I only skimmed this paper, but it doesn't mention floating point (it's only modeling the FNN as a function on reals), and I don't think you can extract a working FNN implementation from an SMT-LIB or Z3 problem statement, so I think you have to take on faith the correspondence between the implementation you're running and the thing you proved correct.
But that's the actual problem we're trying to solve; nobody really doubts Kalman's proof of his filter's optimality.
So this paper is not a relevant answer to the question, "how would you prove an implementation of a Kalman filter is correct?"
In most cases the data a kalman filter is working on has some precision which is much lower than the available precision in the floating format you are using. The problem is inherently a statistical one, since the expected precision depends on the statistics of your data source.
So you would probably adopt some conservative approach in which you showed that the worst case floating point rounding error is << some quantile of error due to the data.
That's a start, but you might be able to do better than that; for example, you ought to be able to show that the floating-point rounding error is unbiased.
There is nothing inherently difficult about practical implementations of continuous numbers for automated reasoning compared to more discrete mathematical structures. They are handleable by standard FOL itself.
Because most of the smartest people in the world moved to the U.S. because of the education system, great access to capital, and the fact that they and other smart people could easily move to, live and work with each other in the U.S.
The U.S. also has the largest useful single market in the world (the EU is broken up across many languages/cultures, China is isolated so you can’t really expand out).
The U.S. is actively working to destroy several of those planks right now.
Even the capital plank, which superficially looks strong, is being hurt by the government picking winners and choosers. If the current govt bets don’t turn out to be the right ones we’re looking at an ugly, probably tax payer funded (OpenAI has already hinted at this) collapse.
> Jobs that have a high 0-1 component will still be in the US but jobs that are more 1-n may be offshored.
It used to be (since at least mid last century) and 0-1 and 1-n jobs were focused here. The world becoming smaller allowed a lot of 1-n jobs to move abroad. But we kept 0-1 jobs here.
That used to be the situation when the country brought people from around the world to be educated and then start business here. And historical precedent allowed us to continue thise advantages by having a reputation for it and continuing to support it. Our country for some reason now has decided it no longer wants to take the actions that fill the pipeline for 0-1 innovation.
And the world just like it took over 1-n is going to take over 0-1.
Why you would choose catalyze that change as an American, I have no idea.
I think there are people that generally believe that there is magic dust that says it can only happen on US soil instead of there being structural actions taken to enable it.
We will all very quickly learn that 0-1 can be anywhere that 1-n is.
It is less so about skills of workers. And more so about having lot of investors who are willing to throw money at everything and then even more after the fact. Or to just outright having enough money to buy out the better ideas.
That's not even close to remotely true. If that is the case, why is the UAE throwing their money at US startups and not their own? They have more than enough "capital".
The source for China's energy is more fragile than that of the US.
> Coal is by far China’s largest energy source, while the United States has a more balanced energy system, running on roughly one-third oil, one-third natural gas, and one-third other sources, including coal, nuclear, hydroelectricity, and other renewables.
Also, China's GDP is a bit less inefficient in terms of power used per unit of GDP. China relies on coal and imports.
> However, China uses roughly 20% more energy per unit of GDP than the United States.
Remember, China still suffers from blackouts due to manufacturing demand not matching supply. The fortune article seems like a fluff piece.
China has been adding something like a 1GW coal plant’s worth of solar generation every eight hours in the past year, and the rate is accelerating. The US is no longer a serious competitor for China when it comes to energy production.
The reason it happened in 2021, I think, might be that China took on the production capacity gap caused by COVID shutdowns in other parts of the world. The short-term surge in production led to a temporary imbalance in the supply and demand of electricity
This was very surprising to me, so I just fact-check this statement (using Kimi K2 thinking, natch), and it's presently is off by a factor of 2 - 4. In 2024 China installed 277 GW solar, so 0.25 GW / 8 hours. First half of 2025 they installed 210 GW, so 0.39 GW / 8 hours.
Not quite at 1 GW / 8 hrs, but approaching that figure rapidly!
(I'm not sure where the coal plant comes in - really, those numbers should be derated relative to a coal plant, which can run 24/7)
> (I'm not sure where the coal plant comes in - really, those numbers should be derated relative to a coal plant, which can run 24/7)
It works both ways: you have to derate the coal plant somewhat due to the transmission losses, whereas with a lot of solar power being generated and consumed on/in the same building the losses are practically nil.
Also, pricing for new solar with battery is below the price of building a new coal plant and dropping, it's approaching the point where it's economical to demolish existing coal plants and replace them with solar.
