Maximally, a closed form solution would remove the need for Computational Fluid Dynamics. Any property could be derived from a (presumably expensive) analytic function.
Minimally. It could say that no such analytic function can ever exist. Which would be rather boring.
Turbulent fluids look awfully predictable with their spirals….
That would be surprising IMO. We have closed form solutions to Newton’s Laws plus gravity (albeit not very many of them), we have several closed form solutions to Einstein’s equation in GR, and we have a whole lot of closed form solutions to Maxwell’s equations. But we still use numerical methods to solve interesting problems in all of these fields.
The surface of bugs in Lean is infinitely smaller than the human error involeved in a committee of peer reviewers. It's way more probable to say "it's proven because Lean says so" than "it's proven because a couple of reviewers said so".
Also, if a bug is found, all previosuly proven theorems can be reproven to immediately and conclusively find out if things went wrong somewhere
Exactly, and the advantage is that checking that the problem is "formalized" here is essentially isolated to verifying that the final theorem statement matches the claim. If there are no 'sorry's and the program compiles, then it has been proven. That's the point of Lean.
As the recent "proof" of the Collatz conjecture shows, that's not enough in an adversarial context. Human mathematicians don't submit proofs that take advantage of soundness bugs in Lean. AIs do.
Each word of your answer is carefully chosen. I'll add one sentence though: you let time do its job.
Of course there may be errors in lean, of course AI can take advantage of it, of course "carefully" is full of errors. So the only thing left is waiting to see if the result holds. And yes, it may take 30 years...
That seems to be a recurring theme regardless of the country's economic system. We're two months away from seeing if the US still has a working succession strategy.
I think we're getting to the point where it is difficult to identify the goal post of AGI.
Is it rapid skill acquisition? -> ARC benchmarks are saturated
Is it breadth of knowledge? -> See many ... many benchmarks
Is it ability to do hard tasks? -> see terminal-bench and released outputs.
We are at the point where the starting point for most tasks should be "send your agent to work on it."
So where do we draw the line in a way that doesn't move every 6 months?
The real answer is converting from any format to any other reliably. Text to speech, speech to text, music to video, image to 3D, piloting a drone by converting video feed to rotor speeds, literally any file conversion, like html to pdf, photoshop project to png, png to photoshop project,... turning Toy Story 1 into a series of Blender scenes with all textures, models, materials, lighting, camera movements matched to a tee, should solely be a matter of how long you let the model run. It should never run itself into a dead end. It should instantly know when it is making mistakes, with no human babysitting it.
I can do none of those things.. I hope that I am generally intelligent.
1 year ago we viewed models as tools and agents were just kinda toying around, that we now think the bar is literally an anything to anything converter through one agent is wild.
Professionals in the respective fields CAN do those things. We expect them to notice their own mistakes too. But the bar gets lowered and lowered as AI companies struggle to make ends meet.
Then why does the expensive treatment cost 7 figures? Estimating hospital costs is hard, but a quick glance at many buildings/offices would tell you that they are by no means struggling.
We overpay for healthcare because we must pay, and it has institutional and natural bottlenecks which restrict availability and choice.
Because they are going to allocate as much as they can to that service that is actually using those advanced facilities. The stiches patient in the ER is carrying some load for the cardiac surgery suite just not as much as the person who actually has quadruple bypass. Plus that is just part of it. They're also covering uncompensated costs across the whole system
Even if you only have stitches you want the ER to have those machines just in case the doctor looks at your injury and says "wait, this isn't the standard routine thing everybody has we need to get you into the expensive machines". Probably this will never happen - the doctor will always look and see the standard routine things that everybody has and you don't need the rest.
This is why urgent care exists and is why if you don't have something that you think is life threatening, that's almost always better. If you need more than they can provide, they can and very much will forward you on to an ER
Most of the minor lacerations which require stitches to heal cleanly can be handled perfectly well in urgent care. There's usually no need for ER level care.
Elective surgeries have fallen in price because many no longer occur in hospitals. In the USA, ERs have to treat everyone regardless of their ability to pay. That's why you see a lot of urgent care.
A lot of big enterprises struggle with ai adoption. Either they can't get models/tools approved fast enough, can't provision them in their internal network, or get slammed with exorbitant inference costs.
A big enterprise can drop one (or 4) of these on someone's desk and let them go nuts.
There are many enterprise environments where running modern models is... difficult. Rather than fighting security for months, a user could petition for a mac studio and have rough cost parity with a z.ai subscription.
if they are a heavy user, perhaps they string 4x together.
As a kick-starter project is this thing actually real? My experience with kick-starter has been that the projects are almost universally faked.
I've only contributed to three kickstarters, and they all worked out well. But I think I'm more selective than most people, and generally don't jump on something until it's already been fully funded by other people.
It's certainly overly broad in many circumstances. I've lived in a townhome community with overly aggressive management.
However, "There is absolutely no reason why a single family house needs to be in a mandatory HOA" is easy to refute.
