMs in various situations is always super complicated. Sometimes it's magic; sometimes it's bollocks and all that.1 I don't yet have fully-consistent rules for myself, as things are always changing as well. Terrance Tao just listed a possible set of criteria to consider:

I believe that the creation of visualization apps to illustrate mathematical or scientific concepts is a particularly favorable use case for modern coding agents, as many of the downside risks attached to other LLM use cases are limited:

  1. Not mission-critical. As such apps are not authorative sources of truth and only used for secondary purposes, a small positive error rate in the output can be acceptable.
  2. Stand-alone. As the applets are not destined to be incorporated into a larger codebase or literature, the technical debt incurred by delegating all the coding to an LLM agent is bounded.
  3. End product is deterministic (and sandboxed). As the applets run on a deterministic language (Javascript), are sandboxed against file or internet access, and do not make any LLM calls at run-time, security and privacy concerns are minimal, and the applet can be maintained without continued premium LLM access or resource-intensive compute.
  4. Not replacing primary skills. While deskilling is the tradeoff one accepts when relying on these tools to accelerate output, I am perfectly willing to forego the opportunity to keep my Javascript skills at a high level, as this is a tertiary skill for me at best in my chosen profession. (I continue to manually program in Lean and in Python to keep in practice with programming in general.)
  5. Not competing with humans. To my knowledge, there is no existing human effort that is being duplicated by these applets (the activity in this direction appears to have peaked two decades ago).

I would however caution against unrestricted LLM use when one or more of the above five favorable situations is not in effect.

I don't know if these are the right set of rules (#5 in particular seems insufficiently justified). But I guess the culture war is all about bickering over lists like this (or, I guess, whether any list like this should be used vs. just letting an LLM do literally everything for you everywhere).

1 - For example, in writing this, I noticed that I always screw up the markdown for numbered lists inside of blockquotes. I typically still just leave blank lines between lines/paragraphs in blockquotes; no particular reason why I do it, but it's most noticeable when it breaks numbered lists. An LLM trivially told me a couple different ways I could do it that will display properly. On the other hand, I spent a decent amount of time yesterday trying to troubleshoot something that was crashing intermittently. It gave me some certainly reasonable troubleshooting steps, but when the basic, good ones ran out, it sort of went insane. It never occurred to the LLM to note that there were some additional debug tools I could enable; I happened to find that in a web search leading to a forum leading to documentation shortly after giving up on the LLM.

Unsurprisingly, given that Scott is the Rightful Caliph, I agree that accusations of stochastic terrorism are usually bunk. Moreover, he properly identifies the true fault line:

This liberal solution isn’t trivial. It requires the separate liberal norm of always being against extra-state violence - a norm which is currently less than entirely secure. 39% of young people have a favorable opinion of Luigi Mangione, and during the George Floyd protests several mainstream newspapers flirted with condoning violence in the name of racial justice. If your worldview says that it’s acceptable to lynch sufficiently bad people, then yes, accusing people of being bad is equivalent to calling for their murder, and you have no alternative but to make sure nobody is allowed to criticize anyone you like. This puts you in the position that Winston Churchill called “riding a tiger from which you dare not dismount”; you had better invest all your energy into making extremely sure that you and your friends are the ones calling the shots about who can and can’t be criticized. It sounds exhausting, which is why the liberal solution - bilateral controlled tiger-dismounting - is the choice of most functional societies.

I guess the major question is whether we just need a separate keyword to describe "not sufficiently against extra-state violence in a coherent and consistent way". Follow-on questions that I care less about would be whether people who satisfy this separate keyword are necessarily open to the charge of stochastic terrorism on the terms of their own position on that matter.

It's been a while, but back in the day, Logical Increments was often pointed to as a pretty good guide for approximately how to get in at various price points. It looks like it's still being updated. Not sure if the specific recommendations are now dominated by ads or anything, but even if so, it helps give you a sense of what is a reasonable expectation at different price points. If you're interested in gaming, they give some FPS performance at various resolutions in some games. I have no idea if the games they're referring to are meaningful today. I think they get their performance numbers from other sources. You can use it as a jumping off point for any other specific tradeoffs you prefer. When I last did it, I used them to get myself into the ballpark of about what I wanted and then used PC Part Picker to narrow in on specific components and do a bit more optimization on current prices.

