skybrian's recent activity

  1. Comment on AI helps unlock discoveries hidden in Gödel's notebooks in ~humanities.history

    skybrian
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    From the article: [...] [...] [...] [...]

    From the article:

    Since 2017, the Finnish logician Jan von Plato has led a project at Helsinki University to understand the contents of 16 notebooks that Gödel wrote in the early 1940s. This material – the “workbooks” – is 1,009 pages of densely written text about maths and logic. Much of it is written in a German shorthand, Gabelsberger, that was obsolete even when Gödel was using it.

    Progress in the mathematical understanding of the text was painfully slow – about a page a week – until September, when von Plato enlisted the help of the AI model Claude. Within a couple of days, Claude had provided a comprehensive digest of the entire material, revealing Gödel had proved hundreds of theorems that no one knew about.

    [...]

    In August, at a conference in France about AI and theorem proving, von Plato met computer scientists who suggested that he co-opt the help of Claude in trying to make sense of the workbooks. On his return to Helsinki he began the process, showing Claude his transcriptions of the workbooks, as well as six books he had previously written on Gödel and other secondary scientific literature.

    “In a couple of days, I got to see a 650-page explanation of the workbooks. It had to be controlled page for page, but it’s basically a work that is impossible to do for human beings,” he said. “Humans read one page at a time and we tend to forget things. It takes us a year to read about 50 pages. We just are not able to keep in mind all the different parts.

    “The AI can connect all the pieces in a thousand pages. It can see all of Gödel’s writings as one piece.”

    [...]

    Gödel reacted to Cohen’s Fields medal by saying that he had already proved the result in the 1940s. Yet when pushed for a proof by his peers, Gödel was unable to reconstruct one from his notes.

    The first task von Plato set Claude was to discover if Gödel’s workbooks had a proof of the independence of the axiom of choice, which would reveal that Gödel had been telling the truth in 1966. The answer came back: yes, almost. “He was just one step away,” said von Plato. “There’s one definition that Gödel got wrong, but he had the right definition two years earlier, and so the thought is that he would have arrived at the right definition anyway if he had just continued for a few months. For me, the architecture of his proof is just wonderful. It makes all of these results of set theory follow a uniform pattern.

    [...]

    Von Plato said that when Claude presented him with the reconstructed proof of the independence of the axiom of choice, he ran it through the proof assistant Coq, a program that verifies the validity of mathematical proofs, and it passed. Von Plato believes that had Gödel published his work on the axiom of choice, he would have won the 1940 Fields medal. “Maybe he felt that when Cohen got the medal, that that was something he sort of missed.”

    In further discussions with Claude, von Plato asked the AI model to extract all theorems in the workbooks for which Gödel either had a proof, had sketched a proof or had an idea for a proof. Claude found 663. When these results were put into Coq: “About 400 were verified as stated, about 200 were repaired, meaning that perhaps the statement of the theorem had to be made more precise, or some assumption had to be added. About 50 were false, and this is no wonder. Gödel himself, when rereading his notes, would occasionally add a marginal remark: falsch! [incorrect] or schlecht! [bad].”

    [...]

    Hamkins said: “The fact that there are things in there that resemble [Cohen’s proof] does not mean he had it. It shows he was on the path. You don’t get credit for work you don’t tell anyone about. But Gödel had so many ground-breaking ideas that it is maybe not surprising that his notebooks are full of exciting things.”

  3. Comment on “…and the proof is checked in Lean” in ~science

    skybrian
    Link
    From the article: [...] [...] [...] [...]

    From the article:

    This post is an attempt to explain in simple terms how to interpret claims of the form “this theorem is correct because it was checked in Lean”. The summary is: there is an important signal that can be extracted from Lean code, but if this code is AI-generated then you need to do some tests first. We explain the tests, and note that in many cases (such as the OpenAI theorem dump) these tests have not yet been systematically done.

    [...]

