I think the only reason this wasn't done pre-AI was due to it not being a topic of serious focus. 1989's computers were too weak to handle all the cases. But all the basic ingredients were present in the Kepler conjecture proof. What AI did was lower the effort enough that amateurs who just liked square packings could perform and formally verify such a proof. I consider myself among such amateurs. So this isn't a case of AI stealing mathematicians proofs, or doing something superhuman, its a case of democratization. I am concerned about how AI is affecting math and how the AI companies are behaving, but this isn't the case to be worried about. The calculations for proving this arrangement optimal will always be too big to be checked by hand. However, I'm hoping to produce some nice visualizations of the packing LP or core overlap that rejects each configuration

I do think if Transformers weren't invented you would still be able to train powerful language models, but they would take more ram and be slower so nobody does this.

Symmetric cryptography is safer because one key can easily protect as much data as you need.

Let X = the number of remaining open parenthesis required to reach your target length, and Y = the number of remaining close parenthesis.

Let P(X) = X/(X+Y) * (1 + 1/(Y-X+1)). Generate an open parenthesis with probability P(X), and otherwise a close parenthesis.

This will efficiently generate an unbiased random plane tree. The reason this works has to do with counting the valid ways to complete the plane tree, using a calculation similar to the one in the article.

I think it really comes down to what set of functions you are calling "elementary".

Have you tested this GCs performance? Sometimes a baby GC can be fast enough.

Now, I do agree that LR grammars are messy. Nowadays, they have mostly fallen from favor. Instead, people use simpler parsers that work for the restricted grammars actual programming languages have.

IIRC there is some research into formalizing the type of unambiguous grammar that always uses () or [] as nesting elements, but can use Regex for lexing.

Formats, name collisions or back-button breakage are tangential to the content of the article. Being AI generated isn't. And it does add to the overall HN conversation by making it easier to focus on meaningful content and not AI generated text.

Basically, if the writer didn't do a good job checking and understanding the content we shouldn't bother to either.

AWS has set up proper boundaries between ESC and global AWS. Since I'm based out of the US I can't see anything going on in ECS even in the service we develop. To fix an issue there we have to play telephone with an engineer in ESC where they give us a summary of the issue or debug it on their own. All data is really 100% staying within ESC.

My guess is that ESC will be less reliable than other regions, at least for about a year. The isolation really slows down debugging issues. Problems that would be fixed in a day or two can take a month. The engineers in ESC don't have the same level of knowledge about systems as the teams owning them. The teething issues will eventually resolve, but new features will be delayed within the region.