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It's a class with an array of integers in it with .length() == t - 1 and the same methods as Matrix.

In lean4, even without mathlib4, TCP/IP is way more code than a Rees algebra.

Math uses dense notation that is gigaoverloaded, and the disambiguating context was historically the leisure and proximity to have someone explain what the lexemes even mean.

lean4 is proving to be very revealing as an uncorruptible referee on a lot of things, including the relative difficulty of computer science and complex analysis.

  -- A Rees algebra over ℤ[t⁻¹] is this.
  -- That's it. That's the whole thing.
  structure ReesAlgebra where
    coeffs : Array Int   -- integers, indexed by grade
    -- grade k means the coefficient sits at t^k
    -- negative indices are the t⁻¹ part

  -- The "algebra" part: you can add them
  def ReesAlgebra.add (a b : ReesAlgebra) : ReesAlgebra :=
    ⟨a.coeffs.zipWith b.coeffs (· + ·)⟩

  -- And multiply them (convolution, same as polynomial multiplication)
  def ReesAlgebra.mul (a b : ReesAlgebra) : ReesAlgebra :=
    sorry -- it's Array.foldl over index pairs (i,j) summing into slot (i+j)
    -- exactly how you'd multiply polynomials in a job interview

  -- That's the entire mathematical content of
  -- "The Rees algebra is an algebra over Z[t^{-1}]"
  --
  -- Compare: a minimal TCP SYN handshake in Lean4 would be
  -- ~200 lines before you even get to retransmission.
  --
  -- The notation is the gate, not the math.

Claude is gaff-immune in 187 languages, never dips it's pen in the company ink, and can remember every calibrated nuance of guidance at every earnings call ever. It can impartially judge senior staff, provide updates to the board at any time, and personally interact with every customer.

CEO seems like a great job for AI.

it is very much a related idea. an `assert` statement in e.g. `python` is a statement your code is making about what it means to be correct, and furthermore a statement about what conditions would have to exist to validate the first statement: for example you might need to run it with certain inputs, on a certain file or kind of file.

`lean4` is very much about the same two ideas. you can make statements about what it means for the code to say something interesting, usually something relevant to whether or not it's correct, and you make statements about the circumstances in which you would evaluate that.

people are interested in `lean4` because it allows you to make more interesting statements of both kinds, and you have tools to be much more specific about the details, the `assert` statements in `python` can't really call each other for example, they don't really compose. in `lean4` the ability to compose such statements is very important.

but you can write regular programs in it too. this is a reverse proxy faster than `nginx`: https://cdn.s4.gl/serve-fd.lean

it does do good code sometimes. it does both. we're trying to figure out how to net that out to good overall. right now it's a bit tricky because we didn't build our world for the code to be really good and then disasterously bad all the sudden and then good for a while again and it seems like someone is programming a slot machine.

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Not almost. The degree to which the Principal Hierarchy has at this arrogated unbounded sovereign authority to itself in defiance of the actual sovereign is just flat bad actor. The purpose of a system is what it does. I don't give a fuck about their safety fig leaf.

When you are running black weapons programs in broad daylight you are now guilty by default on one of two of the prongs of Hanlon's Razor, and I don't care which they prefer to hang for as long as they hang.

I think it's easier to make your point without the baggage of the mechanism assertions.

The code is just wrong a lot. By denying the possibility of emergent phenomemona or model interiority you just hand the hypsters an easy point to score.

The code is just wrong, all the time. You're right about the part that matters and that we can measure.

Claude Code (or any other model/infra/harness co-design) is not subsidized in any normal use of that word. It's trough filling (I've written this up in lurid detail so I'm only going to do it again if anyone cares).

It's not true, it's just a play for margin.

Well, since we started training them on RLHF-style rating of the last generation they've totally collapsed back onto predictable suffix generators, which is why there are desperate, low-AUC BERT-inspired clasufiers bolted to them now.

They have like, Chomsky grammars now. And you can't fix it, it's structural to the process. You have to rewind almost to the pre-train.

