I think progress per dollar spent has actually slowed dramatically over the last three years. The models are better, but AI spending has increased by several orders of magnitude during the same time, from hundreds of millions to hundreds of billions. You can only paper over the lack of fundamental progress by spending on more compute for so long. And even if you manage to keep up the current capex, there certainly isn't enough capital in the world to accelerate spending for very long.
Probably by just thinking about it and working to incrementally improve their answers. I'd expect plenty of people solved it before them but never published or publicized their solution. It's quite logical in many ways. For instance just thinking about the problem abstractly:
- You can only have 9 queens and they're going to want to be as centrally placed as possible with as little overlap as possible.
- The black king will need to be tucked in a corner and covered by a minimum of his pieces and nonchecking pieces of your own.
- All your other pieces, if useable, will probably end up on the edge of the board since minimizing the number of squares they block is likely to be more impactful than maximizing the number of squares they cover.
There's probably other heuristics I'm not considering, but just with those 3 you're already well on your way to the solution. So you'd lay out the pieces, and then try to find a way to do it one move better, and iterate! The concerns I'd have: pawn promotion can complicate things dramatically. Pawns can promote to 4 different pieces which would technically be 4 different moves. And a pawn can have up to 3 different paths to promote - so that's 12 possible moves tucked in a very tiny space. And then king placement - castling can add up to 2 more moves, and so compensating for that (and the corresponding rook position) adds some complexity.
Composing such a position is much easier than mathematically proving that there isn't a better one. Perhaps there is an elegant proof. Perhaps they had reasoning that proved that they couldn't do better while composing it. Probably involves plenty of case distinctions. So I decided to just let a computer reason through it, also because human minds are fallible ^^
Glancing at it a chess players first instinct looks to be the "solution".
Assume all pawns are queens, then maximize queen moves, work backwards from there. Couple of other "obvious" assumptions such as minimal black pieces, which means shoving the king in a corner but somehow not in check, Rooks cover the next largest amount of space so they're going in corners, bishops will be mirrored, etc.
Not to say it isn't still impressive, but I always wonder how many "sane" positions there are for solving a puzzle like this in the first place. The paper quotes some huge number and someone else says it's a smaller, but still massive, number, but when you look at the stated goal and start from some obvious starting points, start working out rules (obviously 4 queens right in the middle blocks other queens and costs space), and eliminate symmetrical positions, well you're left with a decently solvable problem. At least compared to the kind of shit that's usually brute force solved.
Edit:
This is actually a fun one to think about for a bit the more I look at it.
It quickly becomes apparent that your basically getting 7 moves out a of a rank/column MAX, so you maximize for that first.
It quickly becomes apparent that the knights L move shape is also the optimal way to start tiling your 9 queens to maximize for squares taken.
As I said before the black position obviously has to be the dead minimum, and it makes sense that'd be a king and 2 pawns due to various end game stuff (basically impossible to prevent the king from being in check otherwise while taking up as much space as possible).
Once you know you're doing that with the black king you'll want to "block" the remaining space with pieces that can't threaten it, so you shove a bishop adjacent (which can still take the pawn), and figure you're going to mirror that bishop because that's kinda how bishop's work in play/mathematically.
It's actually quite neat to see how each step sorta leads you to the next one, like one of those metal puzzles or the sudoku's with unique rules and only 1 or 2 starting numbers.
Still i'm positive if I hadn't seen this picture first I probably NEVER would've gotten this answer correct, but I do think i would've come closer than I ever expected.
Edit 2:
Ahh i do see they have at least one or two solutions that are 218 where there's only 2 black pieces. I'm somewhat surprised that's a possible legal position but so be it. Interesting that still leads to the same net realestate. Thats the one area i'd expect to gain something if you could cheat.
In addition to it being fun to do it yourself, it's still possible for an amateur to beat the pros in certain areas like finding new comets (like 2I/Borisov).
It's kind of ironic that a nominally communistic government doesn't believe that the people have agency to act on their own, guess it reflects their own fears. I hope Xi lies sleepless at night worrying about the Chinese people getting rid of him.
