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Cake day: July 19th, 2023

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  • Other Scott has clarified his position on citational standards in a comment on his blog:

    Wow, that’s really cool; I hadn’t seen [a recent independence result]. Thanks! Given all the recent claims there have been to lower the n for which BB(n) is known to be independent of ZFC, though, I would like to establish a ground rule that a claim needs either a prose writeup explaining what was done or independent verification of its correctness, ideally both but certainly at least one, rather than just someone’s GitHub repo.

    In contrast, the Gauge’s standard is that a claim needs reproducible computable artifacts as supporting evidence, with inline comments serving as sufficient documentation for those already well-versed in the topic, and any supporting papers or blog posts are merely a nicety for explaining the topic and construction to the mathematical community and laity at large. If a claim is not sufficiently strong then we should introduce more computational evidence to settle the question at hand.

    For example, Leng 2024 gives a construction in Lean 4. If this is not strong enough then the Gauge could be configured to compile a Nix-friendly Lean 4 and expend some compute in CI to verify the proof, so that the book only builds if Leng’s proof is valid. Further critique would focus on what Leng actually proved in terms of their Lean 4 code. Other Scott isn’t convinced by this, so it’s not part of the story that they will tell.



  • Here’s a few examples of scientifically-evidenced concepts that provoke Whorfian mind-lock, where people are so attached to existing semantics that they cannot learn new concepts. If not even 60% of folks get it, then that’s more than within one standard deviation of average.

    • There are four temporal tenses in a relativistic setting, not three. “Whorfian mind-lock” was originally coined during a discussion where a logician begs an astrophysicist to understand relativity. Practically nobody accepts this at first, to the point where there aren’t English words for discussing or using the fourth tense.
    • Physical reality is neither objective nor subjective, but contextual (WP, nLab) or participatory. For context, only about 6-7% of philosophers believe this at most, from a 2020 survey. A friend-of-community physicist recently missed this one too, and it’s known to be a very subtle point despite its bluntness.
    • Classical logic is not physically realizable (WP, nLab) and thus not the ultimate tool for all deductive work. This one does much better, at around 45% of philosophers at most, from the same 2020 survey.

    @gerikson@awful.systems Please reconsider the use of “100IQ smoothbrain” as a descriptor. 100IQ is average, assuming IQ is not bogus. (Also if IQ is not bogus then please y’all get the fuck off my 160+IQ lawn pollinator’s & kitchen garden.)



  • Okay, one more post. I re-read Scott’s coverage of free will. Here’s something he doesn’t understand: given the Free Will theorem, it’s not possible to build a Newcomb predictor which does well, and Newcomb’s paradox can’t get off the ground. The way I like to think of it is that we can build a Conway coin: a handheld device that uses the orientation angles of the wrist to contextualize an indefinite measurement over a 50-50 discrete distribution (with exponentially small possibility of erroring out and requiring a second measurement!) by using the wrist orientation as an orthogonal 3D basis and invoking Bell-Kochen-Specker. A predictor cannot reliably influence its victims when they are equipped with Conway coins; the paradox dissolves.

    It’s very funny, given this, that Scott wants credit for the Free Will theorem. He seems to think that the theorem is about a straightforward rewording of EPR in terms of KS, rather than a fairly deep insight about the indeterministic nature of reality. For example, there’s no indication that he has accepted “Conway’s shock”: there is no experimental evidence in favor of determinism once we notice that most experiments circularly assume that their underlying theory under test is deterministic. Conway insisted that this should shock the reader, as it once shocked Conway himself. Kochen 2017 is an excellent and self-contained explanation of Kochen’s view which complements Conway nicely; Conway himself ranted for about 6hrs on the topic in the 2018 Free Will Lectures, if you want the whole story.



  • I didn’t know about the history of Halting! I’m still reading, but I’ve already started planning out some nLab and esolang wiki edits. I guess I can no longer put off learning about Turing degrees; I previously thought beeping Busy Beavers were a novelty.