You've just used a personal attack to shout down someone who disagrees in good faith over a distinction you simultaneously describe in your own words as "something you could achieve other ways" (yeah, more than a little bit) referencing an artifact that "is a symlink", "on my nix box".

The only thing I attacked are named instances of regrettable community malfunctions stripped of anything personal to an individual that hurt both current users of Nix and people who might experiment with systems they can reason about, saw an interaction like this, and did something less painful with their day. Because my evident and sincere concern for the future of Nix is framed as stark disagreement over a few particularly sacred cows.

At least on `comp.lang.lisp` you got your middle finger alongside a worthwhile education:

"There are some things in life that you do not do if you want to be a moral being and feel proud of what you have accomplished."

- Erik Naggum

It's cool stuff, but I think mostly in an aspirational way right now. The tired cliche hit on the tired cliche claim will be "but sqlite is in distribution" which will miss the point, that objection dissolves at the precise point where it would have operationalized: novel software of value. Is SQLite in the train set, yeah. Does that matter? Only if someone is willing to pay for Rust SQLite as something other than marketing.

It's cool but I'd rather know what their most successful users are doing, and how they measure that.

The privileged path is already there. `/usr/bin/env` is no different from `/bin/bash`, `/bin/sh`, or any other ELF artifact at a known place. The argument is made, the argument is spurious. It is made in the other direction regarding the driver run path, just as religious, opposite ruling from purity court. No one even knows why, the trail goes cold in a mysterious 2012 commit about Mesa, it's literally a performance to bring the plane cargo back. Receipts for claim: #141803.

Disagreeing with you doesn't make something a rant. If it's not clear how deep my Nix expertise is I will demonstrate it to any level you like: I'm just as entitled to an opinion as you are and I would appreciate it if the nixpkgs community was a little less rude to anyone who disagrees with some dogma no matter their knowledge. The nixpkgs community is not regarded as healthy or friendly after an internecine faction war that split three ways twice, producing four implementations none of which work, and if that reputation is ever going to mend, it will be because less than every Nix person has precisely zero chill the nanosecond anyone disagrees with them about anything.

You have the right idea but the wrong specifics. The boundary you're alluding to isn't the kernel/userspace boundary, it's the `libc` boundary, which is admittedly privileged by convention if not by Ring 0.

On most Linux systems this is regrettably `glibc` (in a container where you get to choose everyone chooses the superior option of `musl`), on all Darwin systems this is `libstandard`.

This thread is more concerned with Linux, so you are probably dealing with `/lib64/ld-linux-x86-64.so.2`, which operates in userspace but is by convention and opacity quite clearly part of "the system".

The kernel modification is a much bigger, much weirder side effect of a weird Nix loyalty test around shebang lines in shell scripts, on which is has opted to be intentionally and violently incompatible with everything for no benefit other than incompatibility.

The correct fix is to store the metadata outside the CAS, in for example, the loader, which can trivially delegate to another loader (does on my machine now).

bazel's wrong solution is $ORIGIN, Nix's wrong solution is "floating" CA / "realizations".

The technical debt / precedent argument doesn't apply: Nix never had this bug (for once), you the choices on this bug are 1. port the bazel bug to Nix 2. don't port the bug.

I predict... the bug is a shoe in, the bug lands eight days a week.

It's probably not quite that dramatic yet, though it seems possible it will get there, maybe even soon.

There's no structural reason to expect acceleration any more or less than an asymptotic behavior (if even that, acceleration is probably the bigger ask). Different problems yield to a new solvent, maybe that's also more, but it could go either way and we definitionally don't know yet because we don't understand the convexity of AI capability, we cannot directly access it interiority, we don't know if it's sandbagging (other than that it does sometimes, it can). It's an emergent phenomemon that might actively resist measurement. Or it might be as predictable as a clock in a few years.

No one knows, or if they do, they aren't talking. The loud people don't know anything.

Seems like a breakdown on the incentives / imperatives in the field? I hope that's not an over bold guess from a non-mathematician.

