I'm no expert but, from what I understand, the idea is that they found two 3D shapes (maybe 2D skins in 3D space?) that have the same mean curvature and metric but are topologically different (and aren't mirror images of each other). This is the first (non-trivial) pair of finite (compact) shapes that have been found.
In other words, if you're an ant on one of these surfaces and are using mean curvature and the metric to determine what the shape is, you won't be able to differentiate between them.
The paper has some more pictures of the surfaces [0]. Wikipedia's been updated even though the result is from Oct 2025 [1].
Is it the case that 'they' are simply two ways of immersing the same two tori in R^3 such that the complements in R^3 of the two identical tori are topologically different?
If so, isn't this just a new flavor of higher-dimensional knot theory?
They don't appear to care about the images of the immersions or their complements, aside from them not being related by an isometry of R^3. They're not doing any topology with the image.
In other works, they have two immersions from the torus to R^3, whose induced metric and mean curvature are the same, and whose images are not related by an isometry of R^3. I didn't see anything about the topology of the images per se, that doesn't seem to be the point here.
As others mentioned, tool use wasn't restricted to homo sapiens. I think this makes sense, no? We didn't spontaneously use tools, it must have evolved incrementally in some way.
I think we see shades of this today. Bearded Capuchin monkeys chain a complex series of tasks and use tools to break nuts. From a brief documentary clip I saw [0], they first take the nut and strip away the outer layer of skin, leave it dry out in the sun for a week, then find a large soft-ish rock as the anvil with a heavier smaller rock to break open the nut. So they had to not only figure out that nuts need to be pre-shelled and dried, but that they needed a softer rock for the anvil and harder rock for the hammer. They also need at least some type of bipedal ability to carry the rock in the first place and use it as a hammer.
Apparently some white-faced Capuchins have figured out that they can soak nuts in water to soften it before hammering it open [1].
No, we could have had something which other previous species didn't that unlocked the use of tools. Otherwise if no species could be the first, or it would be deemed spontaneous, no new skills could be unlocked.
I will blame overlong copyright term lengths. 70 years after authors death or 95 years after publication, allowing most recent work to enter the commons effectively after a century, or more, from now [0].
This is the rare case when Europe is even worse. Metropolis, the 1927 Fritz Lang film, is out of copyright in the United States but will still be in copyright in Germany until 2047: 120 fucking years.
It’s preposterous, and offensive to anyone’s intelligence to claim that this is about incentivizing production; does anyone seriously believe there is a potential artist out there who would avoid making their magnum opus if it could only be under copyright for 119 years?
The problem is, copyright law is no longer about artists, if it ever was: it’s about corporations, i.e. maximizing the value corporations can extract from intellectual property.
"Why prediction markets aren't popular" [0] gives some compelling arguments (to me) about why prediction markets haven't caught on and probably never will.
As I understand it, the main argument is that for prediction markets that aim to incentivize the thing they're predicting, better to invest in the thing directly. Otherwise, "prediction markets" are successful precisely when they can't influence the outcome, like sports betting.
I remember finding the election betting interesting last presidential election, but I also remember that it was spiked when Musk invested to change the odds.
Musk, being the world's richest person, is something of an outlier. He can afford to give free money to the market for longer than anyone else, and the size of the market might not be big enough to handle the imbalance.
There's a level of irrational spending which only institutional investors can counterbalance, and they might not have the risk appetite to get into a single market on a relatively less regulated platform that could rug pull them.
My understanding is that unchecked wealth only remains that way until its owner acts irrationally on a stock exchange, at which point it is quite rapidly checked and becomes someone else's unchecked wealth.
Which is to say that Elon Musk can inflate any market he wants, but only by losing sums of money that will become increasingly significant as more and more people find out about the free cash giveaway.
There’s no functional difference in how markets work when 99% of wealth is owned by a handful of kings vs 99% of wealth being owned by a handful of oligarchs.
I don't really think so. You just swapped the term king to Oligarchs. In fact the Oligarchs are even worse because people think that they have freedom when they might not in fact have such freedom in the first place.
I don’t have an opinion on if it’s worse or not because some people mistakenly think they are free.