    Ugh, I forgot how rough the Gödelian sections are. So, to be overly dramatic, Gödel’s Completeness doesn’t have anything to do with Gödel’s Incompleteness, other than that they both involve first-order logic. Completeness says that if all models of a theory validate a statement then the statement is a theorem; for example, in all rings, 2 + 2 ≈ 4 because that’s how addition semantically works, and Gödel merely gives the recipe for tearing that down to axiomatic constructions. However, not all rings validate all theorems of integers; I recall that Lagrange’s theorem is a counterexample, perhaps? The issue is ω-consistency, as you mention; a theorem that says “for all integers” actually becomes “for all elements of the ring”, which can be more than just the integers! Unrelated: (First) Incompleteness says that there is no finite set of first-order axioms for natural numbers which does not also have some other non-standard semirings as models too. There is no conceptual conflict; model theory happens to be richer than expected. Or, to use the extremely technical language of Smith 2008, “the semantic completeness of a proof system for quantificational logic is one thing, the negation incompleteness of certain theories of arithmetic quite a different thing.”

    The subtlety of Turing machines that “prove consistency” or “disprove consistency” can’t be overstated. I’ve recently struggled with writing machines that study Con(ETCS) without success. Another good example: I’ve yet to see a Turing machine that halts iff the Collatz conjecture is true/false, and it might not be possible. What’s really frustrating is that there is a way to climb to Gödel’s and Turing’s results in like five lines, as long as you’re willing to use…

    CATEGORY THEORY (organ sting, peal of thunder, Vincent Price laughter)

    I already wrote this up for esolangs here. If you want this fully worked, see Yanofsky 2003. So, copying and pasting, we have Turing’s Kleene’s Post’s Halting:

    Theorem (Lawvere’s fixed point, Cantor’s version). In any Cartesian closed category, if there is an arrow t : Y → Y such that t(y) ≠ y for all y in Y, then for no A is there a weakly point-surjective arrow A → [A, Y]. (Lawvere, 1969)

    Corollary (Undecidability of Halting for computable universes). In no computable universe is there a total arrow N → [N, 2] which decides whether a coded arrow is defined at a coded point. (Yanofsky, 2003)

    And the contrapositive gives us a variant of Rice’s theorem which implies Gödel’s Kleene’s Rice’s First Incompleteness:

    Theorem (Lawvere’s fixed point, diagonal version). In any Cartesian closed category, if there is an weakly point-surjective arrow g : A → [A, Y] then Y has the fixed-point property. (Lawvere, 1969)

    Corollary (Kleene’s second recursion, Rogers’ fixed point). In any computable universe, N has the fixed-point property. (Kleene, 1938; Rogers, 1967)

    Corollary (Rice’s theorem for computable universes, external version). In no computable universe is there a total arrow N → 2 which decides whether a number is the code of a provable statement in some sufficiently-strong language of arithmetic. (Yanofsky, 2003)

    I like your thoughts on real vs complex. I recognize that I benefit from a century of hindsight, but it’s so curious that this is even a big deal to begin with. Heunen & Kornell 2022 recently showed using CATEGORY THEORY (wolf howling, willow groaning in the wind, witch cackling) that real- and complex-valued Hilbert spaces are the only two models, and I gather that it’s been known in folklore for a long time. Similarly, Born’s rule comes from Gleason’s theorem, full stop. It’s enough to say that we’re in a 3D universe and it just be like that.



  • It’s because of research in the mid-80s leading to Moravec’s paradox — sensorimotor stuff takes more neurons than basic maths — and Sharp’s 1983 international release of the PC-1401, the first modern pocket computer, along with everybody suddenly learning about Piaget’s research with children. By the end of the 80s, AI research had accepted that the difficulty with basic arithmetic tasks must be in learning simple circuitry which expresses those tasks; actually performing the arithmetic is easy, but discovering a working circuit can’t be done without some sort of process that reduces intermediate circuits, so the effort must also be recursive in the sense that there are meta-circuits which also express those tasks. This seemed to line up with how children learn arithmetic: a child first learns to add by counting piles, then by abstracting to symbols, then by internalizing addition tables, and finally by specializing some brain structures to intuitively make leaps of addition. But sometimes these steps result in wrong intuition, and so a human-like brain-like computer will also sometimes be wrong about arithmetic too.

    As usual, this is unproblematic when applied to understanding humans or computation, but not a reasonable basis for designing a product. Who would pay for wrong arithmetic when they could pay for a Sharp or Casio instead?

