Technically, the actual statement in Galois theory is even more general. Roughly, it says that, for a given polynomial over a field, if there exists an algorithm that computes the roots of this polynomial, using only addition, subtraction, multiplication, division and radicals, then a particular algebraic structure associated with this polynomial, called its Galois group, has to have a very regular structure.
So it's a bit stronger than the term "closed formula" implies. You can then show explicit examples of degree 5 polynomials which don't fulfill this condition, prove a quantitative statement that "almost all" degree 5 polynomials are like this, explain the difference between degree 4 and 5 in terms of group theory, etc.
Sure, you can do that. The parent's point is that if you want this mapping to obey the rules that an actual definition in (say) first-order logic must obey, you run into trouble. In order to talk about definability without running into paradoxes, you need to do it "outside" your actual theory. And then statements about cardinalities - for example "There's more real numbers than there are definitions." - don't mean exactly what you'd intuitively expect. See the result about ZFC having countable models (as seen from the "outside") despite being able to prove uncountable sets exist (as seen from the "inside").
Yeah, that's more or less how I feel about it as well. I would even go further and say that the existence of the open world makes the Legacy Dungeons worse. It's quite unfortunate because in terms of visual design and architecture, they're some of From's best work; however, they tend to be full of the same enemies you've already fought multiple times in the open world, taking away from the feeling of venturing into the dangerous unknown that I personally find so compelling about these games.
It's also unfortunate that this looks like a game with a lot of build variety, that would really lend itself to multiple playthroughs, but actually playing through the content again sounds like a pain. Going through the wiki and making a list of places I actually need to go is not my idea of a good time.
This is just plainly false. While not quite as bad as the average Ubisoft game, Elden Ring's world design is very similar to Elder Scrolls, Skyrim in particular. Most of what the author brings up are aspects of the game not related to the open world. The open world itself is not nearly as trend-bucking as a lot of other game design decisions From Software make, which is honestly a bit disappointing. In general, Elden Ring is their closest game to a typical AAA title, a lot of the quirks and contrarian elements from their earlier games are absent in it.
You don't have to, and I personally also find small-talk with strangers rather tedious, but in the specific cases brought up by the author, it sounded like he would've saved himself time by just briefly explaining his reasoning. Which also would've had the nice side-effect of treating his interlocutors as rational human beings worthy of a measure of respect.
Fundamentally, a lot of knowledge we possess as individuals is socially constructed, in the sense that we trust the process and the institutions that created it. Even if this knowledge can, in principle, be verified, it is usually impractical for an individual to do so.
Putting science aside, how can I be confident that the basic facts presented in, say, a NYT article, are correct? I can trust the reputation of the NYT as an institution, and I can also trust that any inaccuracies in the article will be called out by other publications. But if I feel everyone's in on a conspiracy to push a particular viewpoint, then I need to anchor my knowledge in a different institutional framework - even if that might just be a random Facebook group of strangers, or my weird uncle, or a niche radio station.
This, incidentally, is why the censorious push against "disinformation" is misguided in principle. It's sweeping the underlying problems under the rug in the hope that they disappear spontaneously. In an open society, truth can only be established as a result of public discourse, anything else is just the representation of the perspective and interests of some authority. Whatever its source, the seemingly growing distrust in public institutions will not disappear simply because we make social media companies remove its most obvious symptoms.
> You think John Carmack was the only one trying to make 3d games when Doom came out? Thousands of programmers where trying to. Does that make him a 10x programmer in your opinion? Or more like a 1000x?
I think the idea of 10x programmers gets so much pushback because it's often bundled with this kind of toxic hero worship. There's a difference between acknowledging the impressive ability of outliers, and idolizing heroic one-man efforts as the pinnacle of what we should all aspire to as software developers.
Incidentally, Carmack was not the only programmer on early id Software games, and Doom was far from the first 3d first-person game made. Arguably, it wasn't even that ambitious compared to, say, Ultima Underworld, but the programmers working on that get much less immediate recognition.
As a matter of fact, these discussions often remind me of that famous IGN quote of Warren Spector. Except we really should know better on HN.
That honestly sounds like a failure to communicate with the researcher first and foremost. If it's difficult to prioritize the fix internally due to organizational politics, that's one thing, but that shouldn't stop the bounty team from communicating the status to the researcher. In fact, that should be the simplest part of the whole process, as it's completely within the purview of the bug bounty team. If they handle that right and build some trust, they might be able to successfully ask the researcher for an extension on disclosure.
Case in point, Apple likely could have come out of this looking much better if they didn't ignore and then actively lie to illusionofchaos. That really isn't a very high bar to clear.
So it's a bit stronger than the term "closed formula" implies. You can then show explicit examples of degree 5 polynomials which don't fulfill this condition, prove a quantitative statement that "almost all" degree 5 polynomials are like this, explain the difference between degree 4 and 5 in terms of group theory, etc.