HOA's provide a way for managing shared infrastructure that would not be feasible for a single home owner. Common examples of basic infrastructure include roads, storm water management, lighting, and even community wells. I would argue that is the primary purpose. Not all neighborhoods are in a municipality either.
Not all neighborhoods are in a municipality either.
why is that? and why is the county or state government not taking over the responsibility then? for example in germany a democratic local government is guaranteed by basic law, so a neighborhood outside of a municipality is practically not possible and considered a violation of basic law.
Municipalities in the US are the same type of institution as HOA, self-organized to maintain property. Just like you may not have an HOA you may not have a municipality of any kind. Counties and states are usually not equipped to do maintenance work, same as the federal government. I also don't understand the preference of city government over HOA - it's not like cities don't have codes and you can do whatever you want with your property. It's subdued now but couple years ago we had anti-zoning posts as frequently as we have anti-Flock. Who creates zoning? The city does.
the difference is that HOAs are private and not state actors, when they really should be. that has some constitutional implications. they are not democratic because usually only property owners are voting members based on the size of the property. in a municipality everyone living there gets one vote.
you are right that in practice the difference may not be that noticeable, but i believe that not being state actors is a significant distinction. if it acts like a government, and if it quacks like a government it should be a government and be subject to those same rules.
not having a municipality of any kind in my opinion is an oversight of state/federal law. people should have democratic representation whereever they live. HOAs don't provide that.
What do you mean they are "private"? HOA literally means the association of all home owners, who are members and set, follow, and enforce its bylaws. It's a public institution, same as a municipality. The difference is in how each is established and controlled, but neither is private.
A homeowner association is a private, legally-incorporated organization that governs a housing community, collects dues, and sets rules for its residents.
A public institution is a juristic person in the United States which is backed through public funds and controlled by the state.
HOAs are not controlled or funded by the state, no more than Private Businesses are. municipalities are controlled by the state.
if municipalities have the same reach into how people manage their homes like HOAs do then the distinction may not matter. it is however a legally significant distinction.
one point where the distinction matters is that HOAs can limit your freedom of speech, while municipalities can not.
By your definitions public companies do not exist - most public companies are not funded by state. But sure, in this framework HOA's are "private" but so are the municipalities - they are not funded by state. And, obviously, everything is controlled by state - we have laws and regulations, both from the state and from the federal government.
>if municipalities have the same reach into how people manage their homes
Municipalities have bigger reach because they also control what you do inside your home. Codes are more expansive and detailed than any HOA bylaws and cover interior much more than the exterior. And, of course, the municipality controls if you can live in your house at all and can kick you out if it wishes so.
we are simply using a different definition of public and private. i am using the legal one: public is government, private is everything else. i explained why the distinction matters and what effects it has.
your points are valid but arguing about the definition of what is public isn't helpful.
same goes for government control. you are not wrong, but again, the legal difference in what that control is matters. private entities have constitutional protection and rules that are clearly defined and distinct from the protection and rules for public institutions. the control the government has is simply different and that difference matters.
the bigger reach of municipalities doesn't go away in HOAs because most HOAs are within a municipality. that makes HOAs at best redundant, at worst you have to suffer both. at least with municipality you have democracy on your side. HOAs are controlled by owners, everyone else is second class. that's not a democracy. the result is that the combination of government and HOA gives you less freedom than government alone. HOAs don't replace the government, they don't make it go away.
HOAs in my opinion should be treated like government entities because they are given quasi government like powers without the same checks and balances that government has. they aren't and for me that's a problem.
We are not in a court, so even if there was a legal definition of "public", which does not appear to exist, it would not matter. The question is why HN "urbansits" are so livid about HOAs and want to replace them with municipalities. The reasons I see are pretty bizarre: while not having both makes some sense (in case you optimize for the absolute minimum regulations over everything else), this thread is specifically about replacing HOA with a municipality in case when only the former is present, which means more regulation. Your democracy argument makes no sense to me: the vote is always restricted, in HOA to owners (or rather to properties themselves, a husband and wife co-owning a home don't get two votes), in a city - to residents (and on some matters, to property owners only). In neither everyone can vote.
HOAs are already treated as government entities - their bylaws are not different from the city ordinances, their fees are as same as city taxes and they are hard to get rid of. I imagine you mean something else since in your country the government is descending from feudal lords and your municipalities have started as fiefs. But in the US only similar government is at the state level, the states have constitutions and laws, everything else is what you would call "private" - townships, PTAs, school districts etc are essentially corporations.
In the past, a professional job might mean extended periods of travel by rail etc with little work to do. A small acreage farmer has to wait for plants to grow.
The advent of factories with limitless and constant demand for labor is a new development of the industrial revolution.
That doesn't mean that there isn't any downtime though. Most activity would be confined to daylight hours if nothing else. You'd probably do less on rainy days, and avoid hard work during the peak heat hours in the summer.
Minimally. It could say that no such analytic function can ever exist. Which would be rather boring.
Turbulent fluids look awfully predictable with their spirals….
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