    It is worth noting that of the 290 OpenAI theorems which come with Lean code, around 38 of them have the property that the Lean code does not even state, let alone prove, the main theorem of the paper. And OpenAI never claimed that it did! They just said “here is some Lean code which goes with this paper”. Sometimes the code just states and proves some intermediate results — my impression is that OpenAI decided to go live when some of the formalizations were incomplete, so just dumped what they had. To give a concrete example: paper 194 claims to prove Lech’s multiplicity conjecture in commutative algebra, with no restriction on dimension, residue field or characteristic; this question has been open since 1960. The headline theorem in the corresponding Lean code can be checked to be Corollary 5.4 of the paper — already an impressive achievement, but not the headline result.

    [...]

    When Anthropic formalized a proof of Fermat’s Last Theorem in Lean, they asked me to take a look at the 13 million lines of code which they had generated. I downloaded it onto my machine, dumped it into a sandbox (because who knows what AI-generated code will do, it can in theory delete all your files) and attempted to compile it; I very quickly ran out of memory. I told Anthropic that I was unable to make any claims about what they had done until I could see the code base compiling, and they gave me temporary access to a machine with 96 cores and 500 gigs of ram. I could then compile the code.

    Of course, with a more reasonably-sized codebase it is possible to compile the code on a reasonably-sized machine. For example OpenAI’s resolution of the Navier-Stokes problem is 640K lines of code and compiles fine on my laptop.

    [...]

    Even if the Lean code compiles and passes all these tests, and is thus overwhelmingly likely to be a correct proof of a theorem, this does not mean that any corresponding pdf also contains a correct proof! The Navier–Stokes lost in translation paper demonstrates the opposite in fact, for the Navier-Stokes write-up; whilst all the tests above have been run for the Navier–Stokes work, there are instances where the pdf proof and the Lean proof diverge. In these cases, who knows if the pdf proof is OK! My understanding is that some experts have been using AI to informalise the Lean proof back into English in order to read the argument, rather than ploughing through the slop in the pdf.

    [...]

    “It’s true because it’s checked in Lean” can be made to make sense. But one has to do some work beyond “the Lean code compiles”. Your frontier AI model can do all of this work. But it needs to be done, and (depending on the amount of Lean code in the proof) it may be computationally costly.

    1 vote

  5. Comment on The underappreciated political importance of "everywhere millionaires" in ~society

    skybrian
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    From an opinionated blog post by the authors of The Everywhere Millionaire. (The book is based on their research. I previously posted a link to a review of their book in the New Yorker.) [...] [...]

    From an opinionated blog post by the authors of The Everywhere Millionaire. (The book is based on their research. I previously posted a link to a review of their book in the New Yorker.)

    Consider a few examples of what we mean. In “Oligarchy and the Great Evasion,” Krugman wrote:

    The large majority of U.S. businesses are in fact pass-through businesses, and it’s fair to say that most of them aren’t “real” businesses like, say, car dealerships or restaurants. They are, instead, basically legal fictions created for tax purposes.

    Most businesses in America are pass-through businesses. They account for nearly half of employment. Their industrial mix is far more representative of the American economy than traditional corporations. This statement reflects a failure to appreciate how much the structure of American business has transformed since the 1980s.

    Moreover, as we have shown in our research and in our book, auto dealers and restaurants are some of the biggest generators of top pass-though profits in the economy. In fact, auto dealers are number 3 on our rankings of 4 digit pass-through profit generating industries with top-1% owners.

    [...]

    We agree with Krugman that the recent rise in billionaire wealth has been dramatic. But it’s important to put the scale of Forbes billionaire growth into perspective with the other rich and powerful actors in American society. Even at the very frothy public market valuations of the current moment, the Forbes list amounts to around $8 trillion or roughly 4.3% of total household wealth. Meanwhile, based on the most recent SCF, Everywhere Millionaires are probably worth more than $63 trillion or 38% of total household wealth.

    Likewise, we are not aware of any Everywhere Millionaires who have the power to shut off internet on the front lines in Ukraine. Scrutinizing economic and political power deployed in antidemocratic ways is an essential public service.