    Bonus: Everybody in the industry knew how many transistors were in Casio and Sharp’s products. Moravec’s paradox can be numerically estimated. Moore’s law gives an estimate for how many transistors can be fit onto a chip. This is why so much sci-fi of the 80s and 90s suggests that we will have a robotics breakthrough around 2020. We didn’t actually get the breakthrough IMO; Moravec’s paradox is mostly about kinematics and moving a robot around in the world, and we are still using the same kinematic paradigms from the 80s. But this is why bros think that scaling is so important.


  • Wolfram has a blog post about lambda calculus. As usual, there are no citations and the bibliography is for the wrong blog post and missing many important foundational papers. There are no new results in this blog post (and IMO barely anything interesting) and it’s mostly accurate, so it’s okay to share the pretty pictures with friends as long as the reader keeps in mind that the author is writing to glorify themselves and make drawings rather than to communicate the essential facts or conduct peer review. I will award partial credit for citing John Tromp’s effort in defining these diagrams, although Wolfram ignores that Tromp and an entire community of online enthusiasts have been studying them for decades. But yeah, it’s a Mathematica ad.

    In which I am pedantic about computer science (but also where I'm putting most of my sneers too, including a punchline)

    For example, Wolfram’s wrong that every closed lambda term corresponds to a combinator; it’s a reasonable assumption that turns out to not make sense upon closer inspection. It’s okay, because I know that he was just quoting the same 1992 paper by Fokker that I cited when writing the esolangs page for closed lambda terms, which has the same incorrect claim verbatim as its first sentence. Also, credit to Wolfram for listing Fokker in the bibliography; this is one of the foundational papers that we’d expect to see. With that in mind, here’s some differences between my article and his.

    The name “Fokker” appears over a dozen times in my article and nowhere in Wolfram’s article. Also, I love being citogenic and my article is the origin of the phrase “Fokker size”. I think that this is a big miss on his part because he can’t envision a future where somebody says something like “The Fokker metric space” or “enriched over Fokker size”. I’ve already written “some closed lambda terms with small Fokker size” in the public domain and it’s only a matter of time until Zipf’s law wears it down to “some small Fokkers”.

    Also, while “Tromp” only appears once in my article, it appears next to somebody known only as “mtve” when they collaborated to produce what Wolfram calls a “size-7 lambda” known as Alpha. I love little results like these which aren’t formally published and only exist on community wikis. Would have been pretty fascinating if Alpha were complete, wouldn’t it Steve!? Would have merited a mention of progress in the community amongst small lambda terms, huh Steve!?

    I also checked the BB Gauge for Binary Lambda Calculus (BLC), since it’s one of the topics I already wrote up, and found that Wolfram’s completely omitted Felgenhauer from the picture too, with that name in neither the text nor bibliography. Felgenhauer’s made about as many constructions in BLC as Tromp; Felgenhauer 2014 constructs that Goodstein sequence, for example. Also, Wolfram didn’t write that sequence, they sourced it from a living paper not in the bibliography, written by…Felgenhauer! So it’s yet another case of Wolfram just handily choosing to omit a name from a decade-old result in the hopes that somebody will prefer his new presentation to the old one.

    Finally, what’s the point of all this? I think Wolfram writes these posts to advertise Mathematica (which is actually called Wolfram Mathematica and uses a programming language called Wolfram BuT DiD YoU KnOw) He also promotes his attempt at rewriting all of physics to have his logo upon it, and this blog post is a gateway to that project in the sense that Wolfram genuinely believes that staring at these chaotic geometries will reveal the equations of divine nature. Meanwhile I wrote my article in order to win an IRC argument against make a reasonable presentation of an interesting phenomenon in computer science directly to Felgenhauer & Tromp, and while they don’t fully agree with me, we together can’t disagree with what’s presented in the article. That’s peer review, right?





  • It’s important to understand that the book’s premise is fairly hollow. Yudkowsky’s rhetoric really only gets going once we agree that (1) intelligence is comparable, (2) humans have a lot of intelligence, (3) AGIs can exist, (4) AGIs can be more intelligent than humans, and finally (5) an AGI can exist which has more intelligence than any human. They conclude from those premises that AGIs can command and control humans with their intelligence.