I meant that from the perspective of how market forces play out, hyper concentration of wealth into a few actors looks the same whether the title of the those actors is “king” or “oligarch”.
You start losing the wisdom of the crowds effect the market gives if you have a handful of people making the decisions for the entire market
I've also created a slightly modified version that includes graphics for the moon phases and different highlighting parameters, depending on whether it's a new or full moon [0].
That the FOSS bazaar broke off into megachurches while still maintaining a healthy small scale and independent bazaar [0]. That FOSS sustainability is much more complicated than just "throw money at it".
That there's "metal paste" [1].
That the zodiac killer's messages have been cracked for five years now (I didn't know they were cracked to begin with) and that it was a shift and substitution cypher [2]. The telltale clue was that the symbol frequency was uniform but under shift it become non-uniform.
How to solder those pesky connectors that come on the tiny servo motors you can get from Aliexpress [3].
That Firefox only has 2.3% market share [4].
Multiscale 3d truchet patterns are freakin complicated [5].
That prioritizing tasks by the linear combination of priority and effort remains a good strategy.
• Z408 (July 1969): Solved in days by Donald & Bettye Harden.
Message (with misspellings): “I like killing people because it is so much fun it is more fun than killing wild game in the forrest because man is the most dangeroue anamal of all to kill something gives me the most thrilling experence it is even better than getting your rocks off with a girl the best part of it is thae when I die I will be reborn in paradice and all the I have killed will become my slaves I will not give you my name because you will try to sloi down or atop my collectiog of slaves for my afterlife ebeorietemethhpiti”
• Z340 (November 1969): Solved in 2020 (after 51 years) by David Oranchak, Jarl Van Eycke, and Sam Blake; FBI confirmed.
Message (with misspellings): “I hope you are having lots of fun in trying to catch me that wasn’t me on the TV show which bringo up a point about me I am not afraid of the gas chamber becaase it will send me to paradlce all the sooher because e now have enough slaves to worv for me where every one else has nothing when they reach paradice so they are afraid of death I am not afraid because i vnow that my new life is life will be an easy one in paradice death”
Do you know what the single, most effective way to ensure end-of-life projects open sources the software and hardware? It's if it's *open source*.
Not assurances that if they meet their funding goal they'll open source. Not a pinky promise to open source in the future. Not magnanimous decision by upper management to open source if the business fails.
It's open sourcing from the outset so that people who invest in their technology can be assured they've fulfilled their promise to the community.
Pay for products that produce open source software and hardware. Pay artists that put out libre/free work. Demand projects that ask for money and "will open source in the future" open source now before taking your money.
In my view, finger wagging at corporate entities not open sourcing their products after end-of-life amounts to posturing.
> Pay for products that produce open source software and hardware. Pay artists that put out libre/free work. Demand projects that ask for money and "will open source in the future" open source now before taking your money.
This is the most important part. The markets can be shifted in our favor if the consumers unite and vote with our wallets. Even the biggest MNCs can't resist the demands by a united consumer front. Well known brands have been disappeared after they offended their customer base.
This is very difficult in practice, but not impossible. It will need a cultural shift among consumers and that will need a lot of grassroots work by a group of dedicated individuals. But it has been done before - for example, consider the role FSF played in making free software so common. To begin with, consumers have to be taught to believe in and rely on our collective bargaining power, instead of reluctantly accepting exploitative corporate bs. The next will be to take smart decisions on each product. Obviously, only a small group within the society would know what is harmful and what we really need. We should develop a culture where the concerns and recommendations of the subject experts are quickly disseminated among the larger consumer community.
I know the above sounds too ambitious. But it's not nearly the hardest goal anyone has achieved through sheer will. Whenever I raise this point in relation to any specific topic on HN, someone always replies with a cynical, dismissive and defeatist take, often arguing that the consumer-hostile product has the 'market demand'. They rarely address the market manipulation that the manufacturers resort to, and the fact that those poor product choices are the result of missing consumer vigilance. Besides it's easy to sound smart by scoffing at someone else's suggestions. But it takes hard work to make a positive impact on society with an original idea.
> The markets can be shifted in our favor if the consumers unite and vote with our wallets
This is very naive. "We can solve the climate emergency if the consumers unite and stop living the way they live", sure. But obviously the consumers don't do that, even knowing that their children will die because of it.
