3,965 karma · joined April 14, 2013
Truth is some sort of value judgment that is outside the scope of formal systems. And looking at how bizarre Gödel statements are, it's unclear if there's any particular justification for declaring them to be true or false.
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?
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.
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.
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.
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?
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.
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.)
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.
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.
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?
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.
After a lot of investigation, we discovered that only photos uploaded by one specific (prolific) person had this issue. And it was caused by their software putting some nonsense exif DPI data in the image that was ignored as nonsense by every renderer except outlook. The format is a minefield of features with inconsistent support.
But I suppose that's part and parcel with actually being used. And that's somewhat better than the alternative.
But this just raises the question of what it means to be larger in time than space. You can look at it in terms of multiples of Planck distance or time, but I think there's a more enlightening way to look at it. If you express the speed of light in those Planck units, it's 1. But the speed of light is also the maximum speed of causality. Any causally-bound system must run long enough for chains of causation to propagate, usually far below the speed of light in practice. This means that basically anything that exists within the bounds of our manipulation must be happening at scales where there is far more time involved than space.
We all exist below the diagonal because the diagonal is the bound at which the ways chemistry and biology work no longer even are theoretically possible.
This thing where we've traded societal trust for profits for the companies destroying it is a bad choice, and section 230 is what enables it. Let it all burn. Bring back small communities with internal trust relationships. Growth is not an automatic good.
(No, pointing out that I wouldn't be allowed to post this isn't a clever gotcha. The whole point of advocating for change is that it would affect me too.)