aureate

The Collatz conjecture is a question about positive integers, so enumerating and checking all the possible counterexamples is trivial, albeit requiring infinite time. It has been verified up to 2.36×10^21. It could turn out to be false, but nobody's going to find a counterexample as surprisingly simple as the one Claude found for the Jacobian conjecture, which would be like finding a Collatz counterexample in the first few billion integers or so.

... Or would it? The Jacobian counterexample seems like an especially simple, near-trivial integer-coefficient polynomial, but I haven't seen any thorough analysis of how "hard" it would have been to find by brute force, and I haven't seen Claude's reasoning.

It's not a great way of inferring software quality, but I think the numbers for both Bun and Claude Code are pretty bad.

cpython has ~7,000 open issues, but ~70,000 closed ones, a 1:10 ratio. Bun's ratio is above 1:2.5, while for Claude Code it's slightly over 1:6.

Much more importantly, though, Bun's oldest issue is from Sep 2021, while Claude Code's is Feb 2025. cpython's oldest issue dates from June 2000 (presumably migrated from an older tracker). Claude Code has very nearly the same total number of issues (open + closed) as cpython at around 77,000, but Claude Code has done it in a year an a half whereas cpython has taken 26 years to get there.

It's a good comparison to pick, as it can't be explained by popularity. For all the real-world use Claude Code sees, it's nowhere near what cpython sees, even over the year and a half in question. Bun, meanwhile, is hitting these numbers while not even being the mainstream choice for what it does (node still holds that crown afaik).

The port of Bun, which has >5000 open github issues, is used in Claude Code, which has >11000 open github issues. Do people use Bun in things that are expected to work reliably? Have any such projects tried the upgrade yet?

Surely that outcome requires that the capital retains its value/usefulness. One advantage of crypto and AI is that they can utilise massively parallel computational resources (and don't have tight latency requirements, like gaming) in an age where we've hit the physical limits of sequential computation.

If the "higher capital" that results from an AI boom consists of massively parallel computational resources that currently can only be fully utilised by AI and crypto, and if those things turn out to be a bust, the "higher capital" only has value if we find something else to do with it.

Maybe we will...

Am I right in thinking the Bun rewrite hasn't actually been released yet? There was a big kerfuffle when it was merged to master and people seemed to be behaving like that meant it was all done and dusted (as does this article), but it looks like the last release is still 1.3.14 from April so presumably general users are still on the Zig version? Is there a timeline for release?

Yes, I think I understand it (or am at least on the way to understanding it) now. Thanks!

Ah, interesting. I see "homogeneous coordinates" are covered later in the book I've just started reading (Projective Geometry, Coxeter) as a way of representing projective space. I think that's the link I couldn't see.

Thanks!

Tiny nit / check of my understanding:

It was already widely understood that projective geometry allowed one to represent rotations and translations in R^3 with a single linear operator on R^4.

I think it's projection operators (in linear algebra) that allow one to do that, not projective geometry [1]. The latter, AIUI, studies projective spaces and projective transformations on them (which differ from vector spaces and their transformations by including "points at infinity"), contains no concepts of length or angle (and therefore no equivalent of translations and rotations) and is in some sense "geometry with only the straightedge, no compass".

Curious if I'm just missing something there, though. I'm no expert on any of this.

[1] https://en.wikipedia.org/wiki/Projective_geometry

Lovely game! Takes a bit of fiddling to get the hang of it, but so do most puzzles worth doing. The instructions are clear, the presentation is great and I like the decision to prioritise a fun game over representing real Gerrymandering accurately. It looks like a lot of thought has gone into this.

See the paragraph beginning "Yet terms and conditions also apply."

Assuming your two uses of "model" have the same meaning, I'm mad that people are seriously suggesting we scrap representative democracy in favour of government by LLM output.

They're not plausible or internally consistent for reasons in my edit. It's not the Fermi "paradox" that rules them out. There could easily be interstellar civilisations in the Milky Way that we haven't observed. They just wouldn't work anything like the ones in Star (Wars|Trek).

It doesn't though.

The galaxy is ~100,000 light years across and likely to contain at least 100 billion planets, of which we've only just developed the ability to even detect the existence of ones substantially closer than 1000 light years without assistance from gravitational lensing, i.e. in less than a millionth of the volume of the galaxy.

