jltsiren

The argument is ultimately constitutional. If pensions based on past contribitions are private property, the government can't avoid paying them when it's no longer economically sustainable. The obligation remains even if the government is no longer capable of honoring it. Political choices and ordinary laws can't change that. The only way out is amending the constitution and socializing the private property.

It's a bit more complicated than that. It can be argued that if there is a clear link between contributions and pensions, promised pensions based on past contributions are private property, with the usual protections. I don't know the situation in Spain, but Finland at least has made that choice.

If you choose that (or if your legal system determines that), you need to be proactive with keeping the pension system in balance. While you can change what you promise in exchange for future contributions, substantial changes to what you have already promised can easily require constitutional amendments.

I recently chose a Studio Display over the alternatives, because I wanted something with an integrated camera to use as the primary display. There are already too many devices on my desk, so anything that needs an extra cable or comes with a battery that must be charged feels like a poor choice.

And I don't really see much value in high refresh rates outside gaming. The difference between 60 Hz and 144 Hz is minimal in most uses. Given what displays were in the 90s and 2000s, I would have chosen a different career if I was too picky about display quality.

The challenge is the initial reduction from an arbitrary problem in NP to the problem you want to prove NP-complete.

In the usual approach, you assume a nondeterministic Turing machine (or equivalent) that solves the problem and a time bound (which can be an arbitrarily large polynomial). You then create a boolean expression that can be satisfied if and only if the Turing machine accepts the original problem instance. Unfortunately all constructions so far have included the time bound as a factor of the size of the expression.

It's been a long time since I seriously thought about complexity theory, but I'd say no. For similar reasons to why complexity class E is not closed under polynomial-time reductions.

The most important component in the time bound is of the form 2^{n / polylog(n)}, which is subexponential. But if you have reduction from another problem that increases instance size quadratically, the algorithm for the other problem is no longer subexponential. Which means we are still essentially in the same neighborhood as before.

It's a huge result if true, and probably the first major AI result that affects the papers I read. But since the boundary in the hypothesis was kind of arbitrary, breaching it should not significantly change our intuition on complexity classes.

He says he is a Protestant, and he probably identifies as one. He may believe he believes in Jesus Christ, but does he actually believe, or is he just fooling himself? Can you even know if you genuinely believe in something, because you are always the easiest person you can fool?

There are many doctrinal differences between different branches of Protestantism. Lutheranism teaches that while good works do not imply faith, faith does imply good works. The absence of good works can therefore seen as evidence for the absence of faith, from that perspective.

The entire republican tradition (with a small r) rests on the assumption that leadership is a common skill. The society is supposed to give ambitious young people opportunities to demonstrate their skills, and then select the most capable ones and give them increasingly challenging roles. At any given time, there should be an order of magnitude more potential leaders (with the necessary skills and experience) than what the society actually needs. And the leaders should be replaced often enough, to avoid giving them the idea that they are somehow special.

It seems to me that you are comparing two kinds of business-minded people. Some want to sell tailored products to individual customers, while others want to sell one-size-fits-all products to many customers.

You could also focus on problems. What are the actual problems you want to solve? Can you use software to solve them? Do you still need to buy that software from other companies, or is it now feasible to have sufficient in-house expertise to develop it yourself?

This project has repeatedly appeared in the national news since 2024, when Google first acquired the land. It's the largest investment ever made in Finland (at least by some metrics), so people are obviously paying attention.

And now it's probably going to be delayed by months or even years. Whatever Google was trying to accomplish, this wasn't a smart way to do it.

There is usually a standard language people learn at school. It's mostly used as a written language or when you want to sound formal. In more casual situations, people tend to use their favorite dialects. Or maybe an intermediate form between the standard language and the dialect, if that feels more appropriate.

European pension systems have multiple components. There is usually a minimum guaranteed pension based on residency alone, which is paid if you don't have enough income from other sources. That can be supplemented by a separate housing benefit.

The main component is usually something similar to US Social Security, except that contribution rates are higher (16% in Sweden). Benefit rate (at any given retirement age) is usually close to a linear function of total contributions, adjusted for inflation. Most people expect to get most of their retirement income from that component.

Then there are supplementary components, such as voluntary or union negotiated private pensions. Some of them are a bit weird, such as the Swedish defined contribution plan with a mandatory 2.5% contribution.

The more famous the problem, the more reputation matters. There is no shortage of papers claiming to prove P vs. NP in either direction. Nobody is taking them seriously, as everyone has a strong prior that people trying to publish such results are cranks.

Mathematicians need to rethink what is the purpose and value of doing pure mathematical research in the future. Until know, they have mostly valued the creation and systematization of human knowledge. From that perspective, Lean proofs mostly increase confidence in the human knowledge. But they don't contribute directly to it, as a formal proof is unlikely to contain insights that are not present in the human proof.

Grigori Perelman's papers were considered promising mostly because they were written by Perelman. When there are too many papers to read, the reputation of the authors becomes the most important signal of quality. Formal peer review tries to spread the attention a bit more evenly, but it doesn't scale too well.

America is pretty much the only country with elected prosecutors. Everyone else considers it a career position, and then incentives are different.

If the Ents were real, everyone in Finland would be long dead. That 300 hectares represents about 0.5 days of logging.