    However, what if we analogize AGIs and humans to humans and housecats? Cats have a lot of intelligence, humans can exist, humans can be more intelligent than housecats, and many folks might believe that there is a human who is more intelligent than any housecat. Assuming intelligence is comparable, does it follow that that human can command and control any housecat? Nope, not in the least. Cats often ignore humans; moreover, they appear to be able to choose to ignore humans. This is in spite of the fact that cats appear to have some sort of empathy for humans and perceive us as large slow unintuitive cats. A traditional example in philosophy is to imagine that Stephen Hawking owns a housecat; since Hawking is incredibly smart and capable of spoken words, does it follow that Hawking is capable of e.g. talking the cat into climbing into a cat carrier? (Aside: I recall seeing this example in one of Sean Carroll’s papers, but it’s also popularized by Cegłowski’s 2016 talk on superintelligence. I’m not sure who originated it, but I’d be unsurprised if it were Hawking himself; he had had that sort of humor.)


  • I think that you have useful food for thought. I think that you underestimate the degree to which capitalism recuperates technological advances, though. For example, it’s common for singers supported by the music industry to have pitch correction which covers up slight mistakes or persistent tone-deafness, even when performing live in concert. This technology could also be used to allow amateurs to sing well, but it isn’t priced for them; what is priced for amateurs is the gimmicky (and beloved) whammy pedal that allows guitarists to create squeaky dubstep squeals. The same underlying technology is configured for different parts of capitalism.

    From that angle, it’s worth understanding that today’s generative tooling will also be configured for capitalism. Indeed, that’s basically what RLHF does to a language model; in the jargon, it creates an “agent”, a synthetic laborer, based on desired sales/marketing/support interactions. We also have uses for raw generation; in particular, we predict the weather by generating many possible futures and performing statistical analysis. Style transfer will always be useful because it allows capitalists to capture more of a person and exploit them more fully, but it won’t ever be adopted purely so that the customer has a more pleasant experience. Composites with object detection (“filters”) in selfie-sharing apps aren’t added to allow people to express themselves and be cute, but to increase the total and average time that users spend in the apps. Capitalists can always use the Shmoo, or at least they’ll invest in Shmoo production in order to capture more of a potential future market.

    So, imagine that we build miniature cloned-voice text-to-speech models. We don’t need to imagine what they’re used for, because we already know; Disney is making movies and extending their copyright on old characters, and amateurs are making porn. For every blind person using such a model with a screen reader, there are dozens of streamers on Twitch using them to read out donations from chat in the voice of a breathy young woman or a wheezing old man. There are other uses, yes, but capitalism will go with what is safest and most profitable.

    Finally, yes, you’re completely right that e.g. smartphones completely revolutionized filmmaking. It’s important to know that the film industry didn’t intend for this to happen! This is just as much of an exaptation as captialist recuperation and we can’t easily plan for it because of the same difficulty in understanding how subsystems of large systems interact (y’know, plan interference.)


  • I’m gonna start by quoting the class’s pretty decent summary, which goes a little heavy on the self-back-patting:

    If approved, this landmark settlement will be the largest publicly reported copyright recovery in history… The proposed settlement … will set a precedent of AI companies paying for their use of pirated websites like Library Genesis and Pirate Library Mirror.

    The stage is precisely the one that we discussed previously, on Awful in the context of Kadrey v. Meta. The class was aware that Kadrey is an obvious obstacle to succeeding at trial, especially given how Authors Guild v. Google (Google Books) turned out:

    Plaintiffs’ core allegation is that Anthropic committed largescale copyright infringement by downloading and comercially exploiting books that it obtained from allegedly pirated datasets. Anthropic’s principal defense was fair use, the same defense that defeated the claims of rightsholders in the last major battle over copyrighted books exploited by large technology companies. … Indeed, among the Court’s first questions to Plaintiffs’ counsel at the summary judgment hearing concerned Google Books. … This Settlement is particularly exceptional when viewed against enormous risks that Plaintiffs and the Class faced… [E]ven if Plaintiffs succeeded in achieving a verdict greater than $1.5 billion, there is always the risk of a reversal on appeal, particularly where a fair use defense is in play. … Given the very real risk that Plaintiffs and the Class recover nothing — or a far lower amount — this landmark $1.5 billion+ settlement is a resounding victory for the Class. … Anthropic had in fact argued in its Section 1292(b) motion that Judge Chhabria held that the downloading of large quantities of books from LibGen was fair use in the Kadrey case.

