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You're right, I either misread your comment or got confused with a different comment or something.

But I do think the Mitsui point is relevant; in particular, the claim that the citation is supposed to back up is:

"Moreover, even assuming that Heppner intended to share these communications with his counsel and eventually did so, it is black-letter law that non-privileged communications are not somehow alchemically changed into privileged ones upon being shared with counsel."

But the distinction Mitsui is actually making is rather different: between communications "for the purpose of obtaining or rendering legal advice" and not; that's at best orthogonal to Rakoff's claim; and the other two cases I mentioned pretty explicitly make the opposite case: documents written with intent to share with counsel, and then actually shared with counsel seeking legal advice, are in fact covered under privilege. The assumption being that the documents are not "pre-existing", they're created as part of the process of communicating with counsel.

But yes, I agree that the "third-party" point separately undermines privilege in many contexts.

no, Heppner's attorney-client privilege argument wasn't that the conversation was privileged inherently because it was legal consultation with Claude, but that it was privileged as personal notes made in preparation for consultation with counsel and then actually communicated to counsel, see Ford-Bey v. Professional Anesthesia Services and Greyhound Lines, Inc. v. Viad Corp.

Rakoff makes two arguments against this:

- privilege was broken because Claude/Anthropic is a third party; but I don't think he successfully distinguishes Claude from say Google Docs/Translate/Gmail in this regard (he just notes that Google Docs isn't usually claimed to confer privilege on its own; but this is not the claim being made about Claude either); and see NYSBA ethics rules 820 and 842)

- he quotes Gould v Mitsui: documents do not "acquire protection merely because they were transferred" to counsel; but that same case says they do acquire protection if communicated "for the purpose of obtaining or rendering legal advice"

The ruling explicitly overrules Shih, thus making exactly that argument:

Shih, of course, is not binding on this Court, and this Court respectfully disagrees with its holding. As relevant here, the court in Shih principally concluded that the work product doctrine is not limited to materials prepared by or at the direction of an attorney. Id. But that conclusion undermines the policy animating the work product doctrine, which, as one of the cases cited in Shih explains, is "to preserve a zone of privacy in which a lawyer can prepare and develop legal theories and strategy 'with an eye toward litigation.'"

The overruling of both Shih and the standards laid out in NYSBA ethics opinions 820/842 (and various other state bar associations, and the fact that apparently no one tried to challenge those in court until AI) without real discussion of implications seems rather unusual; and that's a rather charitable reading to avoid the crazier "Claude is a person" framing

also, he quotes Gould v Mitsui: documents do not "acquire protection merely because they were transferred" to counsel; but that same case says they do acquire protection if communicated "for the purpose of obtaining or rendering legal advice"

I don't know much about the Kingdom of Jerusalem per se, but even today many Jews say prayers specifically written after the Crusades https://en.wikipedia.org/wiki/Rhineland_massacres So the symbols of "hope and triumph of establishing Christianity in the Holy Land" do not evoke particularly positive connotations, even aside from the usual modern opposition to that particular mission.

Ah, sorry. I have a (bad?) habit of using newlines as sentence separator in informal contexts, and HN likes to eat newlines if they're not doubled. I'd edit but it's too late now.

eh this "plagiarism" framing is overreaching there were two proofs in the paper: countability of algebraic numbers and uncountability of reals countability of algebraic numbers is a rather trivial induction on countability of rationals/pairs of numbers, which Cantor already knew about Cantor himself did prove uncountability of real numbers; Dedekind just helped him clean the proof up to me it seems like Dedekind's assistance was the kind of thing that might merit an acknowledgement, or possibly even joint authorship if subspecialty norms are generous, but far from a novel contribution on its own; unlike the uncountability of reals which was genuinely important and nontrivial. Dedekind, like Cantor, had other very important contributions, but certainly no claim on what Cantor is known for; and the context with Kronecker meant that this would prevent the work from ever being published. Also, this article doesn't actually show Dedekind was specifically upset by the "plagiarism", there may be any number of other reasons they may have stopped corresponding; and Dedekind's "hope this is useful" comment to Cantor can be read as permission to use it for his purposes

I think there are much better argument for mandatory jury duty, like the fact that it's an inherent and explicit part of the preexisting Constitution, and that was not explicitly repealed nor (as far as I know) considered.

But the Court chose not to use those arguments, perhaps because they are less absolute and don't apply as cleanly to the draft.

Personally, I think that jury duty as it is today (no real pay, sometimes very long trials, "hardship" completely at the discretion of the judge) is actually a substantive violation of the principles of liberty that the 13th Amendment (along with the rest of the Constitution, notably the 5th Amendment) was meant to protect; (though I myself would likely enjoy actually being on a jury, and am fortunate that I can afford it/my work would likely pay).

And I don't think it would've been crazy to require an Amendment to institute a compulsory military draft, or better yet interpret the 13th Amendment to allow the draft (and jury duty) on narrower grounds but use it to better protect soldiers against various abuses inherent in the current military power structure and lack of exit option.

