I am sorry about the negative feelings and associations you have towards RC. Let's think constructively: What are 1-2 points you would do differently?
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Eh, every school db should be able to service a student called "Robert'); DROP TABLE Students;--", and every public facing LLM should still work even if asked to calculate the last digit of pi - that fulfills two noble purposes: 1) is fun and teaches whoever is responsible for the service some valuable lessons in craftsmanship or 2) if the service is built robustly (i.e. simple token limit and time limit per user), that's an easy way to gain street cred
That is well-known I assumed and continue to assume.
> I'm not seeing the direct link you're talking about
You are stating that link yourself; indirectly: "though I consider it unlikely that he is [being unaware of any mathematical history]". Why is it unlikely, precisely?
- Maybe because it is unlikely that he recieved the mathematical teaching that frequently does not contain history of mathematics (wild! I wonder which university you have in mind in particular) that you seem to be refering to?
- Maybe because his writing is evidence that he is interested about, incorporates and refers to history of mathematics, refer for example to https://terrytao.wordpress.com/2008/01/04/pcm-article-genera... or https://terrytao.wordpress.com/career-advice/theres-more-to-...
- Or maybe because he is quite the opposite of a person that never ventures outside of their own area; being blind for other fields, or ones own history; as evidence by being famously collaborative across different fields, having a popular blog where he writes about non-mathematical topics too and last; him being one of the main proponents of foundational topics such as formalization of mathematics; or the use of LLMs for mathematical research.
Does all that really make it more likely to you that Tao is not aware of the existence of counterexamples like those the commenter above mentioned - more likely than the commenter simply having missed a nuance or taking something out of context?
If so; I would be genuinely curious why - people work differently, and I am always happy to learn, or close gaps in my own understanding.
Which I don't see a reason for Anthropic and "Open"AI not to, given their not so stellar track record with IP of individuals/entities-that-are-not-rich-enough ;)
"But I realized after a while that talking to people casually about Fermat was impossible, because it just generates too much interest, and you can't really focus yourself for years unless you have this kind of undivided concentration, which too many spectators would have destroyed."
But yes; him reaping the benefits of himself having the idea first was part of it too; as far as I am aware.
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Which is still something completely different than some anonymous organisation keeping mathematical research secret because it is better for hype reasons. One is competition between individuals or groups within a field; the other is boring and sometimes borderline nihilistic generating of mathematical knowledge as an marketing asset.
Also note how the quote by Tao is in all likelyhood not meant as an absolute; rather than a statement of a trend - a handfull of counterexamples do I no way change anything about the truth value of Tao's quote.
On the other heand; consider how absurd it would be if "... in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science ..." would indeed be a misstatement; which would imply that far more promising research directions were not shared with the broader community (i.e.: published). I wonder what different reading of that counterfactual there could be other than secret societies that kept their discoveries and research directions to themselves - which we just learned about (since we would otherwise not be refering to the secret societies and their supposed promising research directions).
All pretty straightforward, I would say - both that "misstatement" is hopefully based an overly strict reading of Tao's quote, and that mentioning Tao's background as one of the fields leading practitioners is relevant as well. Again; to make sure: A few counterexamples achieves nothing here. It would need to reach a certain threshold of such counterexamples before we will have to write the history of mathematics; and before Tao actually made a misstatement here.
Simply look up all the many, well -supported and -researched known correlations with ADHD first. In the second step, you can construct the set of all possible correlations, and subtract the well-researched ones if it. What is left is the set of correlations that are either not explained by ADHD (the big majority I would assume) or explained by ADHD, but as-of-yet unknowingly so.
This might be a bit anticlimatic, but clinical psychology is pretty straightforward study design and statistics, and set theory is not that new either, so... no big surprises I am afraid.
That is one of the reasons why I would love to see - reasonably priced - paid services, or even have governments offer them (as in: Source is open, hosting is being paid by the government). Given the role social media, the internet and so on plays today, it might make sense to treat this as a common good.
But that side track aside; I think that privacy respecting, ad free products can be offered for cheap, if their goal is only to finance themselves, development and gain a small margin. And true, network effects / buyin is real, but I also think that the market for ad-free digital spaces/services will continue to grow, as hopefully people become more and more aware of how precious and limited their attention really is.