China’s breakneck development is difficult for many in the US to grasp (root causes - baselining on sluggish domestic growth, and possessing a condescending view of China). This article offers a far more accurate picture than of how China is doing right now: https://archive.is/wZes6
I don’t remeber much details about the situation in 2021. But China is in a period of technological explosion—many things are changing at an incredible speed. In just a few years, China may have completely transformed in various fields.
Western media still carry strong biases toward China’s political system, and they have done far too little to portray the country’s real situation. The narrative remains the same old one: “China succeeded because it’s capitalist,” or “China is doomed because it’s communist.”
But in reality, barely a few days go by without some new technological breakthrough or innovation happening in China. The pace of progress is so fast that even people inside the country don’t always keep up with it. For example, just since the start of November, we’ve seen China’s space station crew doing a barbecue in orbit, researchers in Hefei working on an artificial sun make some new progress, and a team discovering a safe and efficient method for preparing aromatic amines. Apart from the space station bit—which got some attention—the others barely made a ripple.Also, China's first electromagnetic catapult aircraft carrier has officially entered service
about a year ago, I started using Reddit intensively. what I read more on Reddit are reports related to electricity, because it involves environmental protection and hatred towards Trump, etc. There are too many leftists, so the discussions are somewhat biased. But the related news reports and nuclear data are real. China reach carbon peak in 2025, and this year it has truly become a powerhouse in electricity. National data centers are continuously being built, but residential electricity prices have never been and will never be affected.China still has a lot of coal-fired power, but it continues to carry out technological upgrades on them. At the same time, wind, solar, nuclear and other sources are all advancing steadily. China is the only country that is not controlled by ideology and is increasing its electricity capacity in a scientific way.
(maybe in AI field people like to talk about more. not only kimi release a new model, Xpeng has a new robot and brought some intension. these all happends in a few days )
> China is the only country that is not controlled by ideology and is increasing its electricity capacity in a scientific way.
Have recently noticed a lot of pro-CCP propaganda on social media (especially Instagram and TikTok), but strangely also on HN; kind of interesting. To anyone making the (trivially false) claim that China is not controlled by ideology, I'm not quite sure how you'd convince them of the opposite. I'm not a doomer, but as China ramps up their aggression towards Taiwan (and the US will inevitably have to intervene), this will likely not end well in the next 5-10 years.
I also think that one claim is dubious, but do you really have to focus on only that part to the exclusion of everything else? All the progress made is real, regardless of your opinion on the existance of ideology.
I mean only on this specific topic: electricity. Arguing with other things is pointless since HN has the same political leaning as reddit so I will pass
I don’t have one now. I used to post lots of comments on china stuff but I got banned once and every time I registered a new one it will be banned soon. I guess they banned all my ip. So I only go anonymous now
It's absolutely impressive to see China's development. I'm happy my country is slowly but surely moving to China's orbit of influence, especially economically.
"Not controlled by ideology" is a pretty bold statement to make about a self-declared Communist single-party country. There is always an ideology. You just happen to agree with whatever this one is (Controlled-market Communism? I don't know what the precise term is).
I cannot edit this now so I want to add some clarification, it just means on this specific topic: electricity, china dont act like us or german, abandoned wind or nuclear, its only based on science
How does this work with other countries not enacting 32-hour workweeks?
This will be a repeat of manufacturing going outside of US due to reduced standards (labor and pollution) and therefore cheaper manufacturing in China. And due to that blue collar work got destroyed in the long term.
Logically, unless there are high trade barriers for software/services/goods from countries that don't have similar standards, long-term, these jobs will just shift there.
One of Henry Ford biggest push was for a 5 day work week when no one else did it. Why? Because it meant workers had two days of week to spend money which increased consumer spending and look at the US today. Our consumer spending is about 2/3 of our GDP spending. I'm not saying you're wrong. But there's more to "drive your workers to the bone means we get better productivity and economic conditions". The biggest mistake the US is making is not capitalizing harder on onshoring + robotics.
On the flip side I would argue that European countries have largely fell flat or negative because employment law is too generous and it forces companies to be too cautious in hiring. I don’t know what the right balance but I am not sure going for even fewer hours is the right move.
I assume we agree that working less produces less (which reasonable people debate) since otherwise competition from abroad wouldn't be an issue.
If that is the case, then adding trade barriers also doesn't fix anything. Adding the trade barriers would ultimately just produce a lower standard of living. You'd essentially have an isolated system and the system is now producing less, so necessarily there will be less for everyone in the system.
