ogogmad

I think we should create a masculine-sounding word for "nurse", like "(patient/care) (guardian/maintainer/technician)". Nursing still sounds like breastfeeding (check the etymology!), which I'd reckon sounds offputting to most men.

Neologisms are cringe, but demeaning men is as well.

Wow. That went over the heads of both a Harvard student and an Atlantic journalist.

username checks out

The Jewish Talmud uses Epicurus's name as a term meaning "heretic".

Once you have a bicameral syntax*, is there much point left in formal language theory? For instance, why would you still need complicated notions like LR(k) grammars (which Wikipedia confuses with LR(k) parsers)? I ask out of genuine confusion: I've been reading about formal grammars, and have even added to Wikipedia - but I'm still puzzled as to why PL designers might choose to have hard-to-parse syntaxes. Why don't people instead adopt an intermediate syntax like Rhombus's shrubbery notation†?

* - https://parentheticallyspeaking.org/articles/bicameral-not-h...

† - https://docs.racket-lang.org/shrubbery/index.html?fam=Rhombu...

I think BC's features are equivalent to:

- Python's native integer handling, which already has no size limit.

- PLUS part of the Decimal module in Python's stdlib: BC's floats are DECIMAL by default, not binary.

- PLUS an implementation of Bessel's J function, while neglecting Bessel's K.

- Some features for base conversion using `ibase` and `obase`. So, I suppose you can output numbers to base 60. [EDIT: Correction from earlier: ibase is allowed to be at most 16, while POSIX allows for the maximum value of obase to be at least 99, which therefore does allow for formatting output to base 60.]

Good point. But what if `i` does not divide `ans` evenly? I suppose you could use floats and then round.

  me@localhost:~> bc
  d=1; for(i=21; i < 41; i++){d *= i;}; print d; print "\n";
  335367096786357081410764800000
  n = 1; for(i = 1; i < 21; i++){n *= i;}; print n; print "\n";
  2432902008176640000
  d/n;
  137846528820

* - What it does contain is sine, cosine, exponential, log, arctan, and Bessel J (?!?!?!?!)

This is one of the most interesting comments I've read on this website.

See the recent breakthrough "Erdos Problem 1196" which experts couldn't solve for 60 years until ChatGPT Pro did. ChatGPT's key idea was the use of the "Von Mangolt function" which it showed could finally settle the problem. Terry Tao has condensed the AI's proof to around a page. The problem was well-known to experts (in the field of number theory) but it was a Large Language Model that ultimately solved it - which it did without human help!

Maybe it's a good idea for SWEs to consider using LLMs to train themselves into new careers -- just in case.

Most other "knowledge" professions -- by which I mean teaching, programming, some engineering, and the arts -- are even further along into obsolescence. That said, you can still use the knowledge gained in a knowledge profession to convert into a more hands-on profession. We might have a bit longer before humanoid robots destroy all hands-on job opportunities as well. Once that happens, every person will be equally poor and destitute.

That's a provocation of sorts, maybe. However, I'm curious how Israel's invasion was supposed to stop that. Either they would occupy part of Lebanon, but open up their soldiers to attacks from irregulars, which doesn't seem any better for Israel. Or, they would expel tens of thousands of people AND occupy parts of Lebanon, which would still expose the Israeli occupiers to attacks from just outside the new border.

If Israel was going to kill tens of thousands of people, it had an obligation to have a plan which wasn't completely stupid. I don't see what WASN'T stupid about it.

Hezbollah was formed after Israel's 1982 invasion of Lebanon, which killed 17k+ people, mostly civilians, and which Israeli historian Ilan Pappé said was mainly unprovoked (see below). Israel's explanation for why they decided to risk killing tens of thousands of non-Israelis - which is ultimately what their invasion did - was highly dishonest.

The reason for Israel's invasion of Lebanon in 1982:

Israel said it invaded Lebanon in June 1982 to stop PLO attacks from southern Lebanon and push Palestinian fighters far enough north to protect northern Israel.† The immediate trigger was the attempted assassination of Israel’s ambassador in London, Shlomo Argov. But that attack was carried out by the Abu Nidal group (based in Iraq), not the PLO, and Israel used it as the opening for a much broader war: destroying the PLO’s power in Lebanon, besieging Beirut, weakening Syrian influence, and trying to install a friendly Lebanese government. So, bluntly: there was a real security problem, but the 1982 invasion was also a war of choice and political engineering, not just self-defense.

† Right before the June 1982 invasion, the "they were shelling Galilee" line is weak: even the IDF says that after the July 1981 Habib ceasefire, "from July 1981 to June 1982, the Israeli-Lebanese border was quiet."

Jews

What does this word mean in the year 2026?