    But let’s not blame every policy failure on a small number of billionaires, and, in doing so, absolve everybody else responsible for fixing our current policy problems. The power to legislate still resides with the Congress. The power to regulate many markets is reserved for the states and localities within them.

    [...]

    Elon didn’t want the massive tax cuts in the OBBBA extended, which did not go to the tech billionaires. He didn’t benefit from the reduced EV demand, which came when the EV credits were abolished. He benefitted little from the new deduction for car loan interest passed in that bill, since financing car purchases is a small part of Tesla’s business.

    Who drove these changes and reaped the rewards? The Everywhere Millionaire car dealers who reside in nearly every Congressional district and represent many of them directly. Elon lost big in the midterm election, despite spending half a billion dollars. Meanwhile, dozens of Everywhere Millionaires will return after the election to the new Congress and to state and local government positions across the country.

    1 vote

  7. Comment on Data centres have become a dirty word and a political issue in much of the world – has Sweden made one we can all love? in ~tech

    skybrian
    (edited )
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    This is caused by being in too much of a hurry. Big Tech has been building huge data centers for at least twenty years and it wasn't an issue before. Google, at least, was making good progress on...

    This is caused by being in too much of a hurry. Big Tech has been building huge data centers for at least twenty years and it wasn't an issue before. Google, at least, was making good progress on being carbon-neutral. They funded (and still fund, via investment and advance-purchase agreements) many alternative energy projects.

    But due to the AI gold rush/arms race, now everyone including Google is in a huge hurry to build as many as they can, as quickly as possible. So they do whatever they can to reduce the time to build them, and sometimes that means natural gas turbines and taking old power plants out of retirement.

    Data centers aren't fundamentally bad for the environment, because they run on electricity and their main inputs and outputs are immaterial. They can easily run on green energy and there are multiple ways to cool them. It's a much easier problem than converting the airline industry to use green energy (for example). Done right, it can also be better for the environment than farming.

    Therefore, the goal of regulation should be to slow things down and do things the right way. For example, a stiff carbon tax on electricity used by data centers would encourage them to use green energy even if it takes longer, and to upgrade data centers currently using natural gas to something greener.

    It's also true that data centers don't employ many workers once they're up and running. In a way, that could be seen as good, since it allows rural areas to stay rural, instead of turning into suburban sprawl. And because they're so profitable, they can be a good source of local tax revenue. That's a matter of governments negotiating good deals with tech companies in return for having permission to build.

    It's easy to get people to oppose things, but it would be better to convince them that there can be local advantages to this trend. It requires smart negotiations to make sure the local community benefits rather than being taken advantage of.

    But in an era of widespread skepticism and distrust, how can a community's government representatives gain the trust needed to do the negotiations? It requires the community to trust that they're both smart and honest.

    5 votes

  8. Comment on Big balk: On Big Walk, Independent Games Festival, and the present unpleasantness in ~games

    skybrian
    (edited )
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    Perhaps the reason we disagree is that, having used LLMs for coding a fair bit, I don’t really buy that what you’re describing is possible. I don’t think we’ve gotten to the point where anyone...

    Perhaps the reason we disagree is that, having used LLMs for coding a fair bit, I don’t really buy that what you’re describing is possible. I don’t think we’ve gotten to the point where anyone could come up with an innovative, fun to play, award-winning game without talent. The AI tools I’ve used can come up with a working demo and that’s pretty impressive. But the UI will have a lot of things wrong with it and there will be plenty more work to do to make something good.

    So, I would still be impressed by the talent of a game developer who used AI to make a game that’s actually good, versus something that’s obviously slop. I would consider it a sign of talent and I’d be interested in knowing more about how they managed it. Maybe it’s not the same kind of talent as developers who don’t use AI, but they clearly know something. I’d be interested in seeing the results of competitions where you’re explicitly allowed to use AI.

    I also don’t think using AI should be considered “not making an indy game.” That seems like a retcon. The word “indy” is a bit vague, but it seems like it’s about not having the financial backing of a large game studio. Using AI should allow indy developers to make more ambitious games, but it would still be in service of fulfilling the artistic vision of a few people without major funding.