As far as predicting the future, I can't do that. But just briefly looking, it seems like capable enough gaming PCs are currently not obscenely unreasonable. Probably still on the "somewhat overpriced" side, but honestly not as insane as one might think.

I would say that I began my career doing more problem solving, and I try to retain some of that, but I do a lot more problem setting now. Do you have any specific questions?

Not being sure what you're looking for, I'd maybe say, "You can just do things." Nothing is really stopping you from thinking deeply about the "why" of what you're doing. The scope of your thinking may be limited by the number of folks you can influence into working on the problems you think should be set. There are more formal ways to be able to exert such influence (e.g., you're given some sort of formal authority over resources/people who pretty much have to follow the direction you set), but informal methods work pretty well, too (e.g., you persuade others over time that they should pay attention to the concerns you pose, especially as they see examples of how you posed a problem and it led to important results).

There's a lot of haranguing about who "won" and who "lost", as though there is some pigeonhole principle with those two possibilities. It's entirely possible that the US did not (or will not) accomplish its objectives (paying costs along the way) while Iran also was badly damaged. War is generally a negative-sum affair. That is not to say that some years from now, we will look back and think that such a case became reality; either side could still sufficiently "win". Just to say that it's also possible that neither party really "wins".

I don't actually care all that much about the actual process you use for evaluation of things like probabilities/payoffs (honestly, I don't even care that much about Pascal's wager). The point is that, in principle, one could conceivably do such. Obviously, any particular process is subject to a variety of scrutinies.

to actually do this you would have to go through and compare every religion on earth.

There's always going to be some limitation. When I'm coming to my personal beliefs about my own academic field, for example, I certainly don't read every single paper that is published, even though some might be amazing. That doesn't mean I can't ever come to beliefs.

See, you say

Well yes.

But then you try to argue for no. Both on the probabilistic argument and beyond. You seemed to have embraced the idea that there's no way for you to assess probabilities, but then you say

I can find arguments that make established religions less likely to be true.

Even going beyond probabilities, you had said

there is no way to distinguish between a religion that is made up by humans and one that is actually correct.

But now you seem to think there are ways to conclusively show that a religion is false.

Perhaps you'd like to take a chance to try to reconcile some apparent contradictions? I'd be interested in getting to the decision theory question possibly posed by your final sentence, but the contradictions above may make it impossible for us to construct a well-posed decision theory problem.

Interestingly, the base Pascal wager makes sense without any infinite suffering at all. Regardless, there are a variety of ways of handling it, especially if your concern is that Roko (a person) is just making up a basilisk.

It is just not sustainable as there is no way to distinguish between a religion that is made up by humans and one that is actually correct.

This seems to be your real objection, not the multiple religion concern. You think it's just impossible to actually assess anything involved, including probabilities. Presumably, that means it's also impossible for you to assess the probability that atheism is true.

As they say, "unless those days were shortened, no flesh would be saved"... or something like that.

Pascal's wager is nearly the earliest example of decision theory, and it hardly makes sense to say that the many religions concern simply breaks decision theory. One can do a variety of things to analyze the probability space as well as the payoff space. For an example simplification, suppose there are two possible mutually exclusive levers you could pull, each with some chance of giving you massively large/infinite utility, and P(A pays out)=0.999 while P(B pays out)=0.001. (This is obviously an extreme case, but that's just to build intuition.) Alternatively, one can adjust probabilities such that maybe there's a third mutually exclusive lever that you can pull which has a guaranteed payoff of 1 or whatever. One can make further refinements.

Most of their edge in other markets comes from cheating (buying secret data) and grinding (trading all the time and trading with more capital than they deserve, because it was handed to them). My analysis should be superior to them in a live sports game where they can't pull these dirty tricks.

You should just cheat yourself. Scale up. Way way way up. Start your own sports betting ETF. Or possibly recognize that if betting on sports with capital that was handed to them, more than they deserve, is cheating, then some folks are about to start cheating against you in sports betting, too.

It is a binary state though.

This is quite the claim about a concept that is known to be rather messy. Multiple entire books have been written by philosophers of ethics trying to explore the nature of consent, because it is, indeed, rather messy. One may desire to collapse all the messiness down to a binary state, but that is a significant enough of a claim that it likely requires yet another one of those books written by a philosopher of ethics to argue for. Probably not something that's going to be settled in a MottePost.