    Anthropic’s agreed to delete their copies of pirated works. This should suggest to folks that the typical model-training firm does not usually delete their datasets.

    Anthropic has committed to destroy the datasets within 30 days of final judgement … and will certify as such in writing…

    All in all, I think that this is a fairly healthy settlement for all involved. I do think that the resulting incentive for model-trainers is not what anybody wants, though; Google Books is still settled and Kadrey didn’t get updated, so model-trainers now merely must purchase second-hand books at market price and digitize them, just like Google has been doing for decades. At worst, this is a business opportunity for a sort of large private library which has pre-digitized its content and sells access for the purpose of training models. Authors lose in the long run; class members will get around $3k USD in this payout, but second-hand sales simply don’t have royalties attached in the USA after the first sale.


  • It’s worth understanding that Google’s underlying strategy has always been to match renewables. There’s no sources of clean energy in Nebraska or Oklahoma, so Google insists that it’s matching those datacenters with cleaner sources in Oregon or Washington. That’s been true since before the more recent net-zero pledge and it’s more than most datacenter operators will commit to doing, even if it’s not enough.

    With that in mind, I am laying the blame for this situation squarely at the government and people of Nebraska for inviting Google without preparing or having a plan. Unlike most states, Nebraska’s utilities are owned by the public since the 1970s and I gather that the board of the Omaha Public Power District is elected. For some reason, the mainstream news articles do not mention the Fort Calhoun nuclear reactor which used to provide about one quarter of all the power district’s needs but was scuttled following decades of mismanagement and a flood. They also don’t quite explain that the power district canceled two plans to operate publicly-owned solar farms with similar capacity (~600 MW per farm compared with ~500 MW from the nuclear reactor), although WaPo does cover the canceled plans for Eolian’s batteries, which I’m guessing could have been anywhere from 50-500 MWh of storage capacity. Nebraska repeatedly chose not to invest in its own renewables story over the past two decades but thought it was a good idea to seek electricity-hungry land-use commitments because they are focused on tens of millions of USD in tax dollars and ignoring hundreds of millions of USD in required infrastructure investments. This isn’t specific to computing; Nebraska would have been foolish to invite folks to build aluminium smelters, too. Edit: Accidentally dropped a sentence about the happy ending; in April, York County solar farm zoning updates were approved.

    If you think I’m being too cynical about Nebraskans, let me quote their own thoughts on solar farms, like:

    Ag[ricultural] production will create more income than this solar farm.

    [York County is] the number one corn raising county in Nebraska…

    How will rotating the use of land to solar benefit this land? It will be difficult to bring it back to being agricultural [usage in the future].

    All that said, Google isn’t in the clear here. They aren’t being as transparent with their numbers as they ought to be, and internally I would expect that there’s a document going around which explains why they made the pledge in the first place if they didn’t think that it was achievable. Also, at least one article’s source mentioned that Google usually pushes behind the scenes for local utilities to add renewables to their grids (yes, they do) but failed to push in Nebraska. Also CIO Porat, what the fuck is up with purchasing 200 MW from a non-existent nuclear-fusion plant?


  • [omitted a paragraph psychoanalyzing Scott]

    I don’t think that he was trying to make a threat. I think that he was trying to explain the difficulties of being a cryptofascist! Scott’s entire grey-tribe persona collapses if he ever draws a solid conclusion; he would lose his audience if he shifted from cryptofascism to outright ethnonationalism because there are about twice as many moderates as fascists. Scott’s grift only continues if he is skeptical and nuanced about HBD; being an open believer would turn off folks who are willing to read words but not to be hateful. His “appreciat[ion]” is wholly for his brand and revenue streams.

    This also contextualizes the “revenge”. If another content creator publishes these emails as part of their content then Scott has to decide how to fight the allegations. If the content is well-sourced mass-media journalism then Scott “leave[s] the Internet” by deleting and renaming his blog. If the content is another alt-right crab in the bucket then Scott “seek[s] some sort of horrible revenge” by attacking the rest of the alt-right as illiterate, lacking nuance, and unable to cite studies. No wonder he doesn’t talk about us or to us; we’re not part of his media strategy, so he doesn’t know what to do about us.

    In this sense, we’re moderates too; none of us are hunting down Scott IRL. But that moderation is necessary in order to have the discussion in the first place.