This is a description of one portion of math... one that's very easy to get tunnel vision towards when undertaking a very formal undergraduate mathematical education. And that's especially true if it was alongside a computer science education, which is precisely the branch of math concerned with formal systems being used in calculation.
I've done both of those things. I know what you get taught. But I've kept my math education going for the 25 years since then. I've talked to practicing mathematicians about what they do. I've learned a lot about the scope of math.
As an aside: most people really dislike it when I say that they should be much more precise about different numerical systems. The integers are not a subset of the rationals. They are entirely different constructions, but there is an isomorphism between integers and a subset of the rationals that preserves the integers' ring structure within that subset of the rationals and a few other aesthetic concerns. You can see why no one wants to communicate like this, even if they acknowledge it's technically correct. So I know all about pushing symbols around.
But I also know that pushing symbols around isn't the whole story. Pushing symbols around is only useful as a final check. Do you want to validate that 1+2=3? Pushing symbols around can help. But how do you decide that the ideas behind 1, 2, 3, +, and = are worth having precise and compact representations?
Math doesn't just use formal systems to generate proofs. It's not enough for symbols to be arranged neatly according to some rules. Math is also the process of creating the sets of symbols and their rules and communicating to other people why this set of rules and symbols is interesting. What ideas get preserved when you are working with this system? What is it an abstraction over?
You have a weird definition of "smuggling". I say it outright. Because I follow it up with a description of the actual practice of math: it's the study of abstraction. That's not a frame. That's just what math is.
It's elegant if all you're concerned with is whether a conjecture is true or false. Answered, move along!
But mathematics is not a collection of facts. Mathematics is the study of abstraction. And what do you learn from a single data point? What can you abstract from that?
That's why just being a counterexample isn't really interesting. There has to be more than "counterexample" for there to be something to abstract. Was it generated from an analysis of the problem? Can the counterexample be generalized to explore the problem further? Is the counterexample a surprise in a way that suggests something is missing from current understanding?
Being a counterexample doesn't mean that something isn't interesting to a mathematician. But it's also not the interesting part.
Bluesky has a data store, handles account authorization, and runs a web app that provides a UI to access the backend services. That's an instance, whether they call it one or not. Refusal to admit this is obfuscation for reasons I cannot understand.
As Led Zeppelin once said, "you know sometimes words have two meanings". That definition of wealth is all well and good for books about how markets are magical fix-everything pixie dust. But it's not the definition of wealth that applies when used to describe a person. A wealthy person is not someone with a lot of things. That's a hoarder. A wealthy person is someone who can use their economic power to shape the world around them.
It is literally impossible for everyone to obtain wealth. Wealth isn't a number or physical circumstances. Wealth is having economic power over the people around you. Success is a little more nebulous, but when thought of as a relative of wealth it's similarly contextual.
The danger isn't everyone but you getting wealthy. The danger is that wealth tends towards concentration. And it tends to concentrate around people who are already wealthy. The danger is, bluntly, that things will get worse for all but a few and most people will be so caught up in a red queen's race that they can't see how to stop.
Yeah... I've got a whole lot of experience with "you can't do this thing the obvious easy way because iOS is too important." This isn't about fantasies of Apple being your savior. This is about HTML and CSS that Apple has decided not to support.
I don't believe it's possible to work in web dev and not run into this. It's a constant annoyance that semantic markup and declarative layout just have entire swaths of features unsupported on a garbage browser that you can't even say is unsupported because it's the only option on iphones. If it was up to me I'd just tell iPhone users that's what they chose. But businesses don't get to be as petty as I get to. And that's ultimately the point here. Apple is using their market dominance to force working around their poor support of standards on everyone else. They should be shamed for this shameful behavior.
The article is about how Apple is underdelivering in browser features and compatibility while pretending they aren't. It's about Apple. Apple. The ones responsible for a great many features not being supported in all browsers.
What does a web dev have to do with Apple's choice? How do you improve Safari by not using features it doesn't support? What does your comment have to do with the argument the article is making?
You can not-quite-trivially download all versions of a game that have been uploaded to steam, as long as you own the game. And that's a download like as an installers you can run, not just overwriting your current active steam install.
