It is an asymptotic result that gets more and more correct as n -> oo. In fact the constant 0.143 may have corrections proportional to 1/n with an arbitrary prefactor. The guy cites an older simulation study https://arxiv.org/abs/0808.400... that starts comparing numbers for n >= 21 where it is correct to several decimal places.

It's supposedly designed to be good at matrices. In fact, it more or less looks like a modern Fortran and that's esactly what they wanted it to be. I have worked a bit with it and while I haven't run any benchmarks it seemed reasonably fast. After my initial excitement I am not so sure about Julia any more. For one, I have worked on some Fortran 2003+ code and it is not clear why we need another Fortran which hasn't matured as long. And then, from lurking on the mailing lists, it becomes clear that Julia hasn't been designed by experts in language design but more by enthusiasts with a vision. That is not necessarily bad, but I am afraid that it leads to some design errors that only come to light once the language and compilers have matured a bit. And then it may be very difficult to correct (like the GIL problem in Python). Bottom line: Modern Fortran is quite nice to write and will provide the ultimate in speed. Python is equally nice to write with scipy/numpy and almost always fast enough for my data analysis. If I had the need for a bigger program with parts that are limited by raw speed, I think I would use Python with the critical parts calling into a Fortran library.

Huh? Isn't the whole point of a login process to _increase_ friction, i.e., to make it harder to access something?

I am not so sure about the 'far surpass'. I do expect at least a 100 million Covid deaths this year and some more in the west in the coming year. Realize that the roughly 2% death rate of all cases, including the asymptomatic in China and Korea was maintained with a top notch medical system. For at least 5 billion people in the world, all sever cases will die and then some more from complications that also a manageable in the west. Even if you optimistically count 60% resistance as enough for heard immunity, that is 3 billion infected with, again optimistically, 5% mortality. Thats 150 million. Even for the rest, especially USA, I would expect temporary breakdowns in adequate medical treatment. Let say, on average in the end 3% mortality. If we can stretch it long enough we may benefit from advances in treatment so we can get it down to 2%, maybe. I.e., 2 billion * 60% infected * 2% mortality is another 25 million in the developed world. To me these are extremely optimistic numbers. I wouldn't be surprised about twice the numbers, i.e., up to 400 million in the next two years.

No ;) Relax. I live and work in Germany, have earned a decent salary for the last 10+ years and consequently pay about 50% of my gross salary in taxes and social security. Actually the gross salary is calculated in some slightly twisted way so in reality I pay more like 60%.

Of course I was simplifying a bit and I obviously know that the first person in a household is the most expensive. But then again your parents (the pensioners) most likely do not live in the same household and should not for a number of reasons.

Keep in mind that I tried to describe why I think it is not unreasonable to expect to keep only a tiny fraction of your salary. Of course this cannot be realized in the current system of ultra-low wages. I am arguing here for (and actually also advocating to go back to) a system where only a small fraction of the population does paid work but then earns enough to support a sizeable number of people.

For Germany, the only country where I can judge the numbers, I would aim for a median gross salary of 80-90kEUR/year and/or a minimum salary at or above 30 EUR/hour. I think this should easily push the employment numbers from no 40 million well below 20 million which to me seems much more sustainable long term.

Well, that's the political part of it. Retired people do not necessarily have to get less if the working age people pay a bigger share of their income as pension contributions. Remember that until about 40-50 years ago a median salary would be distributed among at least 5 - 6 people (mostly kids, and your wife, then). So technically, only 20% of the income was available to the one that earned it. In a time where there are fewer kids and more older people there seems nothing wrong with an arrangement where you pay 80% of your income for pensions

You are optimistic. IANAE (Economist) but as I read the stock indices we have had no growth outside of bubbles since around the year 2000. We may, of course, have a few more bubbles to prolong the time to the implosion. 30 years sounds a lot, though. That would need on the order of three more bubbles. What have we left to hype? Big Data, CRISPR, that's 15 - 20 years after the current QE bubble bursts. What then? Chinese-Europen Space Race, maybe?

Economically it is not a problem. It is only the PR that has been used for decades that is problematic. There is not point in having pension funds that accrue an interest (and that indeed rely on growth). A country generates a certain GDP in each year. It has to be decided politically what share of the GDP the working population, the pensioners, the sick, and so on deserve and than it has to be distributed according to the agreed upon scheme. After this it is gone and next year a new distribution has to be made. The crucial point is that your pension contributions are not in any way 'saved' or 'invested' for you but instead they are immediately spend on the current generation of elderly. Therefore the amount of pensions you are going to receive is also totally uncorrelated with the amount you paid earlier. If the population is getting younger and the economy is thriving you may indeed receive much more than you paid. But in these circumstances also prices will likely go up a lot because everybody has more money to spend so you are going to need it. If, on the other hand, the population is shrinking and the country is in the middle of a deep recession, you may receive much less than you paid earlier. Still no problem: Nobody has money so things will be cheep. However, if you think about your contributions as savings you could think they had a negative interest rate. They have not. You never saved anything, you paid your granny. However, apparently it seemed easier politically to sell your pension payments as savings with interest at a time when you could easily create that illusion. Now we have the problem that most people believe this is actually true while it never was.

s/good outcome/bad outcome

Why? I don't know why I should care about today if 2300 is not going to be better. Life seems far from optimal today, so if my purpose is not to gradually improve circumstances such that in the long run (so, realistically in a couple of centuries at the earliest) they are approaching an optimal state why should I bother at all? Then it seems to be simpler to just all die tomorrow. Then there is no human suffering anymore and the planet will be better off anyway.

1950's tech does not sound so bad to me. And imagine that crushing economy in 1900 would probably have made WWI less technical and more like a Napoleonic war. Still pretty bad for those involved but most likely less devastating for the general public. Also it would have produced a clear winner so may have avoided WWII. Combined with less polution & no internet this does not seem like a pretty good outcome. But of course it is hard to predict from today's prespective and would have been impossible to see in 1900.

However today we know that we need to be at zero carbon world wide in 10 years. There is no way we can still achieve this without crushing a lot. We may have been able to do it pretty mildly if we had started focusing fully on it 40 years ago. Now I think we can only try to crush anything at seems remotely disposable, take stock in 20-30 years and may then be able to reestablish a few things that, in hindsight, we had crushed unnecessarily.

I am middle aged now, so I am fucked anyway. I can either struggle through the necessary fundamental changes for the next 30-40 years and maybe see how things start to improve by the end of my life (given I live long enough) or I will be able to witness the mounting problems of climate change until, when I am old living standards will be pretty bad, society will be pretty transformed to the bad from continiously fighting the climate refugees and medical care will be minimal because we will of a dwindling economy. I would strongly prefer the first option but I a pretty certain I am going to get the second.

Fuel efficiency cannot have any effect in 2040 given that we need to be carbon neutral worldwide by 2030 at the latest

given that by The Paris Agreement we need to be carbon neutral world wide at the latest by 2040. As we probably cannot eradicate peat/coal burning everywhere in the world by that date, the industrialized countries need to be carbon neutral ten years earlier and decidedly carbon negative by 2040. Having any private transport based on fossil fuels in 2040 in the west seems to be totally out of question.