enasterosophes

It's a good question. It's easy to assume they're talking about R^126 (where R is the reals) but digging a bit deeper I don't think it's true.

The Kervaire invariant is a property of an "n-dimensional manifold", so the paper is likely about 126-dimensional manifolds. That in turn has a formal definition, and although it's not my specialization, I think means it can be locally represented as an n-dimensional Euclidean space.

A simple example would be a circle, which I guess would be a 1-dimensional manifold, because every point on a circle has a tangent where the circle can be approximated by a line passing through the same point.

So they're saying that there are these surfaces which can be locally approximated by 126-dimensional Euclidean spaces. This in turn probably requires that the surface itself is embedded in some higher-dimensional space such as R^127.

Unless you're talking about a compiler built into the kernel, I don't see that anyone is in a position to dictate to each distro what compilers they package.

I feel like we're working at the same company. Not just this comment but your others on the same topic. I've seen all the exact same mistakes over the last year. The company wants to grow fast so hires quickly, but then the people hired quickly underperform, so then they're fired quickly, but firing people quickly results in fear, grief and guilt for everyone who hasn't been fired "this time". The top talent never feel comfortable in this cold mercenary culture, so they don't settle in and soon move onto somewhere less cut-throat.

> I can't find that bit in the article and I haven't heard it before: could you share some more?

The second paragraph has what you want. From the article:

> The App Tracking Transparency (ATT) framework used by Apple on iPhones and iPads since 2021 makes the use of third-party applications too complex and hurts small companies that rely on advertising revenue ... The system harms "smaller publishers in particular since, unlike the main vertically integrated platforms, they depend to a large extent on third-party data collection to finance their business," the agency said.

Is there another way to interpret this than that the agency wants to protect advertizing and data collection practices by small businesses?

I thought Pot8o expanded to Potuberneteo

This is just an ad.

Would it be fair to say that you also don't appreciate solo rpgs?

I've found chatgpt useful for trying out D&D settings that I don't normally get to experience in my usual group. It loses the plot after a while, but it's enough for me to figure out whether I dig the setting enough that I would want to pitch it for a real game.

I'm not convinced it's deliberate dishonesty. Just a communication disconnect. Firstly, it can take time from the first yellow flags to the full realization that there really is an incident underway, secondly it needs someone to decide how to communicate that incident, and thirdly the engineers who are actually working on the incident need to be able to get on with it instead of being pestered for an update every 10 minutes.

I'm the same age as you. I think it would be difficult to disentangle reduced focus from changed internet usage.

Personally I'm trying to watch less youtube. When I want a break from work, I try to go read a book for a while instead of taking the "mental junk food" option. I can't provide an objective report on whether measures like this help, but they do feel better.

> Yet another reason to buy MP3s from known bands and musicians and just listen to it offline.

Or FLACs, if you can get them, which you can on bandcamp. I've got a terabyte of music in my offline playlist. It takes a few months to cycle through everything, then top it up with any new discoveries and latest releases before the next cycle starts.

> My guess is that mathematical research utilizing these systems is probably the future of most of the field (perhaps to the consternation of the old guard). ... Terence Tao has a great blog post about this, specifically about how proof assistants can improve collaboration.

Yeah, that was a great blog post. As someone who started in mathematics but ended up in computing, I read it and realized, hang on, he is talking about taking a devops approach to mathematics. It definitely struck me that this is the way of the future: mathematics transformed from almost a humanities-like discipline into an engineered enterprize.