I did not, but like all the facts you mentioned so far, this is not a surprise at all for me (if that was the intention), since it does not contradict any belief I had about first millenium france. It is an interesting fact, though!
> Anyway, you don't seem to be taking me seriously
That's not the case, and I am sorry if I came over as such; I would not have tried to argue my points if I would not have taken you seriously. English is also not my native language, which might contribute to more subtle points being missed/misscommunicated.
> to be reading as a confrontational argument something that I meant as a friendly and helpful nudge towards digging deeper instead of making assumptions
You see, that's the issue; your nudge would only be helpful if I indeed did not dig appropriately deep yet already; which may or may not be, but instead of verifying it first, you told me things that I either knew already, or that did not address my point at all, which was irritating. I am all for infodumps, everytime, everywhere, love 'em. What I took issue with was that you seemed to assume a lack of knowledge, and decided to nudge, seemingly not considering the possibility that you might have completely missed my point.
Which is, succinctly stated: "Surely we should be able and are able to make educated assumptions about all aspects about anytime anywhere of human history; with the strong assumption that we do not have time machines and are therefore are limitited to guessing (or theorising, if one wants to use the fancy word), not measuring or anything or anything of that sort. It is perfectly understood that it's all guesswork, that might be mightly off regarding how it really was - and if we are lucky, the theory is not totally off".
You seemed to take this as a much stronger claim, as is evidenced by you bringing up exceptions to the "rule" more than once; that would only make sense if you literaly believe that statements such as "most of the books in the old testament were written for with an audience in mind that mostly viewed being the first born son a special, higher social condition" was meant in its absolutes (or with absolute certainty), which it was not. Anectodes, counterexamples and so on are meaningless when it comes to statements of bigger trends. They would only be relevant if they would turn out to be a common occurance, or when the source mentions the homosexuality of a monk in passing, without making a big fuzz about it for example - a possible indication that non-hidden homosexuality amongst monks might have been at least tolerated, and maybe even not-rare in first millenium france in at least that monstery. Or was not an issue to the person who reported that. Or it was a smear campain (not all sources are reliable). And so on and so on... (Note: I don't doubt that a homosexual monk named Flora existed back than, it might be well established that he did. I am just using that fact as an example)
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To wrap up: Infodumps/facts? Heck yeah! Exchange? Yes please. The two of us talking past each other? That's not an exchange, yes. Simply assuming I do not know something instead of verifying it? Heck no, I firmly reject that. If you would have shown me where I was wrong, a nudge would have been appreciated, but as I read it, even now, you simply misunderstood my claims - then, the nudge was missplaced, and came over as patronizing to me.
I think I understood now where it went wrong and what you tried to bring across. Appreciate the facts you droped; I am more the top-down than bottom-up type, but facts like those are interesting to me nonetheless.
I will also stop this thread; in case it helps resolving open ends: "most of the books in the old testament were written/edited/composed for with an audience in mind that mostly viewed being the first born son a special, higher social condition" was and is my intended claim; independent of who the individuals where that wrote these books, of periods where social hierarchies within the intended audiences at time of writting/editing/composition changed, and so on and so for. Yes, that audience encompasses a bit amount of time and space. Still, people who are paid to think and write about this seem to majorily agree with "most of the books in the old testament were written for with an audience in mind that mostly viewed being the first born son a special, higher social condition", if I did not wildly misread the current consensus of academic research. Again, this is a big picture claim; no singular counterexamples or short time periods can change the assumed validity of that statement, only once new sources or new interpretations of old sources indicate a different quantitative historic reality than previously assumed.
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All the best & happy nerding!
The reasoning behind it is that I want to put as much logic as possible into the harness where it is deterministic, controled and fast - My goal is to make agentic coding usable for my purposes even with small local LLM models. Those might botcher generating Prolog queries sometimes, but they might might be able to used my API/interface/whatever reliably (and then the harness does everything else under the hood, including instantiating the Prolog templates and running the queries)
Interesting, thanks for sharing!
I plan to give it my own shot with vibing my own harness; I plan to use https://glean.software/ as the central database for everything code, then for documentation. After that, it could be used for bookkeeping for reasoning in a style similar to what you describe; after all, Angle, the query language of Glean, is a https://en.wikipedia.org/wiki/Datalog with some extras (I don't know which yet), so stuff like onthologies could be queried quite well, I would guess.