I do think that mandatory road duty is about as direct a violation of the purpose of the 13th Amendment as anything else the state could do. I think the (explicit) argument that the takings and due process clauses protect your money but not your labor is patently ridiculous.

Yeah, I'm saying the Supreme Court is obviously wrong to allow it on the grounds that they do

So, like compulsory jury duty and the draft, this would be directly against the 13th Amendment.

Then again, according to the Supreme Court, even forced, unpaid road duty (chain gangs anyone?) is an inherent power of the government, so maybe this is ok.

In view of ancient usage and the unanimity of judicial opinion, it must be taken as settled that, unless restrained by some constitutional limitation, a state has inherent power to require every able-bodied man within its jurisdiction to labor for a reasonable time on public roads near his residence without direct compensation.

https://supreme.justia.com/cases/federal/us/240/328/

(spoiler alert: according to the ruling, the US Constitution, including Amendments, does not limit this power; and this is in fact cited as justification for upholding the draft)

integers exist

Mostly as an abstraction on top of a continuous wavefunction/quantum field

Spacetime ends up being discretizable

As far as I know this is speculative and usually assumed by physicists to be false; it's definitely not a required feature of quantum mechanics per se, and as far as I know not of any other well-accepted theory.

Note that in general, a physical instantiation of an undecidable problem must be specified/realized to _infinite_ precision; that is, for any such system S, and for any eps>0, there is a perturbation p with distance d<eps (eg, move a billiard ball an arbitrarily small amount) that is provable; this is analogous to the fact that existence of solutions to Diophantine equations is undecidable, but the theory of real closed fields is decidable, which means that the only undecidable case is when an equation has solutions _arbitrarily close_ to integers, but never quite an integer. I am not a physicist, but I don't believe any physics actually cares about infinitely-precise setups.

For what it's worth, while I find this "obvious" as well, given the Church-Turing Thesis etc, Nobel Prize-winning physicist and philosopher Roger Penrose famously does think that human brains require access to non-computable insights to do math.

Godel's proof relies on the self-referential nature of the Godel sentence; without that, his theorem does not apply. Generally you need arithmetic, but also (something equivalently expressive to) universal quantification. Physical theories do not need to include that.

Note Godel's proof is mechanically exactly analogous to Turing's proof of the undecidability of the halting problem, because ultimately it's the same thing (Curry-Howard, Prolog, and all that). So you can bypass arithmetic, but you can't really bypass self-reference; just like programming languages need some looping or recursion (or equivalent expressiveness) to be Turing-complete, mathematical theories need universal quantification to be subject to Godel's Incompleteness Theorem.

Of course, you can have a physical theory that _is_ Turing-complete, say the Newtonian billiard ball model (and, y'know, we can build computers); but that doesn't mean the theory will necessarily tell you, as a static, measureable physical fact, whether a particular physical process (say, an n-body system) will ever halt or loop, or go on forever with ever-increasing complexity; so you could (in principle, in Newtonian mechanics) build some (mechanical!) physical system that simulates the Goldbach conjecture, or looks for solutions to an arbitrary Diophantine equation, but if there are no integer solutions you'll never actually be able to show it; the theory is incomplete in the mathematical sense, but just as complete a description of reality's rules.

(dupe: https://news.ycombinator.com/item?id=45762892 )

And again, almost every statement in this paper is wrong, including the main claim

Almost every statement in this paper is wrong.

The central claim in particular is not proven because a physical theory P need not be able to express statements like "there exists a number G, which, when interpreted as the text of a theory T, essentially states that the theory T itself is unprovable in the broader physical theory P" as an empirical physical fact.

More general analytic proof: https://math.stackexchange.com/questions/2268833/why-is-frac...

Heh, apparently ChatGPT gets touchy when you explore creative ways to make earth less inhabitable than Mars, especially around pathogens and grey goo

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I'm not an expert/lawyer, but this does seem to indicate that the situation is a bit more complicated than either "pernicious myth" or "probably illegal" in general (but much closer to toast0's understanding); my interpretation is that you can either avoid an 80% threshold of "disparate impact" or you can in theory formally validate that a particular test measures/predicts performance at a particular job; that all sounds compatible with "companies do it in the open, but very few, and you can easily get in trouble for doing it wrong" https://www.law.cornell.edu/cfr/text/29/1607.15

Curious if people here have used Glean, if they can share impressions, pricing, or anything else

I read this paper some 10 years ago, and have always wondered whether these ideas are implemented in industry. I know people use Denotational Semantics in academia, but eg I want an actual language that can encode the language-independent "meaning" of both a c++ template library and a Python program in a composable way, and also express and prove refinement relations between different specifications and implementations.

You can implement the "nonstandard arithmetic" suggestion using bignum integers backed by an infinite tape (subject to availability of said infinite tape). Finite integers have a Halt symbol, non-finite ones simply don't. Arithmetic on non-finite integers is not computable, but individual digits generally are. Any finite integer is computably less than any non-finite integer. "Less than" between two non-finite integers is not generally computable, therefore not defined. "Not equals" is semidecidable, so generally all "not equals" statements between two non-finite integers are defined, but "equals" mostly isn't. printf on a non-finite integer will simply print out infinite digits one by one. You can also define and generate non-finite integers from any computable sequence of integers. size(void*) can be defined as eg 1111111... (Repeating forever, in an arbitrary base).