To be clear, I think that for some situations (many situations), there is a clean enough mapping from the complex mental state that was present in that situation to a binary consent state. But that mapping is not always clean. One can hold as an axiom that, in theory, such a mapping must always exist, but that would either be an axiom or a claim. If it's a claim, I think it's hard to look at the existing academic work and believe that it has been conclusively shown.

There's a pretty long history of dirty theists making arguments along the lines of, "Let's compute how inconceivably improbable it is for intelligent life to spontaneously develop out of simple dead matter." I don't really subscribe to such arguments, but that is neither here nor there. It may be the case that you are unaware of the typical battle lines that have been drawn when they do so. Not being aware of such would be a reasonable explanation for your confusion.

I must admit, I did not have "intra-atheist squabble over aliens results in arguments that intelligent life may be extremely improbable" on my bingo card. Handwavy BigNum arguments are a typical part of the arsenal. Isn't the entire point of the unfalsifiable multiverse idea to construct a handwavy BigNum argument?

Kavanaugh wrote:

The only apparent principle unifying the four disparate exceptions listed by the Court in Wong Kim Ark—especially in light of the exception for tribal American Indians—is that the parents in all of those varied circumstances were not U. S. citizens and were citizens of other nations, whether tribal or foreign. An exception for those born in the United States to foreign parents unlawfully or temporarily in the country is consistent with that principle and therefore with the Fourteenth Amendment.

and

And most starkly, plaintiffs cannot convincingly explain their view that the children of tribal American Indians are not constitutionally entitled to birthright citizenship, while the children of foreign citizens unlawfully or temporarily in the country are constitutionally entitled to birthright citizenship.

Among other things, Thomas wrote:

Like temporary visitors, tribal Indians were not completely subject to the jurisdiction of the United States. The United States did not have the right to impose personal taxes on them—hence, “Indians not taxed.” Their personal affairs remained subject to the jurisdiction of their tribal nation. “The right of self-government” was “secured to each tribe, with jurisdiction over all persons and property within its limits, subject to certain exceptions, founded on principles somewhat analogous to the international laws among civilized nations.” The United States did not interfere “with the disposition, or descent, or tenure of their property, as between themselves,” or “prove their wills,” or subject them to the “laws of marriage and divorce,” or subject them to the “laws of the United States, against high treason.” Tribal Indians did not owe the United States primary allegiance and did not receive from it complete protection.

and

But, the Court cannot explain why tribal Indians were not “subject to the jurisdiction” of the United States if they happened to be born outside Indian lands while foreign temporary visitors were. It is true that tribal Indians belonged to “alien and sovereign” nations and that the United States’ relations with them implicated “intersovereign concerns.” Ante, at 12. But, temporarily visiting foreigners also belong to “alien and sovereign” nations, and the United States’ relations with them also implicate “intersovereign concerns.” It is difficult to understand why China, for example, would be less alien or less sovereign than the Cherokee Nations. It is also difficult to understand why tribal Indians would be less entitled to American citizenship if born on non-Indian land within the United States than children of birth tourists who immediately returned to China.

Alito wrote:

the Court cannot explain why the Fourteenth Amendment did not confer citizenship on children born in the United States to tribal Indians. As explained, federal law governed those children and their parents to the extent the Federal Government wished. If the Court were right that the Citizenship Clause applies to anyone who is born here and is subject to our laws, then the Fourteenth Amendment would have conferred citizenship on all tribal Indians. But the exception for tribal Indians was well-established at the time and remained until Congress eliminated it by statute.

In fact, overturning it would have been legislation from the bench almost as bad as Roe.

I mean, that's not really what "legislation from the bench" means? Take, for example, Kavanaugh's position that 14A doesn't require it either way, but Congress can legislate either way, wouldn't really be "legislation from the bench". It would instead be giving room for legislation. Typically, "legislation from the bench" means that the Court rules in a way that precludes legislation from making the decision. Somewhat ironically, that's kind of what the Court actually did here. By analog, Roe was legislation from the bench, where the Court decided the question in a way that didn't allow for any legislative choice, whereas Dobbs is probably not legislation from the bench, as it's saying that the legislation rests with the legislatures.

Of course, just because something is "legislation from the bench" doesn't mean that it's wrong; the Constitution may really, actually, say the thing.