In 2015, https://en.wikipedia.org/wiki/AlphaGo came around and latest from there on, AI was associated heavily with NNs, deep learning and so on (but not with the transformer architecture which became popular later, the foundational paper itself was published in 2017: https://en.wikipedia.org/wiki/Attention_Is_All_You_Need).
If you squint a little, the linked project is basically a https://en.wikipedia.org/wiki/A*_search_algorithm with optimized implementation, heuristics and so on. I also think that A* was associated with AI due to its use in path finding in early robotics - But I am not sure!
please don't assume about me, almost all of what you wrote was known to me prior before reading your comment. That information regarding XVII century England for example is something I would have supposed, but did not know for sure; I just knew the equivalent for German society at that time.
> When was that exactly? I believe the oldest extant versions are from around 300 AD. We have a rough idea of when certain books might have been written, but that is open to debate, and strong arguments have been made that put the origin of certain parts of these books centuries apart. Even the composition of a 'canonical' version of these books collections is not really clear before a certain point that is several centuries removed from the time in which we think they might have been originally written.
Yeah, 300 AD would be a sensible starting point. I am strictly talking about ancient Israel, during the time where the old testament was composed, where the exact point in time does not even matter for my claim, because my claim is: "The society that composed the OT was primarily patriarchical during most of the perioud where the OT was written, edited, read, to such a degree that it would be a mistake to pretend it was not." Nobody claims to have a time machine, of course.
Here are some well-reputated sources that strengthen my claim, and are congruent with what I rememember from my own readings of the Code of Hammurabi and the Old Testament way back:
- "Hennie J. Marsman, Women in Ugarit and Israel: Their Social and Religious Position in the Context of the Ancient Near East (Brill, 2003)". Massive comparative study of the ANE, her conclusion: [AI/]She concludes that while women had more rights than often assumed (they could sometimes buy land or engage in trade), the societies were undeniably patriarchal in their legal architecture. High priesthoods, kingships, and tribal elderships were exclusively male domains.[/AI]
- "Hans Jochem Boecker, Law and the Administration of Justice in the Old Testament and Ancient East (1980)", summary: [AI/]Analyzing the biblical Covenant Code, the Babylonian Code of Hammurabi, and Middle Assyrian Laws, Boecker points out that women were legally disadvantaged. For instance, in many ANE legal codes, a woman's sexuality was treated as the property of her father or husband. Boecker writes regarding ANE legal codes: "There cannot either, of course, be any question of the legal equality of men and women"[/AI]
- https://en.wikipedia.org/wiki/Women_in_the_Bible:
"Ancient Near Eastern societies have traditionally been described as patriarchal, and the Bible, as a document written by men, has traditionally been interpreted as patriarchal in its overall views of women.[1]: 9 [2]: 166–167 [3] Marital and inheritance laws in the Bible favor men, and women in the Bible exist under much stricter laws of sexual behavior than men. In ancient biblical times, women were subject to strict laws of purity, both ritual and moral.
Recent scholarship accepts the presence of patriarchy in the Bible, but shows that heterarchy is also present: heterarchy acknowledges that different power structures between people can exist at the same time, that each power structure has its own hierarchical arrangements, and that women had some spheres of power of their own separate from men.[1]: 27 There is evidence of gender balance in the Bible, and there is no attempt in the Bible to portray women as deserving of less because of their "naturally evil" natures."
Heterarchy being present would not render the society non-patriarchical, especially when it comes to matter like the one that started this subthread, in that geneology trees should be viewed through a patriarchical lens, and that it is more likely that those elements are something familiar to the intended audience (which is not some small religious elite, mind you, the opposite, those narratives were written for a deeply religious society, with a scripture-based religion).
> Put simply, what I meant with my previous comment was: we have literally no idea if the people who wrote these supposed genealogies in Exodus were in fact practicing these inheritance legal forms you mentioned.
Of course not, put that way, we know basically nothing about anything and could simply abandon the discipline of academic history.