This is exactly the cynical, dismissive and defeatist take that I was talking about. Yet, we have numerous examples of this dismissal being wrong. Right now, free software is something we take for granted. But you have no idea what sort of great achievement it was for the early pioneers. Microsoft even used to call it evil.
> We can solve the climate emergency if the consumers unite and stop living the way they live
This is wrong in two ways. The first is that it is a strawman. The consumers are the biggest emitters. The big corporations, militaries and billionaires are. Second, we did solve a related problem with market pressure - the stratospheric ozone depletion and the ozone hole.
Again as I said before, it's easy to call it naive or scoff at it any number of ways. But people have achieved much harder goals. And that takes a lot of skill and effort.
> Second, we did solve a related problem with market pressure - the stratospheric ozone depletion and the ozone hole.
If you think that the ozone problem was remotely of the same level of difficulty as climate change, then you don't understand the problem.
> But people have achieved much harder goals.
There is no much harder goal than surviving on Earth, and we are measurably not only completely failing, but we keep accelerating in the wrong direction! We are making it worse, faster everyday.
> If you think that the ozone problem was remotely of the same level of difficulty as climate change, then you don't understand the problem.
Ozone depletion too was a global problem that needed international coordination to solve. But the reason why it was solved while the climate change crisis wasn't, isn't the 'level of difficulty' you're referring to. It's the perverse economic incentives behind the centralized fossil fuel trade. Unlike ozone depltion, climate change issue was known at least as early as 1892. We had more than enough time to find and implement the solutions. But even today when we have viable long term solutions, the pervesion of global politics against them is splendidly evident. We really could have solved the climate change crisis if we wanted to.
That's why I always emphasize shifting the market dynamics - the supply and demand balance. That's the only way we can overcome those perverse incentives. But people simply refuse to connect the dots that deep, instead preferring to insult those who do. And the reason is simple. It will break the comfort bubble that you're in, if you have to take some responsibility to solve it.
> There is no much harder goal than surviving on Earth, and we are measurably not only completely failing, but we keep accelerating in the wrong direction! We are making it worse, faster everyday.
If only there was/were some solution(s) for that.... Oh! Wait!
We have 3 problems that are the consequence of abundant fossil energy:
1. Biodiversity loss. We are measurably living in a mass extinction that is happening orders of magnitude faster than the famous one of the dinosaurs. It is due to what humans do when they have abundant energy. If we all had a nuclear reactor in our pocket, we would still be destroying the biodiversity, so it's not just a fossil energy problem.
2. Climate change. It's only the beginning, and the cause of it is the CO2 we release by burning fossil fuels. Society as we know it depends on abundant energy, and 80% of the energy we use is fossil. The solution to climate change is degrowth, but nobody wants to accept it.
3. Energy abundance. Energy became abundant thanks to fossil fuels, and those are not unlimited. Conventional peak oil was in 2008, and Europe's economy has been slowing down since then (though Americans like to think that it's slowing down because the Europeans are lazy). Eventually (soon), the global economy will slow down because of that. Which will bring global instability (even though now doesn't sound like the most stable it has ever been).
The only solution we have to those is that we need to stop living the way we live, and we need to do it fast. It's already too late so it will hurt, but the faster we react, the lesser it will hurt.
The reality is too bad for most of us to accept it, and by not accepting it we make it even worse. We're pretty much screwed. There is a business to make on "not being defeatist" and offering "solutions" for a "sustainable growth", but that's just business, that won't save us.
> This is the most important part. The markets can be shifted in our favor if the consumers unite and vote with our wallets.
have you even glanced at what touching hardware manufacturing involves? The amount of NDAs alone ends this. anything with a smidge of processor performance requires it, same for virtually every method of manufacturing anything.
> have you even glanced at what touching hardware manufacturing involves? The amount of NDAs alone ends this.
Do you think all that came out of the vacuum? It was set into motion over several decades of gradual erosion of user rights. Ultimately, everything is subject to the laws of supply and demand. If you can't see that far, you're thinking a level too shallow to see the problem and possible solutions.
> FSF did jack squat.