The average Chinese who’s seen China progress by leaps and bounds continuously over the past 40 years probably wants this to keep up. So why change something that’s working?
It only sucks for the people who oppose the ruling party, the dissidents, which is true under any authoritarian government. But most people just go along, this is why such governments can exist. If you grew up barely able to afford a bike and now can afford to drive modern EVs through your modern city, it’s hard to argue the appeal of having it even better.
that is true. the chinese also value community and harmony over individuality. it is part of their culture to go along with the mainstream. it's one reason why china is able to progress so fast. because people are generally united in the countries goals. there is no opposition just for the sake of opposition. opposition would have to have a very good reason, and even then the preference is to not rattle things up. even at the family level. i have experienced that myself.
but i also believe that a revolt is china's greatest fear. not for the sake of the leadership, but for the sake of the country as a whole. because a serious revolt in china would be massive and have many casualties.
this is why china blocks outside information. the less educated older generations lack the knowledge needed to separate misinformation and fake news from the truth. which incidentally i believe is also in part the motivation for the ban in nepal.
the difference is that china was able to block access to the outside before it got hold in the population. it also was able to build alternatives, and china is large enough for the outside not to matter.
china is exploring opening up. there was talk if reducing blocks in the shanghai area. and i believe it will happen as the education of people rises and outside influences become less of a threat.
Discord servers and its most active users were paid NGO workers of Samata Foundation and Hami Nepal, which are very well funded NGOs by The National Endowment for Democracy (NED), which is in turn funded by the US Congress and run by the CIA
Historically, China backed the monarchy (the royal family excluding Gyanendra never really forgave Nehru and Indira Gandhi for abolishing and then nationalizing royal property, as the Shah family continues to only marry Hindu royalty within their caste along with their historic antipathy to a monarchist Hindu Rashtra leading to the INC backing the Nepali Congress and Vanarasi-raised and ideologically Gandhian Koirala brothers) and KP Sharma Oli's Marxist communist faction, while India backed the Prachanda Path communists and the Nepali Congress (NC).
After the move to democratization, India continued to back NC and Prachanda (eg. He and his wife are/were devoted followers of BJP-aligned Baba Ramdev [0][1][2]), but KP Sharma Oli's faction continued to lean pro-China, as he and his peers started their revolutionary path during the Naxalbari uprising [3]. The monarchists (RPP) on the other hand switched to being more India leaning after Yogi Adityanath - the religious leader of the Gorakhnath Math which is heavily patronized by the royal family and Pahari Hindus from Kathmandu to Kashmir - became the Chief Minister of Uttar Pradesh.
Last year, the NC surprised everyone by collapsing Prachanda's government and making an alliance with KP Sharma Oli.
Based on how prominent Maoist Center (Prachanda), RSP, and RPP party workers have been during the protests and even within the discord, I am starting to suspect this was a repeat of the Rajapaksa-Siresena episode in Sri Lanka in the sense that a significant faction was used to undermine the China leaning Oli government.
Sushila Karki is viewed as fairy pro-India - the town she's from is for all intents and purposes Bihar, and she studied at the PoliSci department at Banaras Hindu University during the JP Andolan and when several future Indian political leaders were studying at BHU as well. China also hasn't congratulated her yet but the Indian government did almost immediately after the announcement. Of course, we will only find out once Karki's cabinet is announced.
When faced with a big task and not knowing where and how to start, a trick I like is writing something crappy that is roughly a step in the right direction. For example, if you're building a web browser (huge monumental task), just load a page with your favorite http lib and display it, html tags and all. You know that none of that code will survive, but it's something that you can build on, and in due time you'll come around and replace it with the right design.
They dug out the ground under the church while it was held up by beams secured on each side, then they moved the trailer under the church and carefully lowered the beams onto it.
It's not at all similar, and that doesn't have anything to do with the quality or lack thereof of the viewpoints.
The Notepad++ site is run by the authors and reflects their stance. Putty.org is run by an outside party who hijacks the reputation of the PuTTY project to push their agenda.
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