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Comment Arrokoth is such a neat body. (Score 2) 12

For those who didn't follow it, it's not that it's a contact binary that is so neat in and of itself, it's that when they modeled it, they determined that, the collision that formed it was less than 5 meters per second (less than 11 mph / 18 kph). Like a parking lot fender bender, but with the cars being ~750 billion tonnes.

Comment Re:An AMAZING number of flaws (Score 1) 76

The whole effort of design of software systems is ultimately the effective management of complexity. Complexity of features that provide real world value is the developers problem to manage. If "technical debt just keeps compounding" it is probably best to find a better developer.

I love scapegoating individual developers as much as the next guy, but if you take a look at the Win32 API, you'll find loads of fun "features" such as:

- Every single function that takes a string has two implementations: one that ends with the letter A (and takes its strings as ASCII) and one that ends with the letter W (and takes its strings as UCS-16). And then it has a preprocessor-define (with no suffix) that gets expanded to either one implementation or the other, based on your compiler settings.

- windows.h defines preprocessor-tokens for min() and max(), which means any C++ program that ever calls std::min() or std::max() will error out with a very strange compile-time error, if it included windows.h first; the work-around is to define NOMINMAX first to prevent windows.h from polluting the namespace.

- Modern windows is perfectly capable of arbitrary-length file-paths, but ships by default with a 260-character filepath limit anyway, "to preserve backwards compatibility with older software that expects that limitation to be enforced". To get correct behavior you have to hand-modify your registry; otherwise you find out about this limitation when you go to unzip a .zip file and the unzip mysteriously fails even though the .zip file is valid.

These are all defects that other OS's simply don't suffer from, either because the other OS's were designed correctly from the beginning, or because the people in charge of the other OS's long ago took the hit (in short-term breakage) and fixed the problems rather than letting them linger forever to preserve backwards compatibility.

All Windows developers (good and bad) have to deal with these issues, probably forever, and every line of code they add to work around these problems has to be supported and debugged and tested as well, hence the damage compounds.

Comment Re:Can I pay him not to post? (Score 5, Insightful) 212

That is, isn't this illegal? Or is it just that no other presidency thought of doing this particular cash grab?

Before Trump, it was a cultural norm that a President of the United States was expected to follow ethical and moral guidelines as well as laws; not only because anything less would be dishonorable and a disservice to his country, but also because otherwise he would pay a steep political price for his unethical behavior. Trump's most significant political innovation has taken the form of figuring out how to convince a plurality of the American public that the only real standard for Presidential behavior is "whatever you can get away with".

Comment Re:Why? (Score 1) 155

Yeah, there's two main problems:

1) People entering the wrong fields. For example, medicine really needs workers, at all levels, but not enough people are going into it.

2) Certain manual labour fields, like field work and home construction, because... well, I think we all know why there's a shortage of workers in those fields.

Comment Re:An AMAZING number of flaws (Score 1) 76

Part of it may be a dysfunctional corporate culture, but a lot of it is a consequence of Microsoft's business decision to maintain backwards compatibility at all costs. When you're committed to retaining every design mistake, forever, the complexity of the codebase just keeps rising, which means that less and less of it can fit into anyone's mind at one time, which means more mistakes are made going forward, and the technical debt just keeps compounding.

Comment Re:LLM output is Grey Goo and Ecophagy. (Score 2) 155

Or let's put this another way. Show of hands - how many of you "spicy autocorrect" / "stochastic parrot" people had "AI will start mass-solving Erdos problems" on your forecast list a couple years back? Huh, none of you? Fascinating!

Take some time to reassess your priors. And while you do so, understand that, yes, they are doing logic / reasoning.

Comment Re:LLM output is Grey Goo and Ecophagy. (Score 4, Interesting) 155

They weren't discovered by an LLM. They were known conjectures that were proven by an automated solving language that was linked to an LLM.

I'll take "Things That Didn't Happen For $200", Alex.

Only a handful of meaningful proofs have ever been done by automated formal theorem solvers (the Four Colour Theorem being the most noteworthy example - but its proof is so long that humans can't verify it). By contrast, AI tools have been solving Erdos problems en masse. The majority of them just bog-standard commercial models. In case you need help, the only ones on that list that were hybrid (AI / non-AI) in the actual solving phase are:

1) AlphaProof / DeepMind Prover Agent / AlphaProof Nexus
2) Aristotle (Harmonic)
3) Seed Prover / Seed Prover 1.5 (ByteDance)
4) AxiomProver (Axiom Math)

In each of the above, LLMs come up with the lemmas / strategies but then use Monte Carlo search ("brute force") or likewise to investigate what they came up with. These are a minority. In the "AI Standalone" category, these "hybrid" tools made up only ~20% of attempts and successful proofs. Hybrid tools actually made more of a contribution in the "AI Alongside Literature" (related literature found afterward) and even more of the "AI Building On Literature" (related literature known beforehand) categories, which is the opposite of what people like you expect.

And even with the hybrid tools, it's still the AI doing the heavy lifting when it comes to strategy. Non-AI theorem solvers, again, don't have a spectacular record for churning out novel proofs to unsolved problems. Tools like Lean are more about mathematical rigour - a passive environment that requires a driver (a human or AI) to feed it actual strategies, lemmas, and proof steps. And no, you cannot brute force "strategy" in the vast majority of cases, which is, again, why automated theorem solvers don't have much of a track record with unsolved mathematical problems.

Let's take a random example: the disproof of the unit distance conjecture. It was solved purely by a general purpose commercial GPT model, not custom-trained to mathematics, with no external tools. Read what the various mathematicians reviewing / commenting on it have to say (sections #3 and onward). Seriously, don't skip reading them, actually read them. This was one of Erdos's favourite problems. He mentioned it commonly in his lectures. Essentially every mathematician working in complex geometry has thought about this problem. The approach that the model came up with was highly novel approach, based on CM-fields and class field towers.

I know you don't want to accept this reality, but it is the reality, so you better improve your ability to accept it,. The field of mathematics is already doing so.

Comment Re:It's bots and ragebait, thats why (Score 2) 107

Perhaps the real problem is that there is simply no reliable way to tell a real human's post from a generative AI's post anymore, since by the AIs are trained on the posts of real humans and are asymptotically becoming indistinguishable from them. You certainly can't simply go by post-quality, since the some of the smarter bots are better posters than some of the, err, less-well-informed humans.

Because of that, it's hard to feel good about putting any real effort into a social media conversation, because in the back of your mind you're always wondering: am I engaged in any kind of constructive activity here, or am I just unknowingly humping a rubber doll that Zuckerberg (or somebody) has provided for my amusement?

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