Scholars have to make and do make educated guesses though, which forms a consensus if enough do agree, and the current consensus is still that ancient israel had a patriarchical legal framework, and for example also that women were economically dependent over large amounts of time. Which is also reflect in a lot of books in the OT, which makes sense if 1) the stories where intended to be relatable and 2) the authors used what they observed around them to describe it. That depends on the genre of course, for prophetic books or lyricals books, there are different rules, but when it comes to the stories that have a narrative core, then this absolutely is something that historians consider when it comes to how the intended audience of the literarical work is structured. Constistently so, across regions and times.
The position that "many instances of primogeniture in the old testament would have been something not deeply known and likely experienced first hand by the typical reader" is pretty hard to defend, as I argued above. That is as close to knowing as we can get without a time machine - but if one does not make such (well-founded) assumptions, then much of the humanities, including hermeneutics, stands on shaky grounds.
Yes, in hindsight it makes sense that a eager LLM would exploit bugs in the kernel itself. I have not read the details yet (but want to!) and assume that it is rather related to the layers directly before or after the type-theory core; i.e. that the AI managed to get a correct typecheck by sidestepping a check during in one of the translation steps somehow, by manipulating the kernels result or by going totally hacker mode and swap implementation/overwrite memory; that is just speculation on my part though, I mainly base if on what I know about Haskell and the https://en.wikipedia.org/wiki/Calculus_of_constructions in general that have not that many constructs, and I would assume the variants used in Rocq and Lean are proven sound.
For experimental features where soundness is not proven, all bets are off IMO, but of course, that does not stop bad actors from engagement knowlingly abusing unsoundness for their own gain. Fortunately, that kind of manipulation is easy to verify when one has access to the codebase; I am would assume that something like lints for experimental features exist, or better even, something like a "sound mode". That does not help against hacking the kernel machinery though.
Concluding notes: - In this particular instance, the Collatz conjecture was appearently chosen on purpose to demonstrate the Kernel bug, from the same thread: "Not that this changes any of the above, but I am informed that the person posting the proof was actually aware that this was a Lean kernel soundness bug, and it was not intended to be taken seriously as a solution to Collatz's problem." - IF the code is made public (and it would be highly suspicious if parts of a proof where hidden), then I would assume this kind of hack is 1) easier to spot that other kinds of hack, since the asset-under-attack is really small and 2) there is not so much incentive to use much time/ingenuity/tokens on finding those hacks (the more are found and fixed, the better of course) 3) and they should be easy to defend against, I would assume; my first thought would be the flag I mentioned above that simply forbids all non-sound features, at the cost of limiting expressive power.
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Edit: I checked, and I think it alleviates my worries in the sense that the bug(s) where not in the type theory or its implementation, but rather the machinery around it. Further context below:
That is the incident description (also linked in the x thread you linked, for future readers: https://infosec.exchange/@0xabad1dea/117002106099986943).
The following is from that thread or links from it:
- "Fixes two things: (1) more strict/nuanced handling for structure/proj interactions, and (2) adds methods for enforcing that generated auxiliary data for inductives, constructors, and recursors are more strictly checked against the assertions in the export file." | That is the fix to the non-Lean-kernel that was mentioned. To me, (2) looks firmly like what I meant with "supporting machinery", regarding (1), I do not know enough to have an opinion about it (i.e. how on what layer those interactions happen(ed)) | https://github.com/ammkrn/nanoda_lib/pull/22
- "For example, pipeline wedges (execute this instruction and the core freezes and never executes another instruction) would not be found by these techniques..." | Power and limits of Lean | https://infosec.exchange/@david_chisnall/117003914014196496
- "@mario @shelldozer it very well may be the most formally correct piece of software we've ever produced, but keep in mind it still has to run on a physical computer it's sharing with less-verified software and is also vulnerable to things like Rowhammer-class ram corruption attacks if one wants to intentionally manipulate it. There's no final escape hatch beyond which a computer can be absolutely guaranteed to always compute the correct answer, especially when someone has a vested interest in getting it to output the wrong answer." | Computer-checked proofs run on computers, which brings its own attack vectors, independent of how well the kernel is written | https://infosec.exchange/@0xabad1dea/117002712346315184
personal, cautios takeaway after reading the details: If you use Lean4 to write proofs, or read that a reputable group of mathematicians publizised a Lean4 proof, you are still highly unlikely to be fooled by a bug, and if Fable 5 decides to exploit a 0day in the core Lean4 machinery, that should still be able to be caught quickly.