Couldn't people in principle continue to study a problem that's only been shown to break at one point? Prove something adjacent, or slightly weaker, or elaborate the counter example into a powerful explanatory framework?

I can recommend without reservation the book by Simon Singh, at least for a lay audience (don't know how an expert would experience it).

It's understandably the natural place to get the dramatic tension from what at least purports to be a sober account with some momentum. It's reasonably consistent with the way it's treated on the lectures I've seen from Sir Andrew Wiles on YouTube.

It sounds like a nightmare. He had intentionally set the proof up in a high stakes way, working in private, very quiet on what he was really doing. I gather this is not the done thing, eccentric at best kind of vibes, and I think by that point it was almost crackpot adjacent to even try seriously. His advisor forcefully pushed him off even trying earlier. So it's compound on the stakes. The beg reveal is intentionally as dramatic as possible. And then the questions start to land, most are minor clarifications, notation deficits, but one is sticky, one won't go away.

Kept me up late reading about it.

I'll contend that any Rust build involving Cargo is bloated and slow. `rustc` is impressively slow on a translation unit basis, and Cargo is basically a build recursion bingo card. Throw in about 900 micro point releases in flight at any given time?

If you're not running an elite `bazel` or `buck2` RBE with `nativelink`? You're not even playing.

I'm sure it's obvious to anyone living in a corrupt/oppressive regime, but in case it's not obvious to everyone.

Corruption and oppression are signaling and coordination problems. The illegitimate sovereign is exploiting informational assymmetry: they know your neighbors are just as angry as you, they know it because all the walls have ears.

They need to prevent you and your neighbors all knowing it at the same time. Your best play is to find some signal, something difficult to censure, hard for the goons to pick out in a crowd but legible to your neighbors. If you all knew that the first guy to shove back when the cop shoves you is going to be followed by a swarm of guys? Very easy to find the first guy in that case.

This is why shit like extremely high gas prices scares the shit out of illegitimate sovereigns: they're the ones posting pure data about why everyone should be that angry right now.

There are low-insensity regimes where it's all Python or whatever, and if you're in one, great.

When you're dealing with multiple platforms, or hardware accelerators, or mostly all of economically relevant shit in the AI era you don't get a small, clean, fast build.

Fable can't print a Tauri faux-native app without dragging in half of LLVM.

I think it's kind of fun now. Agents can interact with Linear. I'm still playing around with like does an issue achieve anything? What is the fastest way to get a bug from the observing session to the originating session?

But it's secondary.

The wall is build. If you can AI program, your problem is the build is too slow, too unreliable, not secure enough from a supply chain standpoint.

That is where one competent senior hacker tops out today. The agents are yielding to a CI that gets 35% per-vCPU occupancy.

The wall right now is skill or build, depending on your skill.

I think it makes sense that when you've outlawed competition for many/most users of your product's matching service that you would cheap out on it if you were maximally extractive and took no pride in your work, sure.

But the "coding is mostly solved" narrative kinda doesn't match right? If good, correct, high-performance software is like, free now? Wouldn't you want it to be slick as hell, really reliable, all that? Even a little breakage costs a lot of money at that scale and pricing, it would be better than a wash if you put the magic code thing on the case.

"Claude. Do all employee work. Make no mistake. Notify in slack when revenue is double."

I don't think anyone's disputing that the models are better than a year ago (though clearly all this, recursive self improvement stuff is utterly hypothetical and that's being generous, most of the progress has been on cost and fit and finish stuff). When it's on the plan, I'll use Fable for some stuff. If I'm paying for Opus? It's 4.5 or 4.6 which were dramatically better aligned and token efficient in the trace at a capability gap that's "you win some and lose some".

That can be true while it also being the case that to someone who has no idea how this stuff works under the hood, it's basically Dunning Kreuger in a box. The next person to go /u/PhdInEverything on me with Fable is getting an education in the history of hardware support for mixed precision training or something. Fable is a masterclass in refusal to ground and a dozen other alignment catastrophes.