Adding trade barriers also doesn't fix the threat of an adversarial country working 50% more than you for the next 50 years and as a result having the infrastructure to dominate you in numerous ways.
> I assume we agree that working less produces less
That’s a pretty big assumption. From what perspective, since the “working less” is only the perspective of the worker?
Production is not a zero-sum game that assumes companies make zero effort to invest in more manpower rather than profits.
Profit rates, however, are a significant part of the problem as each US company in the chain attempts to maximize profits they obtain from the next and avoid any competition (often using the legal system for protection). That doesn’t occur in the areas you mention because competition is the name of the game in those countries, which is why they have maximized production and flexibility.
> I assume we agree that working less produces less
Per capita, let's say yes, though I think there are people that assert that individual productivity is higher when working less hours.
But as a whole, probably not. In aggregate companies will pay more people less money, to do the same amount of work, so I think it should balance itself out.
It seems that most peoples of most countries have an unquenchable thirst for more, yes. No one forced the car, the smart phone, the sugary snacks, cheap plastic toys, ... to exist. They exist because people want them.
Maybe certain people think they are made of better clay than the average consumer and should determine what everyone else can buy; that path is a dangerous one...
Maybe certain people shouldn't be so quick to call other people fascists just because they voiced a thought on capitalism's need for infinite growth. Ironically enough, certain people are the thought police here, with a dangerous path...
I didn't claim that anyone did.. If you didn't notice, I just used the same construct as the person above me to throw out accusations with deniability.. But we all know what they meant, and that was a wild take based on my simple question.
I'm a senior South African software developer (let my add my perspective here).
In terms of hours worked per week, I have rarely worked more than 40 hours per week (and I mean by that that I'm contracted for 40 hours and rarely work overtime). I know people who work more than that, and sometimes much more than that, which is a function of their skills and what kind of job they can secure (as well as their appetite for overtime), but I'd say my situation is fairly normal for people with ze skills. I also worked at a company which did 32 hour work weeks (which they did as a perk to retain people, not because they were forced to).
Software dev skills are quite scarce here, and South African devs are already cheap enough that it is difficult to try and offshore that work (although I know a few SA companies which have contracted companies in India for work). I also know many SA devs who have emmigrated to other countries which themselves have scarce software developers, but where the salaries and "standard of living" is perhaps better.
> Many countries have <40 hours/week and are still thriving.
May I have the list of such countries with a level of prosperity comparable to the US (which seriously consider an $85k tax-free minimum wage)?
Your "everything is still thriving" on paper turns out to be "everyone except the elite is drowning in poverty and they can't complain about it because then their totalitarian government will declare them terrorists or something" in practice. All the time.
You may be right about some parts of Europe, but I think you would be surprised just how prosperous at least the northern part is, despite sub-40 hour work weeks and comparatively high taxes, 5-6 weeks paid vacation and “socialist” politics.
California is the only state I’ve visited in the US, but I would say Scandinavians are wealthier on average/higher quality of life.
> 5-6 weeks paid vacation and “socialist” politics
I'm not even surprised.
Socialist politics are extremely good at ensuring a high standard of living for the elite and shutting everyone else up. Look at any North Korean media outlet (of two or however many) - they're the best in the world, and everyone else is envious of them.
Are you under the impression that North Korea is an actual socialist country? Just because it's in the name it does not make it so. I thought history thought us the lesson about that.
> Socialist politics are extremely good at ensuring a high standard of living for the elite and shutting everyone else
European social democratic politics are usually characterized by the opposite outcome, where high taxes and redistribution means the top 10% is much closer to the average Joe than in ultra capitalist countries. Less inequality in general.
> Look at any North Korean media outlet
If you seriously compare NK to any country in Europe, you have no clue, sorry.
No. Look at the median salary of a full-time worker in Europe and compare it to the US. They are drowning in poverty.
> top 10% is much closer to the average Joe
No. In the US top 10% full-time workers get you what? About 300k? It is way closer to the average US Joe than Europe has it's top 10% to their average poor workers. There is more inequality in Europe than in the US.
> If you seriously compare NK to any country in Europe, you have no clue, sorry.
Why? Because you chose to trust European propaganda and not North Korean propaganda? Ask those who chose to trust North Korean propaganda what they'd tell you.
Notably EU countries don’t produce as many large or global software products. I know they have some companies of renown but not to the degree the US does.
There may or may not be a connection to work habits, but we should find out and then decide if we’re okay with the consequences (like the lowest GDP per capita state (AL) being on par with Germany). Maybe we’re okay with playing second fiddle. But we should know what we’re in for.