With https://en.wikipedia.org/wiki/Lean_(proof_assistant) (and other proof assistants), you need to review only the lines that correspond to the theorem that you want to prove and their types (I am not very experienced when it comes to lean, but I would assume that comes down to a few hundred lines of code, at most). The rest is left to typechecking (which, I would expect many in the field to agree, is at as reliable than your average peer review process in professional mathematics, and likely much more). That's the reason why Lean4 is making such a fuzz now.
That itself is not trivial too, but way easier than reviewing every function and definition used to prove that the theorems have indeed the types they claim.
If one accepts the proof of the https://en.wikipedia.org/wiki/Four_color_theorem, then there should not be new reservations these proofs; except from the maybe new additional failure scenario that the authors (still correctly!) proved theorems that don't state what they think they stated.
To sum it up: There is IMO no domain more suited for using LLMs than mathematical proofs that can be formalized using Lean4. The fact the hype-circle started earlier in software than in maths is due to the difference in monetary incentives I would assume. (Or another, rather radical and not really serious phrasing: "When it comes to Lean4 proofs that typechecks, there is no AI slop" - the theorem being proven might be uninteresting, but the proof itself is very very very very likely to be correct)
> “byte-for-byte equal”
The term itself or its association with LLMs? I would get the latter, if its the former: It's an desirable property to have, I always like seeing people going that far (assuming obviously that they indeed did so, and in the places where it matters!)
This also nudges into how to use it best: By knowing where the "piles" of if training data are (i.e. when it comes to a CLI in rust, I just briefly describe the use cases, and I have a very high confidence the code will work exactly as intended by me since there will be a multitude of examples in the training data), one can predict where the LLM is likely to go wrong an prompt/guard accordingly. This skill grows with domain expertise, and is one of the many reasons LLMs can be (and probably should be) used to outsource busy work, but never understanding and learning. ("never" is a not meant literaly of course - I for one am glad that I do not have to wrap my head around CSS and other frontend topics and go straight to the topics that interest me most)
"Out-Remembering" captures that perfectly, I feel. Also goes nice along with "asking it leading questions" as we know how to do in real live; if you want a person (LLM) to confess (produce output tokens) something, sometimes you do that by leading the interogation (chat, context) to where you think the truth lies.
Agree: Intellectual dishonesty just sucks, period. In any area I think, but the more emotional a topic, the harder so. Changing the axioms of how one views the world when it fits ones point is often either decieving, or the person is not aware of doing it, both options are suboptimal.
Here is the "But" or maybe better, the "but also": What I often observe where atheist + theist conversations go wrong is that the atheist has a preconcived notion of how certain beliefs have a causal relationship with other beliefs, which might not be necessarily true, and the intellectually honest would be to confirm that mental model first before jumping to conclusions. Let me make a, depending on the person, controversial example:
Imagine atheist A and theist T being in an ongoing dialoge, 10m, 15m in, and the topic comes to how Ts faith affect their marriage, what role is does play. T makes the statement that "... and one other thing is that I really like we are both partipating in this beatiful symbol of womand and man being created seperately and for each other ..." - now, what I often observed in real life and online:
A might infer that
- T things that women that are single are less worth or doing it wrong
- T thinks that homosexual couples are less worth or doing it wrong
- Underlying assumption: T thinks less of people that don't try to practise the christian faith
All of that might or might not be true, but by getting angry about their own interpretation of reality rather than asking about it first, the conversation is unlikely to become productive.
Some notes:
- The opposite if of course possible as well, i.e. a T assuming that an A has no morals because they don't believe in God or stuff like that
- In case one wonders how T can be able to believe that the proper thing in Gods eyes is to do X, yet they are at peace with people doing Y, does this not cause cognitive dissonance? Yes, but only under additional assumptions that T might not have all - for example: Society should be structured based on christian values. People should be evaluated on their deeds whether they actually want to work towards God rather than against him. And so on...
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Some might raise the point that it is rare that T voices a strong belief in X, but is compatible with a diverse, inclusive society. To this I counter: I don't care and neither should you! When it comes to me, I will get annoyed fast because I am fine with someone being interested in an exchange between two individuals, but when I am viewed as a representative of some group, then put on your sociology hat and do a survey, I guess. When it comes to you (as in: anyone else): This mindset cements notions that you have about a group - if you do not talk to Ts at all, or be open to their existence, how would you ever be able to correct the (possibly wrong, possibly right) notion that strong conviction and compality with a diverse society is possible?