People don't simply scorn at FSF or anyone else like this just because they don't like it. I guess that explains the sophistication of your arguments.
To your point, market rewards are complex and doesn't always reward closed source. I would say the markets can reward companies that add value, and companies can add value by servicing a demand at reduced costs. One cost reduction measure is to use FOSS. For example, if you're building a data center, one cost saving measure is to use Linux as the underlying operating system over MS Windows.
I partially agree that pressuring consumers has issues, but the consumers we're talking about in this context are programmers, software developers, electrical engineers and other technically minded folk. Many projects only target dozens or hundreds "consumers" and, for those, advocating for purchasing FOSS might be a valid strategy.
I'm open to regulation but it's a coarse tool that favors large corporations. In my opinion, one way to larger regulation is to start small, show value from a growing community adoption and then try to push bigger. Linux was a toy operating system until it wasn't.
One minor point on regulation: From what I understand, there are some stipulations for (US) government grants to ensure FOSS artifacts get produced. I think violations of these conditions is common place. So we needed regulation in this area, we successfully got it and now we see that it's only as good as enforcement.
> For example, if you're building a data center, one cost saving measure is to use Linux
You're giving an example where a proprietary service benefits from open source. It supports the opposite point to what you're trying to say: not only the market rewards proprietary products, but open source actually helps proprietary products. If you open source your code, you risk helping your competitor.
> Many projects only target dozens or hundreds "consumers" and, for those, advocating for purchasing FOSS might be a valid strategy.
Again that's off topic. The goal is to enable technical people to make EOL products work for everyone.
> So we needed regulation in this area, we successfully got it and now we see that it's only as good as enforcement.
Which is a bit of a chicken-and-egg problem: in order for regulations to be enforced, we need the enforcer (a government) to be more powerful than the enforcee. But after we have allowed TooBigTech to appear and become more powerful than governments, it's difficult to expect anyone to enforce the regulations, right?
Such regulation would inevitably introduce exceptions for products with limited-time use (because it doesn't make sense to support everything forever), manufacturers would explicitly mark all products as such, and consumers wouldn't even find it wrong.
New incentives to would hit market reality where most people want cheap devices, not lifetime support for something they themselves consider practically disposable.
If most consumers don't care, regulation won't help. Much like climate change.
I'd like to hope my past work, and activity on social media/forums/mailing lists have been helpful in some way... although I admit I could probably do better. I haven't always been that good at self-promotion.
I'm sorry I don't have a better answer, unfortunately.
I think what they mean is that the data and code itself is libre/free/open [0] [1] but the API access is essentially rate limited for non-paying customers?
Hi, creator of Open-Meteo here. The limits are 600 calls / min, 5.000 calls / hour and 10.000 calls / day. Limits are applied on an IP basis.
This is not ideal for shared hosting services like cloudflare workers, but is the easiest and privacy-friendly way to limit access to fair-use.
Additionally, weather data is uploaded to a AWS S3 open-data sponsorship and you can run your own API instances (even commercially). The only draw back is, that a lot of data needs to transferred. I am working on a S3 cloud-native approach, but it is still in testing.
The free tier is cross-financed by commercial customers that use the service for energy forecasting, agriculture planing or wild fire prevention. There is no external funding, VCs, or whatsoever, the code is build in public on GitHub and I intent to continue running the free API service as is.
Most APIs, even ones you pay for, are rate limited. I don't think having a rate limit changes the open nature of the API. I'm looking forward to seeing if I can plug this in to my Home Assistant install for weather so I can compare it to Pirate Weather which I use now.
Agreed. I think the source code is open and I think the data is open. The by-line is just a bit confusing.
I think what they're trying to say is "Our service is completely open source. Our code is open source and our data is open source. We provide reasonable rate limits to our API access for non-paying customers. See our pricing plan if you'd like to become a commercial user and increase your rate limits".
In other words, if you're an ant on one of these surfaces and are using mean curvature and the metric to determine what the shape is, you won't be able to differentiate between them.
The paper has some more pictures of the surfaces [0]. Wikipedia's been updated even though the result is from Oct 2025 [1].
[0] https://link.springer.com/article/10.1007/s10240-025-00159-z
[1] https://en.wikipedia.org/wiki/Bonnet_theorem
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