I think real reason is less willingness to make massive bets on everything. In ZIRP environment that played out great on paper. But we really have to see how will it do with AI...
Denmark has 37 hours/week. Netherlands is around 32-33 on average AFAIK. Switzerland is ~35 hours/week. Ireland and Austria are also well below 40 to my knowledge.
Most research shows that non-mechanical work (i.e. where you have to think a little), gets a lower work-output above 40 hours/week than below. If sustained, it’s not just diminishing returns, but lower absolute output, even at just 3-5hours weekly overtime.
Sorry, I am not Swiss myself, so I may be completely mistaken.
I read that the average working hours is ~31/week. Digging further into that, it was the number of actual working hours on average (including part time and self-employeds), not what constitutes full-time employment.
Fair enough. Once you get into actual hours worked, you have a lot of people working less than FTE numbers by quite a bit.
For example, once the maternity leave runs out, in finance a lot of couples go to 80% so that with 1-2 days of home office you can always have someone watching the child. It's less money but the nurseries are so crazy expensive in Switzerland that it can actually even be positive in terms of total (edit:net) income.
I am not sure if we are in disagreement, but I believe my point stands: that Switzerland is a rich country despite working less than 40 hours/week on avg (actual hours).
In Norway 40 hours is the maximum legally allowable (other than temporary overtime), most people have 37,5 hour work week. If one in addition count vacation days etc the difference between other countries and the US might be even starker, in total hours per year?
> Many countries have <40 hours/week and are still thriving.
But it's a fiction built on U.S. force projection. It's become apparent that none of these countries could defend themselves against an aggressive competitor.
Well you are comparing a single country of over 300 million (the US) with the countries in the EU that are on average 16-17 million. Do you think that makes sense?
Idk historically some European nations like Germany have been very successful at least at starting wars and people had their hands pretty full trying to defeat them.
I don’t think their past WW2 docility can be attributed to their inability at doing heavy industry or weapons development
I wonder if there could ever be a tariff policy that is automatically proportional some measure of worker/environmental exploitation. I know tariffs are current very unpopular, but maybe they can be used for good?
Neither am I. But how do you prevent countries doing 996 from dominating the market like they did in manufacturing without strict regulation and barriers?
> how do you prevent countries doing 996 from dominating the market
Why do you need to? Is this a manifestation of American exceptionalism, or do you think that overall as a nation you get a better life for your citizens when you're at the economic top?
It's not a manifestation on anything. What's cheaper with better quality will be chosen by the consumer. To get cheaper economies of scale are needed.
My competitor has a contracting factory in Pakistan that has the same labor costs as me, but works for 50 hours, instead of 32 hours. He can produce 36% more per week, while paying the same cost of capital, opex and other costs, even if he pays the same per hour as me.
But if he has 1/10 of the cost of labor and labor is a high % of end product cost, I can't compete and my business is bust, my employees are on the street and we all live from
1. the taxes of the productive people in the society who can sell something competitively outside (to have currency to buy imports)
2. governmental loans to be paid in the future by the people from 1.
I said "more people for less money"[1]. Nothing prevents your company to pay more people to work those 50 hours a week and pay them the same you would pay a single person working them.
[1] Sorry, I said that in a different comment in this thread.
if you step outside our IT bubble absolutely. Manufacturing & Services can produce an awful lot of meaningful, measured value with an extra 8 hours a week.
Engineering isn't an assembly line job, though. If you're brain's tired, you may be on the clock, but you aren't going to be as productive as you would be if you were fresh.
I mean, other countries are working their employees to the bone. Some employee children, some have slavery.
Should we go ahead and bring back slavery for "competition"? I mean, you can't compete with free labor, right?
We have to draw the line somewhere, and that somewhere is arbitrary. We're not changing any decisions here - 32 hours/week is equally as arbitrary as 40.
Look at Germany, their highly profitable companies have moved so much outside of the country, because they can't produce a competitive product inside with the strong unions, well-meaning green taxes and giving too much to the unemployed imigrants coming as social security and benefits.
When you start overtaxing, you are just milking the cow and not feeding her enough. She'd last for some time but then't you won't have a cow and milk.
You're absolutely correct, but most people don't understand how even a simple "village-size" economy works. They think money is just "printed" and "government will enforce our standard of living".
Better work 996, American techies. Never demand higher standards from your owners, or they might replace you with Chinese, and then where would you be?
I feel these agreements are highly asymmetric and are used to gain market advantage by countries that don't have qualms violating these agreements behind closed doors.
This then leads to more pollution.