A very loose translation could be how the "same program", as defined in its lambda calculus form, or as assembly code, is equivalent to dozens of programming languages, all with different goals and ways to reach their goal (declarative vs. imperative, functional vs. OOP, readable for beginners like Python versus APL, ...)
I am playing devils advocate here: Even if it were not divine because atheists happen to be right on that one... even then, the authors and the intended audience of the bible considered it divine - with pretty much the same outcomes when it comes to hermeneutics. That is why I think that both 1) atheists rejecting to do (at least temporary) suspension of disbelief even for the sake of understanding the protagonists, or the authors, or the intension of the text, and 2) christians who just pick whatever forcibly-robbed-of-its-context oneliner fits their particular point view miss out.
Divine or not, this is a work that was composed a long time ago, edited, translated and interpreted by a diverse range of people spanning more than two millenia. Putting in less effort than one would into any other written source only guarantees one thing, the absense of surprises and learnings - if that is the goal, then reading two-three pages and discarding it because its plot seems worse than a C-move is surely the way to success.
That in itself would still make a lot of sense to me though; as far as I know, property and power was mainly transfered through the lines of first born males (so a patriarchy, in the literal sense). If that, social status and so on hinges on who your father, grandfather etc. was, then I think it makes sense for geneology trees to be something important enough to write down, especially in literature that was partially written to capture/produce a peoples cultural identity (i.e. parts of the creation story where written while the jews where forcibly integrated into the babylonian empire, and struggling to keep their own cultural identity. That's another good "use case" for genealogy, I would say.)
Hmm, while I agree that this particular book selection could come of as rather heady, and the author is obviously not doing an exercise in https://en.wikipedia.org/wiki/Plain_English either - but just gauging from the post itself, I find it plausible enough that the auther indeed just loves those books. My red flags: Putting others or other works down, pretending everyone is on the same level of knowledge ("everybody would agree that...", "It's pretty easy to see that...") and in putting the focus onto ones own (percieved or real) abilities. I see nothing wrong in engaging in complex, deep works, but I think some sense of humility should be at least subtly present; If that is not the case over and over again, I either assume that at least some form of signaling is going on, or that the author is genuinely that much out of my leage enough to make it hard for me to connect (I meet people like this in real life, they were often also nice people too, but I could simply not keep up - which is fine, not every crowd is for me and I am not for every crowd...)
On the bible itself: if we are strictly talking about the culture of the western world, I do not think it is controversial claim the bible has been and still is a fundamental element, for better or worse, and often also due to critics and their thoughts. Trying to make sense of the western culture without the bible could be compared to trying to make sense of chinese culture without the writings of Confucius - or a maritine biologist trying to explain the oceanic ecosystem, while working on the hypothesis that geothermic energy cannot interact with oceanic life at all. There will simply be wide, gaping spots in knowledge, and plenty of hacks needed to fix them somewhat.
Since you seem to hold a strong conviction, could you please make more explicit what concretely one would not know / missinterprete regarding the Western culture, not knowing anything about those concepts you listed, but knowing the bible itself back and forth? And to what excent one would need to dive deep into those concepts?
Or in other words: What fundamental concepts in Western culture will we understand if we take you on your word and spend time into understanding those concepts?
Bullet points / pointers would be enough already!
The core pattern was that the Proxy, which was under Nil and above all other Objects regarding inheritance I think.
It re-implemented `doesNotUnterstand:` by: 1) First loading the actual object from the persistent storage and 2) sending the not understood message to the actual loaded object (which might be able to answer the message instead of calling `doesNotUnderstand:` for every message, like Proxy did.
There where if course optimisations and so on, but that was the gist of it.
What I really like about this system was that it was completely transparent to the sender of the message whether they were talking to a proxy, or the already-loaded object, all while being robust, easy to maintain and so ob. Dealing with collections was tricky though (how much to load at once? what about searching for a particular object?...), and would have been aswell for deeply nested object (which they successfully avoided though because as a SaaS-company, they could model the data exactly to their needs).