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.

Also, a vehicle with a manual transmission can be push started.

You can do it with an automatic, if both drivers know what they're doing. You put the dead car into Neutral, get it moving and when the car in back stops pushing, slam the front one into Drive, or possibly Low. Not easy, but I've done it once or twice.

TFS does not say that it has a breathable atmosphere, it says that astronomers have detected Helium in its atmosphere. For all we currently know, that's all the atmosphere it has, and no matter how high the atmospheric pressure is, that's not breathable, at least not by any Earth-like life.

The only one or two power outages I had my entire life in Germany: were planned weeks ahead.

You've been lucky, then. I live now in southeastern Colorado, where it's currently monsoon season. That means lots and lots of thunderstorms, hail and flash floods. (The standard advice for dealing with flash floods is "head for the high ground." We never bother, because we are the high ground.) Lightning and flash floods cause power outages, so they're common this time of year, but generally only for a few minutes.

The biggest outage I ever lived through, however, came before moving up here, when I lived in Los Angeles. That was caused by the Northridge Earthquake, back in '94, a real E-Ticket ride! One of the side effects was a better look at the night-time sky than I'd had since I left the Navy.

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.

I'm retired, and it's long been my habit to update my Fedora box every morning while making breakfast. I agree with you that the kernel's getting updated far more often than it used to be. Recently, it was updated at least three times in one week (maybe four, I'm not sure) which seems excessive. I think that was while they were getting rid of the insecure forms of string manipulation, but I wasn't involved in that and could be wrong.

As a long-time Linux user, I have two questions. First, why does Microsoft insist on holding on to all of these bug patches and security fixes so that they can be released all together on Patch Tuesday instead of being made available right away as Linux does? Second, why do so many people insist on paying money for such a flawed system and putting up with such a slow update pace?

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.

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.

Dang, link didn't post.

Ah, good 'ol "Model Collapse" theory that people have been pounding on for years now, predicting an imminent collapse in model capabilities. How has that been working out for you?

Except what the US is actually facing, at least in the near term, is just the opposite, a worker shortage.

You can't pay royalties to the entire internet. That's not realistic.

What is practical are things like taxes to fund public benefits, or requirements of returning things to the commons (for example, open models).

You're the one making the claim that modern frontier models still make this mistake (they don't), so how about you go to a frontier model, reproduce what you're claiming happens, and click the "share" button and post the link here?

Don't worry, I'll wait.

Your inability to reproduce the thing that you claim happens is duly noted.