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The LessWrong Review [? · GW] runs every year to select the posts that have most stood the test of time. This post is not yet eligible for review, but will be at the end of 2025. The top fifty or so posts are featured prominently on the site throughout the year. Will this post make the top fifty?

Often I see people dismiss the things the Epicureans got right with an appeal to their lack of the scientific method, which has always seemed a bit backwards to me.

The most important thing, I think, is not even hitting the nail on the head, but knowing (i.e. really acknowledging) that a nail can be hit in multiple places. If you know that, the rest is just a matter of testing.

I think what you proved essentially boils down to the fact that a consistent guessing oracle can be used to compute a completion of any consistent recursively axiomatizable theory. (In fact, it turns out that a consistent guessing oracle can be used to compute a model (in the sense of functions and relations on a set) of any consistent recursively axiomatizable theory; this follows from what you showed and the fact that an oracle for a complete theory can be used to compute a model of that theory.)

I disagree with

Philosophically, what I take from this is that, even if statements in a first-order theory such as Peano arithmetic appear to refer to high levels of the Arithmetic hierarchy, as far as proof theory is concerned, they may as well be referring to a fixed low level of hypercomputation, namely a consistent guessing oracle.

The translation from T to U is computable. The consistent guessing oracle only came in to find a completion of U, but it could also find a completion of T (in fact, a completion of U can be computably translated to a completion of T), so the consistent guessing oracle doesn't really have anything to do with the relationship between T and U.

I prefer to keep plans private but I'm making big progress on meditation and mental re-wiring. Am working on a way to publicly demonstrate. Public plans just stress me out. I recently set two pretty ambitious goals. I figured I could use psychedelics to turbo-charge progress. The meditation one is coming along FAST.

The other goal is honestly blocked a bit on being super out of shape. Multiple rounds of covid really destroyed my cardio and energy levels. Need to rebuild those before a big push on goal 2.

a consistent guessing oracle rather than a halting oracle (which I theorize to be more powerful than a consistent guessing oracle).

This is correct. Or at least, the claim I'm interpreting this as is that there exist consistent guessing oracles that are strictly weaker than a halting oracle, and that claim is correct. Specifically, it follows from the low basis theorem that there are consistent guessing oracles that are low, meaning that access to a halting oracle makes it possible to tell whether any Turing machine with access to the consistent guessing oracle halts. In contrast, access to a halting oracle does not make it possible to tell whether any Turing machine with access to a halting oracle halts.

I don't understand what relevance the first paragraph is supposed to have to the rest of the post.

The program expanded in response to Amazon wanting to collect data about more retailers, not because Amazon was viewing this program as a profit center.

Monopolies are profitable and in that case the program would have more than paid for itself, but I probably should have mentioned that explicitly, since maybe someone could have objected that they could have been were more focused on mitigating risk of market share shrinking or accumulating power, instead of increasing profit in the long term. Maybe I fit too much into 2 paragraphs here.

I didn't see any examples mentioned in the WSJ article of Amazon employees cutting corners or making simple mistakes that might have compromised operations.

Hm, that stuff seemed like cutting corners to me. Maybe I was poorly calibrated on this e.g. using a building next to the Amazon HQ was correctly predicted by operatives to be extremely low risk.

I would argue that the practices used by Amazon to conceal the link between itself and Big River Inc. were at least as good as the operational security practices of the GRU agents who poisoned Sergei Skripal.

Thanks, I'll look into this! Epistemics is difficult when it comes to publicly available accounts of intelligence agency operations, but I guess you could say the same for bigtech leaks (and the future of neurotoxin poisoning is interesting just for its own sake eg because lower effect strains and doses could be disguised as natural causes like dementia).

I generally agree, i just have some specific evidence which I believe should adjust estimates in the report towards expecting more accessible algorithmic improvements than some people seem to think.

Just going by the standard that you set forth:

The overall impression that I got from the program was that as it proved profitable and expanded,

The program expanded in response to Amazon wanting to collect data about more retailers, not because Amazon was viewing this program as a profit center.

it took on a larger workforce and it became harder for leaders to detect when employees were following their individual incentives to cut corners and gradually accumulate risks of capsizing the whole thing

But that doesn't seem to have occurred. Until the Wall Street Journal leak, few if any people outside Amazon were aware of this program. It's not as if any of the retailers that WSJ spoke to said, "Oh yeah, we quickly grew suspicious of Big River Inc, and shut down their account after we smelled something fishy." On the contrary many of them were surprised that Amazon was accessing their seller marketplace through a shell corporation.

I didn't see any examples mentioned in the WSJ article of Amazon employees cutting corners or making simple mistakes that might have compromised operations. Instead, they seemed to be pretty careful and conscientious, making sure to not communicate with outside partners with their Amazon.com addresses, being careful to maintain their cover identities at trade conferences, only communicating with fellow Amazon executives with paper documents (and numbered paper documents, at that), etc.

I would argue that the practices used by Amazon to conceal the link between itself and Big River Inc. were at least as good as the operational security practices of the GRU agents who poisoned Sergei Skripal.

A singleton is hard to verify unless there was a long period of time after its discovery during which it was neglected, as in the case of Mendel.

Yet if your discovery is neglected in this way, the context in which it is eventually rediscovered matters as well. In Mendel's case, his laws were rediscovered by several other scientists decades later. Mendel got priority, but it still doesn't seem like his accomplishment had much of a counterfactual impact.

In the case of Shannon, Einstein, etc, it's possible their fields were "ripe and ready" for what they accomplished - as perhaps evidenced by the fact that their discoveries were accepted - and that they were simply plugged in enough to their research communities during a period of faster global dissemination of knowledge that any hot-on-heels competitors never quite got a chance to publish. But I don't know enough about these cases to be confident.

I can think of a couple cases in which I might be convinced of this sort of counterfactual impact:

• All peers in a small, tight-knit research community explicitly stated none of them were even close (though even this is hard to trust - are they being gracious? how do they know their own students wouldn't have figured it out in another year's time?). Do we have any such testimonials for Shannon, Einstein, etc?
• The discovery was actually lost, then discovered and immediately appreciated for its significance. Imagine a math proof written in a mathematician's papers, lost on their death, rediscovered in an antique shop 40 years later, and immediately heralded as a major advance - like if we'd found a proof by Fermat of Fermat's Last Theorem in an attic in 1950.
• Money was the bottleneck. There are many places a billion dollars can be put into research. If somebody launches a billion-dollar research institute in an underfunded subject that's been languishing for decades and the institute they founded starts coming up with major technical advances, that's evidence it was a game-changer. Of course it's possible that billionaire put their money into the field because they had information that the research was coming to fruition and they wanted to get in on something hot, but I probably have more trouble believing they could make such a prediction so accurately than that their money made a counterfactual impact.

A discovery can also be "counterfactually important" even if it only speeds up science a bit. Let's say that every year, there's one important scientific discovery and a million unimportant ones, and the important ones must be discovered in sequence. If you discover 2025's important discovery in 2024, all the future important discoveries in the sequence also arrive a year earlier. If each discovery is worth $1 billion/year, then you've now created $1 billion counterfactual dollars per year every year as long as this model holds.