    Also, I think indy developers should be able to take advantage of new technology as it comes available, and I’m interested in seeing how they take advantage of new tools.

    7 votes

  9. Comment on Big balk: On Big Walk, Independent Games Festival, and the present unpleasantness in ~games

    skybrian
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    This is insider knowledge that I had never heard of. How many people knew these things were hard when the games came out? It seems like you’d need to know the technology’s limitations pretty well,...

    This is insider knowledge that I had never heard of. How many people knew these things were hard when the games came out? It seems like you’d need to know the technology’s limitations pretty well, and many gamers would just have fun playing the game.

    7 votes

  10. Comment on Big balk: On Big Walk, Independent Games Festival, and the present unpleasantness in ~games

    skybrian
    Link Parent
    For me the question is why AI is being singled out versus the many other labor-saving tools that game developers could use. This isn’t like journalism where manipulating photos in Photoshop could...

    For me the question is why AI is being singled out versus the many other labor-saving tools that game developers could use. This isn’t like journalism where manipulating photos in Photoshop could misrepresent the truth. It’s also not like a sports event where everyone agrees on artificial limitations to make the competition interesting. There isn’t even a performance aspect to it, like in music where sometimes we’re interested in what musicians can do by actually playing their instruments.

    You should be able to use all the computer graphics you want when making a game, using any tool, just like you can use whatever trickery or special effects you like when making a movie. it’s mostly fake anyway and the “talent” is how good you are with whatever tools you like to use, not what you could do unaided.

    7 votes

  11. Comment on NVIDIA reportedly preparing to fire Jensen Huang in ~tech

    skybrian
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    NVIDIA's stock price is down a fair bit but I don't see why that would cause a crash? Would the next CEO change NVIDIA's strategy in a way that people will notice?

    NVIDIA's stock price is down a fair bit but I don't see why that would cause a crash? Would the next CEO change NVIDIA's strategy in a way that people will notice?

    10 votes

  12. Comment on Scientists study thousands of giant space shades to cool Earth in ~space

    skybrian
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    We could also relax fuel regulations to allow ships to go back to emitting more sulfur dioxide, which was countering global warming until recently. https://www.nature.com/articles/s43247-024-01442-3

    We could also relax fuel regulations to allow ships to go back to emitting more sulfur dioxide, which was countering global warming until recently.

    https://www.nature.com/articles/s43247-024-01442-3

    3 votes

  13. Comment on California’s utility wildfire liability conundrum could put clean energy projects in a delay doom loop in ~enviro

    skybrian
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    Your argument for nationalizing them seem to be imagining a fantasy federal government, one that’s “open and transparent, and average citizens will have a way to be heard in a way they are not...

    Your argument for nationalizing them seem to be imagining a fantasy federal government, one that’s “open and transparent, and average citizens will have a way to be heard in a way they are not currently heard.”

    But in the real world, we still have the Trump administration to deal with.

    Even assuming the next president is a Democrat, there’s no particular reason to expect that they would do better than California at regulating a California utility. Stories about poor management at PG&E don’t actually show that the federal government would do a better job. Maybe they would be negligent too?

    By the way, some cities in California do have their own public utilities. I thought Alameda Power & Telecom did a decent job when I lived there. More cities handling local electricity delivery themselves might be nice, but it wouldn’t help with delivering power state-wide.

    3 votes

  14. Comment on Weekly US politics news and updates thread - week of November 9 in ~society

    skybrian
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    What did these businesses actually do? Did they do anything to start a dispute with the cyclists? If the cyclists were starting a conflict with people who previously had nothing to do with them,...

    What did these businesses actually do? Did they do anything to start a dispute with the cyclists? If the cyclists were starting a conflict with people who previously had nothing to do with them, I’m not sure free speech rhetoric is enough to justify that, morally speaking.