I actually rely on this quite a lot, indirectly. Beat Saber is a fun game, but it doesn't support a lot of fun features, like walls with boundaries that aren't aligned to the coordinate system. There are mods to add those features, but they haven't all been ported over to the new line of the game since it upgraded the version of unity it's using. So I use one of the mod managers that supports, among other things, maintaining multiple versions of the game in parallel so you can choose what you want to do when you start a game. This feature very explicitly relies on downloading older versions from Steam. Because that's a thing you can do with Steam.
In the same week that Sony announced they'd be ending production of optical media, they also removed hundreds of movies from user libraries that they'd lost the right to sell. I don't really care if they have yet to do the same with games - they've demonstrated they're willing to remove access from paying customers for their own reasons. And there's nothing the owner of a locked-down console can do about it.
Steam exists in a different universe than digital-only games from PSN. Conflating the two because they use the same method of delivery is ridiculous.
Is that actually true? Just because English treats scents as only describable by analogy doesnt mean all languages do. There are a number of languages with scent descriptions for aspects of a smell that are transferrable. [1] That suggests everyone is capable of decomposing a scent into components the same way.
If that's true, we're left with a question equivalent to "does everyone see the same red?". As far as I know, the pure version of that question cannot be answered because subjective experiences of sensation cannot be transferred. And at that point, I'd say the manner in which they're experienced differently is equivalent.
Book people really hate to hear it, but literary fiction follows Sturgeon's law just as much as Sturgeon's own genre. 90% of it isn't worth reading, and that includes 90% of what's fashionable at any given time. You're better off reading books you enjoy than suffering through garbage that you're told you're a bad person if you don't read.
(Literary fiction isn't bad. But for the love of reading, skip anything new and fashionable until enough decades go by for the influnce of fashion to fade. And skip things that aren't enjoyable to actually read.)
If you think of it that way, you have a real problem. It only takes about 10 meters for the weight of a column of water to create enough downward force that it starts vaporizing, at which point no pumping action works. This is why any deep well has a submerged pump. You simply can't pull water upward further than that with negative pressure in the Earth's atmosphere. It must be pushed with positive pressure instead.
This is why the question is interesting. You can't just suck water to the top of a 60 meter tree. There must be some kind of positive-pressure pumping involved.
No, that's actually more destructive in the short term. That was the OP's point. If they actually become something effective, they will utterly destroy the economy. If they fail, they will drag the economy down around them as they go. The least destructive possible outcome is becoming eternal parasites.
No, it's correct. The best (short-term) case is that they become eternal parasites. If they fail to do that, they'll bring a lot down with them when they fall.
Oh, it's worse than that. I've seen a rise in mutation testing, intended to ensure any change in implementation is caught by tests. Think about that for a moment. It's giving a fancy name to creating brittle tests than fail if any line of code is changed.
And this is seen as a good thing, because LLMs are really bad at confining their changes appropriately. Testing is really in a dark place right now.
It's a difference of degree. People expect something that "parallelizes well" to show near 1-to-1 speedup. Double the hardware, double the speed. This is "you can always speed it up, but the hardware requirements can increase at any polynomial rate".
You're describing an interaction with a good server at a good business. (Off of peak hours, if you can take hours and they don'thave anything to say about it.) What do QR codes add except for technical issues?
I honestly cannot recall the last time a server tried to upsell me with even as much as a "do you want a dessert?". But... I suppose that's selection bias. I only go to restaurants that don't require servers to do that BS. They don't want to do it either, you know?
"generally make it flow" is exactly the problem. It's a process of smoothing over any interesting features of the text to replace them with plastic. It's submerging the actual information you wish to convey under a layer of low-entropy noise. The whole signal may still be there, but having to find it under a uniform glossy finish is work for the reader. It's work you didn't need to delegate to the reader.
LLMs generate low-entropy text. That's their entire purpose. But good writing isn't about being as low-entropy as possible. It's about producing peaks and valleys. As a person who's been participating in human-to-human communication your entire life, you probably have a pretty well-developed sense of how to structure the flow of a piece of communication. The small arcs with their ebbs and flows of tension and density provide the reader a rough surface that gives them enough traction to easily move from point to point. Don't let an LLM smooth out all the gaps. It makes it hard for a reader to keep their footing in the text.