If you demand that you can always computably do arithmetic on size_t's, allow storing arbitrary arithmetic or even logical expressions in your bignum integers, and call those bignum as well. Define "less than" on infinite integers based on "alphabetical" order. Then the only thing that is non-computable is (in)equality between two expressions for which non-finite-ness is unprovable under First order logic. Given Godel's Completeness (note, not Incompleteness) Theorem, that should probably meet the definition of a C implementation, though I haven't read the standard.

Have you tried a 1-d kd tree, that at each subinterval keeps track of the largest gap? Should be fairly simple to keep this updated and effectively match/generalize your "coalescing" logic.

Indeed, transformers are just another universal approximator; it doesn't matter exactly what a particular attention head does, whether it's operating as a continuous associative array or kernel smoothing, or simulating a higher-dimensional vector space which exhibits monosemanticity. What OP misses is that in addition to being universal, all that matters is that it's efficiently trainable, and in particular on GPUs and in parallel; that is what makes it better than LZ or any other universal approximator; all else is secondary. If you can make LZ (or anything else) work significantly more efficiently than transformers on GPUs, you can found the next OpenAI and be a billionaire.

You're right, I was thinking of this in the context of an English-speaking country/institution (mostly since I do often see this demand in those contexts as well; to be clear, I think it's a reasonable request, but not a reasonable demand or legal requirement). In the context of a Belgian customer of a Belgian bank it's definitely more surprising; but I also wouldn't categorize it as "inaccurate personal information", but awkward transliteration to a foreign alphabet; as you said, that may be strange and possibly even run afoul of national language laws, but I wouldn't use GDPR against it

[Korean] has as much relevance in Israel as English has in Belgium

Legally maybe, but certainly not demographically/culturally; I mean, certainly there is a difference in the expected probability of being understood, especially given the highly-overlapping character sets

relatively common

I'd love to see some links, all I see used in practice (including in the OP blog post) is semantic search and a bit of clustering

adding a pair of glasses

Actually that (and generally all the SD/VAE stuff) is a great example of the kind of thing I was thinking of, though I have yet to see that concept being used together with a vector database; generally all the user-facing stuff I've seen fits it into the standard "train a model, then do inference" workflow, in contrast to something like semantic search which more obviously focuses on the embeddings themselves

First and third being identical

Definitely related, but I make the distinction between projection/sorting along an axis vs constructing a new vector by addition/subtraction

Manipulate within gaussian space, then return to target space

This is definitely along the lines of what I had in mind, any example of this being used in practice?

Embedding is an overloaded word

Yeah I'm using the term somewhat loosely and broadly here, as basically "a vector in a real vector space where distance represents some notion of semantic similarity"

People do things like SVMs

Who?

Has anyone actually used embeddings for anything other than Approximate Nearest Neighbor and clustering?

Some speculative possibilities that come to mind:

- projection, indexing and sorting on arbitrary axes (eg "hot minus cold", "happy minus sad", "scifi minus realism", "literary minus commercial")

- SVM-style classification in Embeddings space

- word2vec-style reasoning (woman-man+king=queen)

- directly training embeddings (ie, not just taking a layer off an LLM); I know people use contrastive training methods, but I'd expect that other methods might be worth exploring, eg you could train embeddings together with neural nets representing functions, generate functional equations, and calculate MSE loss

But really, I'm just surprised that it seems to be so focused on semantic search, to the exclusion of anything else... Surely there are other interesting applications?

I never really understood the insistence on diacritics. My name is properly written in Hebrew characters, and contains sounds not present in the English language. Many more people use CJK, Cyrillic, Arabic, or other characters. The writing system in use by many people and companies for the English language does not support any of these characters, and nor does it support diacritics. Some variants (in particular, see airlines) use only capital letters, with no spaces or dashes; this also seems reasonable to me (even when my name is somewhat mangled as a result). So just like a CJK/Cyrillic/Semitic name has to be roughly transliterated into Latin characters, and inevitably pronounced differently than in its origin language, why shouldn't the same be true for names with diacritics? Saying that the One True International Alphabet is latin-1 or whatever is rather arbitrary. And no, the solution isn't to give up on cross-cultural communication, nor to require that every human learn all the characters in Unicode.

Robbing a bank is more likely to set you back substantially (infinitely?) via a stay in prison, which is not likely to average out in your favor. But in some cases, ethics aside, it could conceivably be the rational choice, and that doesn't seem so surprising.

That formula assumes that you always have investment opportunities with multiplicative returns. This is not true in practice for many people.

To illustrate the difference, assume the following (simplistic) model: an agent has an income of $1000/period, minimum/subsistence spending of $998/period, and power-law "emergencies" that bankrupt you when you cannot afford to pay. Then the question is: what is more unlikely, a long-enough time without being bankrupted that you accumulate $10M (or even $100k), or winning a $10M jackpot?