    1 vote

  15. Comment on California’s utility wildfire liability conundrum could put clean energy projects in a delay doom loop in ~enviro

    skybrian
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    Okay, I researched this, by which I mean I asked ChatGPT about it. Here's a CPUC fact sheet about PG&E's spending on vegetation management. In 2011-2013, the CPUC authorized less than PG&E asked...

    Okay, I researched this, by which I mean I asked ChatGPT about it.

    Here's a CPUC fact sheet about PG&E's spending on vegetation management. In 2011-2013, the CPUC authorized less than PG&E asked for. After that, PG&E asked for more money and it was approved. So I was wondering why that happened and asked about it.

    Some context: the San Bruno explosion was on September 9, 2010. There was also a settlement about PG&E's 2011–2013 funding levels was submitted on October 15, 2010, under Governor Schwarzenegger's administration, later approved under Jerry Brown's administration.

    Apparently consumer advocates had a formal role in negotiating that settlement. ChatGPT gives me this timeline:

    December 2009 — PG&E submits its request. PG&E proposed spending levels for electric distribution, gas distribution, and generation, including $180 million annually for vegetation management.

    May 2010 — Consumer advocates challenge the request. DRA submitted detailed testimony recommending lower spending forecasts. TURN and other intervenors submitted their own evidence.

    June–July 2010 — Evidentiary hearings. Parties questioned witnesses, examined assumptions, and presented competing estimates.

    July–October 2010 — Settlement negotiations. PG&E, DRA, TURN, and other parties negotiated an agreement covering nearly every disputed issue.

    May 2011 — CPUC approval. The commissioners reviewed the proposed settlement and approved it, with additional conditions and resolution of one remaining issue.

    So, if you want to know what it's like to have a government managing electricity utility spending on infrastructure improvements, this has already happened. And it's still happening. There's another negotiation in process for the 2027–2030 time period.

    Advocating for lower utility rates is explicitly part of their job. California has institutionalized an adversarial process in which PG&E proposes spending, consumer advocates challenge the proposals, and the CPUC makes the final decision.

    So sure, an adversarial process is one way that governments make decisions, particularly in the judicial system. Is it a good way to decide on budgets? The results seem mixed.

    1 vote

  16. Comment on AlphaProof Code: a breakthrough in verifying complex software at depth in ~tech

    skybrian
    Link Parent
    It seems like it would imply that many kinds of "portable," source-code level bugs, which would work regardless of toolchain and architecture, are unlikely to exist, because they would have...

    It seems like it would imply that many kinds of "portable," source-code level bugs, which would work regardless of toolchain and architecture, are unlikely to exist, because they would have affected the particular toolchain and architecture they tested? (Although, perhaps they are still possible because this toolchain might have done something that happened to remove some bugs.)

    I wonder whether this Signal library is normally used on single or multiple threads? Proving things about concurrency bugs would be harder.

    2 votes

  17. Comment on California’s utility wildfire liability conundrum could put clean energy projects in a delay doom loop in ~enviro

    skybrian
    (edited )
    Link Parent
    I got ChatGPT to make a table showing both inflows and outflows for shareholders: Cash flow ($ billions) 2004–2006 2007–2017 2018–2020 2021–Sep 2026 Stock issuance +0.54 +6.18 +9.17 +2.71...

    I got ChatGPT to make a table showing both inflows and outflows for shareholders:

    Cash flow ($ billions) 2004–2006 2007–2017 2018–2020 2021–Sep 2026
    Stock issuance +0.54 +6.18 +9.17 +2.71
    Dividends −0.79 −8.15 0 −0.81
    Stock buybacks −2.68 ~0 0 ~0
    Net equity cash −2.93 −1.97 +9.17 +1.90

    So, looks like even when PG&E was paying substantial dividends in 2007-2017, they were also selling stock, resulting in cash inflows, and the net amount to shareholders was more like $2 billion.

    If you sum up over the whole time period, equity investors overall put more cash into PG&E than they got out. Mostly when emerging from their second bankruptcy.

    So, the story that shareholders profited from PG&E doesn't hold up, in the long run.