In my effortpost, I referred to an old old comment of mine, where I said:

my highest aspirations for most administrations these days is that they give us interesting cases that clear up confusing Constitutional issues... and I think there’s a decent chance the Roberts Court can still do that on some of these matters.

After having (mostly) read the opinions, if I'm judging by this metric, I have to say that Roberts' majority opinion is a fail. To be clear, I am not saying that the opinion is wrong. On the contrary, as the saying goes, the Supreme Court is not final because they're right; they're right because they're final. So, yeah, they're final, and so they're right. But I do not think the majority opinion cleared up the confusion.

I don't think he really cleared up what was going on in WKA. Primarily because for the critical step, he just did what the Court did in WKA - turn to Schooner (DRINK!). One of the primary areas of interest was, in turn, what Schooner did and how it should be understood. On this point, Roberts was somehow even less informative than WKA. He didn't even quote the entire critical passage! Didn't even get to the part about the "implied license" under which people enter the country. As I said in the effortpost, the Court wants the Full Schooner, but it doesn't want to engage with it. It doesn't even touch on the full panoply of hypos that Schooner touched on.

The second major confusing question is how anything works with Indians. Indian law is confusing, yo. He could have at least said, "Indians are weird, yo." But he didn't even do that. I think this is basically the one, crucial sentence:

Indians born under those dominions, he concluded, were not “citizens or subjects of the United States,” but members of “alien and sovereign tribes.” [citing Kent]

Like, what counts as a "dominion"? What is it to be "under those dominions"? Does Roberts think it matters whether an Indian woman, carrying the child of an Indian man, wandered off the reservation and gave birth in non-tribal US territory? How does any of this work?

The biggest, most major sources of confusion are pretty much just swept under the rug.

I don't know that I buy the dissents, either. I at least felt like I learned some things from Thomas that I hadn't seen in the briefs/cases. He gave the most plausible explanation for what could have been the motivating reasoning behind the shift in language from the 1866 CRA and 14A, but I'm not qualified to assess the truth thereof. He really shines in making it visceral how confusing it is to read WKA. And I hadn't quite noticed in reading Fuller's WKA dissent that it could be read as agreeing with the majority that the child of a domiciled alien would be a citizen, but dissenting instead on the grounds that WKA, specifically, was not/could not be domiciled. I need to find time to go back and read it again; as of right now, I don't know whether I think this is a plausible reading or not.

I'd probably want to stew with it all and (re-)read some of the citations before saying who I find ultimately more persuasive. But I'm not sure either of them are "right" (as in, not the regular sense of right; ya know what? we've already covered this). That is, I'm not sure either view really provides a clear, convincing, comprehensive theory that fits all the pieces together and makes it less of an atrocious mess.

So I feel a bit better about my conclusion that the topic is an atrocious mess. I can take comfort that at least Kavanaugh agrees with me that the Constitutional question is "not straightforward". I'd like to also hope that Gorsuch was thinking something similar when, in his brief separate writing, he said, in a somewhat measured fashion, that he thought Thomas' view "better accords with the Clause's original public meaning". I'd like to remember his statement in oral arguments ("It's a mess"), and view him as agreeing with me that it's a mess, and then saying something along the lines of, "If the two best explanations for what's going on are Roberts' opinion or Thomas', I guess, if I have to, I'll take Thomas'." I'm not sure if that's where I'll end up after stewing with it longer, but it seems plausible.

Of course, the Constitutional issue being a 5-4 I think also supports my prior opinion that it is much messier than most people thought going into it.

Oh, and also of course, I feel a bit vindicated in my more recent prediction (in the effortpost here, rather than in my comment years ago at the old old old place) that we were likely not going to get a real, detailed, coherent opinion that cleared stuff up.

Technically Kavanaugh concurs with the ruling because he believes Congress' codification effects this rule, rather than the 14th amendment requiring it.

I'm still digesting it all, but I read Kavanaugh as stronger than that. I think he affirmatively believes that 14A would allow the exact same rule as the EO, but only if it was done by statute. That is, on the 14A Constitutional question, the vote was 5-4.

Have you checked what percentage of the devices have integrations for Home Assistant? If the number is decent, you can at least side-step all the manufacturer apps and put them in one location. May even be able to reassert local control, depending.

Obviously this, but if the question mandated that I consume something that's not in the regular budget, it would probably be a robot mower. That's right around the price point of the good ones that could probably handle the slope in the lawn.