Before Trump, the US had a higher rating than China (though both were bad):
Is there any proof that countries who agree to these accords are cheating behind closed doors?
As far as I can tell it would be a relatively straightforward thing to measure (how else are we getting these per country reports on emissions?)
Given that, I’d expect it to become obvious if they are cheating the accords.
And as far as markets go, I believe quite strongly that’s a failure of our economic system. It fails to account for externalities appropriately. If things were priced with externalities accounted for it would change consumption patterns dramatically
> What kind of leverage does this give countries to penalize others
In the case of China, it's pushed them to make headway in the process of building a manufacturing infrastructure that is more insulated from global energy price swings. IIRC they can also power much of it more cheaply (e.g. solar has no fuel cost), which provides them with a cost advantage.
As we have repeatedly seen, there is also leverage to be had in not having one's country internally levered to global oil prices.
So it provides leverage, but not to directly penalize.
That’s usually true. But the US has more to lose in such a move. So and without the US it loses energy. So this is more about bringing the world to think harder about resource management
2. > Because the doctor will rigorously apply artificial and unreliable diagnostic categories backed up by invalid and arbitrary screens and queries to make a diagnosis. So after this completely subjective and near useless evaluation is completed, your doctor should be able to exercise prudent clinical judgment to decide if Ritalin could be of benefit.
What else can you do for psychiatric conditions? We don't have a magic ADHD-o-meter but know that it statistically impacts lifespan, health, etc. Even for more objective measures like blood glucose, BP, BMI, clinical interventions are based on discrete thresholds that don't exist in nature.
No one is saying that the industry will self-regulate. There is a right amount of regulation and all evidence points that the EU is over that limit. The US is below (probably) but closer.
Europe has a borderline shrinking economy and failed to become a player in the advanced technologies driving the world economy today. It's because they created an extremely hostile business environment, leading to founders going to the US to start their business there instead.
So now Europe is a continent full of people using American made software, running on American and Chinese made hardware, going on American social media to talk about how Europe is totally fine because they only work 9 months out of the year and don't allow young people to become billionaires.
I do think Europe should become more self-reliant. I also work a lot and rarely take any vacation time, but I don't see any sense -- except for egoism -- in working so much just to spread more AI slop online, mislead and polarize societies, or support a genocide. I think Europe has learned its lesson during the World Wars.
Clearly US Republicans, Russia, and Israel drive a push towards nationalism. Republicans and Elon Musk openly campaign for far-right European parties like AfD. You're getting causality wrong, or just don't want to recognize it, because the reality (rightfully) isn't as motivating as your image of it -- at least it shouldn't, but do you care?
>If China is the factory for all of these products sold in the US (and elsewhere of course), then isn't China just accounting for even more US emissions?
China can't have it both ways, they are glibly blaming the rest of the world for their emissions while reforesting due to importing timber from rest of the world illegally.
> The Environmental Investigation Agency says: "The immense scale of China's sourcing [of wood] from high-risk regions [of the world] means that a significant proportion of its timber and wood product imports were illegally harvested."
And research by Global Witness last year said there were "worrying" levels of illegality in countries from which China sources more than 80% of its timber.
I'm not talking about China's position, but thinking about texture of the emissions reductions in the rest of the world.
It's probably fairly unknowable what percent of emissions are for products that will be exported back out from China, but I think it's reasonable to say that when I buy some random wooden table from China and import it into Australia (for example), that I am at least somewhat responsible for those emissions, even if per-country emissions data doesn't reflect that!
I don't think this is some free pass for Chinese ecological behavior overall. My general hypothesis has been that at least some part of emissions reductions in the US and Europe are due to outsourcing. I just don't know how much of it is that.
We shouldn't consider the fact China did much more deforestation to start with and even after all this reforestation China has lesser forest area than the US despite being larger in size:
> The US claims: "China is the world's largest consumer of illegal timber products."
> And, according to studies, that is true.
> The Environmental Investigation Agency says: "The immense scale of China's sourcing [of wood] from high-risk regions [of the world] means that a significant proportion of its timber and wood product imports were illegally harvested."
And research by Global Witness last year said there were "worrying" levels of illegality in countries from which China sources more than 80% of its timber.
Just as with CO2, a better comparison would look at per-capita figures and the destinations of consumption--for instance paper and furniture for export.
It may also take into account the viable land area, lest we also want to condemn Australia for having so much less forest area despite being similar in size to the US.
well, china also has gigantic northern and western regions that cannot be forested. the us doesn't have an equivalent of the tibetan plateau or the gobi desert
https://arxiv.org/pdf/2304.10558