    What about bond holders? ChatGPT was unwilling to guess about cashflow, but debt increased from about $10 billion to $65 billion today and that tends to come from borrowing more money than you can repay.

    And there's now a risk of a third bankruptcy.

    This reminds me of the old joke about how the best way to make a small fortune in [substitute a domain here] is to start with a large one.

    1 vote

  18. Comment on California’s utility wildfire liability conundrum could put clean energy projects in a delay doom loop in ~enviro

    skybrian
    Link Parent
    If I recall correctly, PG&E wanted to spend more on maintenance but the CPUC didn't approve it because it would raise electricity rates. So, no, bad decisions can't all be blamed on the profit...

    If I recall correctly, PG&E wanted to spend more on maintenance but the CPUC didn't approve it because it would raise electricity rates.

    So, no, bad decisions can't all be blamed on the profit motive. Sometimes they can be blamed on politics, too, and it's rather difficult to figure out who deserves more blame in this case. Elected and appointed officials may be operating under bad incentives, like getting reelected, keeping their job, or bad influence from lobbyists.

    Governance is a tricky problem and there are no obvious winners, only kludgy workarounds to try to avoid the worst failures. We would like to have good decision-makers in charge of various organizations, but no method guarantees that we will get them.

    5 votes

  19. Comment on California’s utility wildfire liability conundrum could put clean energy projects in a delay doom loop in ~enviro

    skybrian
    Link Parent
    This is largely irrelevant as far as cash flow is concerned. Most revenue comes from customers either way. Both private and public entities can borrow money. A private company can also raise money...

    This is largely irrelevant as far as cash flow is concerned. Most revenue comes from customers either way. Both private and public entities can borrow money. A private company can also raise money by selling stock and doesn’t have to pay it back on any particular schedule or at all, which is occasionally useful.

    A government entity will have to fund infrastructure and compensate wildfire victims somehow. The problem doesn’t go away, and they can’t stiff the shareholders because there aren’t any. I suppose they could get revenue from taxes rather than utility bills, though, which can be made more progressive and is harder to avoid.

    3 votes

  20. Comment on California’s utility wildfire liability conundrum could put clean energy projects in a delay doom loop in ~enviro

    skybrian
    Link Parent
    Maybe true, but that’s fairly old history now, sort of like blaming the previous administration for current troubles. It isn’t going to help in the current crisis. Some more context: The Tubbs...

    Maybe true, but that’s fairly old history now, sort of like blaming the previous administration for current troubles. It isn’t going to help in the current crisis. Some more context:

    The Tubbs wildfire was in 2017. Though it wasn’t caused by PG&E, they suspended dividend payments as a precaution due to wildfire liability risk (in general). The Camp Fire was in 2018. In 2019, PG&E filed for bankruptcy. They emerged from bankruptcy in 2020. Since the bankruptcy, they’ve raised $38 billion from borrowing and $12 billion from selling stock. They’ve paid out less than $1 billion in dividends. Debt has increased from $40 to $65 billion, paying out nearly $3 billion a year, and interest rates are increasing as debt turns over at higher rates.

    They can borrow money. But funding for either grid improvements or payments to wildfire victims (if there are more wildlifes) will primarily come from revenue - that is, customers. They are already spending more on infrastructure than they’ve getting from operating cash flow, hence the borrowing.

    Utility stocks used to be considered a safe, reliable, rather boring investment, but those days are over, at least in California. Also, California already has some of the highest electricity rates in the country, and many customers can reduce what they pay by installing solar panels, etc. As rates go up, they have more incentive to do so.

    There is only so much utilities revenue available to fund the various things that California would like them to pay for. Utilities are regulated. How much money comes in and where the money goes is largely up to the state, via the California Public Utilities Commission. So someone is going to have to make a decision about how generous to be to wildfire victims versus other possible uses of that money. Or we could, like, not make a decision, in which case, under current law, wildfire victims will likely get most of it the next time wildfires are particularly bad.

    Although, I suppose if the money is already spent on infrastructure, it won’t be there and PG&E will go bankrupt again.

    3 votes