AFAIK (my knowledge is not encyclopedic), the most energetic event in the Star Wars universe is the Death Star destroying planets. Novae are many orders of magnitude more energetic than that and are estimated to happen 80 or so times a year in the Milky Way. We manage to detect 3-4 of those, generally well after the fact, and AFAIK have only observed one happen live once. The Death Star could go on a shooting spree and we'd be vanishingly unlikely to notice.

And as far as electromagnetic broadcasts are concerned, their intensity falls off with the square of distance unless they are directed. Unless ET were to point a hyper-powerful (but hopefully not Death Star level) laser directly at us, we'd be extremely unlikely to have detected their broadcasts by now.

Space is really, really, really big. Big enough by far to make "if aliens are common why haven't we seen them yet?" a question with a trivial, obvious answer. It's the same answer a kid who's just had their first swim in the sea gets when they ask "why weren't there any whales?"

Edit: There are other things that rule out Stars Wars and Star Trek though, ofc. The speed of light isn't really a speed limit (or a speed, as such) and special relativity doesn't prevent you from reaching the stars in your lifetime or even from hopping to another star in a second, but the different time spans experienced by people on different world lines aren't optional.

The Fermi paradox isn't evidence for anything except space being big.

Even if it was a supply chain attack, which isn't known, the agent was in the "build trust" phase. It was supposed to be doing helpful things, even if the end goal was nefarious, but instead it was "reassigning bugs, fabricating unhelpful replies to bugs, and even persuading maintainers to merge questionable code into the Anaconda installer". Running amok seems an apt description even from the viewpoint of the putative attacker!

Surprisingly enough, Turing Award winner and father of reinforcement learning Richard Sutton knows perfectly well what he's talking about. The whole talk is about the need to have the ability to test novel outputs against reality and iterate to find ones that are good. This is exactly what Claude Code, the agent framework, adds to Claude, the LLM, to allow it to find novel coding solutions that actually work.

Which is probably why Schwartz himself doesn't call them origami tori. He calls them paper tori. Here's the paper: https://arxiv.org/abs/2507.14998.

Assume LLMs have conscious experiences. Take a session with an LLM. A prompt is fed to the LLM. It generates some text. Another input is fed in, comprising the previous prompt, the generated text and a new prompt. The model generates some more text. This continues for a while and the session concludes.

Some questions:

1. Let's say we perform the exact same experiment, running the same program on the same computer with the same inputs and the same random seed. The same outputs are produced. The session is byte for byte identical in all the inputs, outputs and internal states. Is the conscious experience of the LLM here the same? If so, in what sense is it the same? Is it a similarity of two separate experiences or is it the same actual experience?

2. Now let's say the program that runs this LLM is rewritten from scratch and run on a different machine. The software and hardware are different but the weights are the same and all the inference calculations produce identical numbers. Is the conscious experience the same? In which sense?

3. Now say the weights are changed but the tokens generated for this particular session don't change. Same conscious experience?

4. Lastly, consider the original experiment. Did the LLM have a conscious experience corresponding to that first prompt and its response? Was that distinct from its conscious experience of the second prompt? Was the first experience then re-experienced every time the first prompt was fed back in as part of the later prompting steps? If so, what about the text of its own that it previously generated and is now fed back into it. Does this generate a conscious experience of its own?

And a further question - a dichotomy:

A. If the answer to 1 above is that the conscious experience is the same in the true identity sense - i.e. only one conscious experience is had, not a separate one in each run, does that imply that the conscious experience exists independently of any particular realisation of this experiment? If running this experiment N times results in exactly 1 conscious experience, is that still true if N=0?

B. On the other hand, if the two experiences are distinct (however similar they may be), how does that fit with the answer to question 4? A single consciousness experiencing the whole conversation in question 4 would seem at odds with the conscious experiences in question 1 being distinct, so doesn't this imply there is no conscious experience of the whole "conversation", but rather a separate conscious experience of each round of feed-all-the-prompts-and-outputs-back-in?

My own response to all of the above is "mu" - unask the question. It is ill-posed, sound-of-one-hand-clapping stuff. I think the questions assume properties that conscious experience simply doesn't have (particularly, the ability to perfectly reproduce the circumstances in which they arise), and that the questions simply don't make any sense in relation to actual conscious experience.

However, that way of thinking follows from a particular world view that many here don't share. I'm curious what thoughts people who take seriously the idea of LLM (or algorithmic, in general) consciousness have on the above questions.