I don’t think "Spectre doesn’t work across process boundaries" is correct as stated; cross-process and cross-security-domain Spectre attacks have been demonstrated. But I agree that "a malicious app can trivially Spectre its way into an arbitrary banking app on a patched iPhone" is a much stronger claim, and I’m not aware of a public demonstration of that exact attack. My point is only that process isolation alone is not, in principle, a complete answer to Spectre-class attacks.

This reminds me of crypto wallets. I also dispute mike_hearn 's:

Smartphone HW attestation is better in every way

They're still prone to side-channel attacks like SPECTRE. Crypto wallets are practically immune because they're air-gapped.

[edit] I just realised that's Mike Hearn of early BTC fame. I suppose he would know what a crypto wallet is.

Can you show me examples where locking down an OS has prevented fraud in banking?

This is a non-sensical remark because it's impossible to "prove" a counterfactual. I find stuff like this incredibly annoying - please don't say this.

ὦ Ευρώπη, this would kick off an arms race. μολὼν λαβέ!

Whenever you solve any hard problem, you start off by finding a complicated solution, which you then scale down to a simpler solution.

LLMs are a "complicated solution" in the sense that they're expensive. Once you know what they're capable of, you can scale them down to something less expensive. There's usually a way.

Also, an important advantage of LLMs over other approaches is that it's easy to improve them by finding better ways of prompting them. Those prompting strategies can then get hard-coded into the models to make them more efficient. Rinse and repeat. Similarly, you can produce curated data to make them better in certain areas like programming or mathematics.

ChaCha20 got discovered using a computer search testing out resistance to certain attacks. Hence, the architecture came first and then the parameters came next. Any link with NN gradient descent? It would likely be an abstract one.

It's more like a situation where you should avoid doing anything. A player in zugzwang who does anything, loses. In chess, it's a position where a player would skip their turn if that option was available, but the rules forbid it, so they're forced to make a move that hurts them.

[edit: Edited to make it clearer that there are cases where only one player is in zugzwang]

Iran has said that it's working on nuclear energy, not a bomb. Their pope-level religious leader said it was haram to have nuclear weapons. I know you can't necessarily trust Iran's word, but can you trust Israel's?

Originally, I did not have any content from an LLM. I still got 2 downvotes. I was saying "BRB, checking the book PDF using ChatGPT Pro ($200 per month)".

It's also more informative because Pro costs $200 per month. Plus costs $20.

An earlier version of GPT Pro solved a well-studied 60-year old conjecture on primitive sets, without human guidance. Short of peer review, which takes a long time, I reckon this is the best way to get an assessment of the author's book, especially compared to HN commenters' vibes.

I'm not sure why I got 2 downvotes for this.

There are non-computational interpretations of intuitionistic logic too, like every single thing mentioned on this page: https://ncatlab.org/nlab/show/synthetic+mathematics

I think stuff like "synthetic topology", "synthetic differential geometry", "synthetic computability theory", "synthetic algebraic geometry" are the most promising applications at the moment.

It can also find commonalities between different abstract areas of maths, since there are a lot of exotic interpretations of intuitionistic logic, and doing mathematics within intuitionistic logic allows one to prove results which are true in all these interpretations simultaneously.

I'm not sure if intuitionism has a "killer app" yet, but you could say the same about every piece of theory ever, at least over its initial period of development. I think the broad lesson is that the rules of logic are a "coordinate system" for doing mathematics, and changing the rules of logic is like changing to a different coordinate system, which might make certain things easier. In some areas of maths, like modern Algebraic Geometry, the standard rules of logic might be why the area is borderline impenetrable.

Proposing

I think GIT is a negative answer to a problem originally posed by David Hilbert. It was not proposed by Goedel originally. I think Goedel's main new idea was (i) inventing Goedel numbering (ii) using Goedel numbering to show that provability from a finite FOL signature, and a single FOL formula, is reducible to an equation involving primitive recursive functions (iii) devising a method to translate FOL statements about arbitrary primitive recursive functions into statements about only the two primitive recursive functions + and ×.

Later work establishing the field of computability theory (or "recursive function theory" as it was then known) generalised the insights (i) and (ii). In light of that, Goedel's only now-relevant contribution is (iii).

When will LLM folks realize that automated theorem provers have existed for decades

This is very misinformed. Automated theorem proving was, sadly, mostly a disappointment until LLMs and other Machine Learning techniques came along. Nothing like the article's result was remotely within reach.

GDP per capita lower than Poland

now poorer than every state in America

You've confused the mean with the median. GDP Per Capita is not a measure of how well-off the people in a country are.

American states have a lot more income inequality than the UK does, which (due to positive "non-parametric skewness", I think) pulls their GDP Per Capita upwards.

"Even more, this coproduct can be thought of as an instance of a dependent pair indexed by a finite set" - I know what the individual terms mean, but I don't get what this is saying.

Use a VPN or Tor browser?

The announcement says:

This was solved by GPT-5.4 Pro (prompted by Price)

See the discussion here: https://www.erdosproblems.com/forum/thread/1196