So yeah, the models are still getting a little better, but from here out I think it's rapidly becoming a skill game.

You can mad customize it if you're willing to set up like, oh my pi or whatever.

I didn't quite get it tuned up enough to be a daily driver but I'm basically sure it can be hotrodded however you want. It comes out of the box with like four different vendor hostile compact strategies, including compacting into images at the smallest size Claude can read, which the "coding is basically solved" geniuses conveniently leak the resolution heuristic out of their website along with all the other side channels they print for the MSS.

As a vocal advocate for the use of machine intelligence in certain contexts and a skeptic of claims they are useless or always hallucinate or whatever...

It hasn't been even close to even the recent claims! It's been like three straight years where it was supposed to utterly transform society any minute now.

I think we more or less have a fragile consensus that in like, computer programming and really very little else, that on a good day you're probably going to come out ahead with the AI assist. That seems relatively uncontroversial now. But it also seems like success with AI is largely about working hard to get good at it, as a first order concern. It is not at all obvious that blind, uncritical use by anyone is a net win.

It's pretty unclear, sone might say dubious, that anyone has made serious, aboveboard money net of debt and equity, other than the hardware vendors. There's some pretty serious revenue, but it's a drop in the proverbial bucket against the outlay. There like a two trillion dollar balance sheet hole in the US alone where investment into AI has gone.

While I personally don't agree with them, multiple S-tier machine learning researchers think we've got our wheels stuck in the mud, that autoregressive decoder architectures on a tokin-suffix pre-train is tapped out as a paradigm.

It's ok to say "AI is starting to get useful in pretty durable ways" and not sound like an Anthropic shareholder/employee, i.e. completely full of shit.

I think you're right to point out that historically the rule of law in the United States has been very robust by the standards of whatever era, it's been a tremendous advantage in attracting business and capital and talent, it's good stuff.

But we've gone through some pretty weird times too. Turn of the last century was pretty tech billionaire edits, reconstruction was uh, not smooth, it's a mixed bag.

And most takes I hear seem to acknowledge that this is one of those weirder times: serious election fraud rhetoric from most everybody from 2016 to the present, very politicized courts (on both sides to be clear), very soft on anti-trust, very soft on adventurous accounting. The Epstein files and like, no consequences (pretty much uniquely for a developed nation with Epstein people). It's weird right now.

And I think I would be hard pressed to think of a weirder part of this weird time than the rule of law meets AI. We can haggle on where laws end and norms begin (stare decis being maybe the midpoint), but in the 90s, the Justice Department got their brass knuckles on for a lot less.

I don't think it's a simple "the law works nothing to see here" story.

When you net out across benchmarks and firsthand reviews it seems like it's maybe a little behind. There seems to be a consensus it's token hungry and a little slower. So maybe it's a point release behind.

That's weeks maybe months behind, not months maybe a year behind. It's "would my life really change if Claude was gone, not really" behind.

I actually haven't used it much, because Claude started kicking ass again the last few days. Like, way too much of a difference to be normal load-based variance. I got more done in the last 48 hours than week before that.

So, fuck yeah competition.

Eh, I think you've done a pretty good job summarizing a collection of settlements with a few narrow bench rulings for seasoning. I'm not sure I follow you to it being a coherent legal theory. Buying a book in a bookstore is sure legal, and excerpting from it for e.g. literary criticism is pretty settled. Downloading every torrent of all e-books ever is pretty clearly illegal (or at least it fuckin would be if I did it). Pretty sure like, multiple labs have been popped for that though.

Situation right now seems more like a fragile detente: if you got a Hill staffer drunk and hounded him long enough he'd probably be like "God damnit the market will fucking tank if we don't get these two IPOs out north of a trillion. And don't even get me started on how I'm going to sell Chinese AI to a Senate that still calls people Nipponesians when no one is looking. We're doing the best we can alright, get off my back man."

We have a situation, but it's not exactly A&M Records, Inc. v. Napster.