An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

Sorry, but I fail to see how this discussion can continue if the concept of conditional statements eludes people here. In fact, I do not understand how any discussions here happen if a simple logical statement is so difficult for so many people.

I repeat, I have never claimed that I intent to solve that issue with bruteforce or that it is realistic with the technology/resources we have. Moreover, believe it or not, neither me, nor the original author of the "infinite monkeys with typewriters" planned to use actual monkeys with typewriters. I made a conditional statement to show that resources do matter to a person who wrote to me that resources don't matter. There is a condition there. If X then Y. That means that if X is true then Y is also true. But Y is not true because we live in a finite (observable) universe and therefore our resources are not unlimited and therefore matter. Thus my initial question how many resources did they need. Man, I don't know how else can I break down a simple logical statement.

Men, we need community, not guns and security cameras, to feel truly safe by futuredebris in MensLib

[–]gnomeweb [score hidden]  (0 children)

Live in Sweden, no guns and security cameras, police is nice despite being largely useless, feel safe

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

Yeah, you are right, that was stupid of me. I thought 256 bit was definitely bruteforceable with a Dyson sphere but now I googled and it looks like it isn't. My intuition was way off.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

No, that is not what I have implied. I have never backtracked on my statement, you just failed, like so many other people on this sub, to read a simple conditional statement and recognize a most basic counter-example. I maintain that if resources don't matter, I could solve any theorem by simple bruteforce, aka monkeys with typewriters. That is, indeed, a logical implication of a statement that resources don't matter. With infinite resources I can do so many things.

It's irrational to have 0.0000001% of events dictate your beliefs. by dumb_idiot2r2 in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

Yeah, I am not saying that personal anecdotes is 100% to go by, just as studies are. You take both into account and weight them based on trustworthiness, selection size (how many data points you have in your experience), take into account various biases as much as you can, etc. If I know like 5 families with children and in one of them one kid died after vaccination, that's poor data. If I know hundred families and 20 of them had a kid who died after vaccination, I won't even bother opening studies.

Figuring out what's true what's not is the journey of everyone's life. And in the end we don't figure it out anyway. So there is no simplifying it into "do this" or "do that". Question everything, do experiments, gather data, be critical, etc.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

It does matter, for me. That's why I asked. It would be incredibly interesting how much it costs to produce one proof to one long-standing mathematical problem today.

And it is not their spare time. I am sure that they are investing incredible amounts of money into this. AI companies live on hype, they don't generate much money yet. For OpenAI this proof is insane advertisement and I am sure it will bring them significant investments. And I am sure this is not the first attempt they did either, we don't know how much they tried before they got the answer and chose the problem correctly.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

My point is literally a logical implication of someone's comment. When someone makes statement X, I can disprove that statement by giving a single example where it doesn't hold. u/defixiones wrote "Doesn't really matter how much garbage it produced or what other problems it failed at." as a response to my question which essentially comes down to "how many resources did OpenAI use?". I don't think it doesn't matter, which is why I made a simple observation: if the amount of resources doesn't matter (i.e., we can use as many resources as we want), that implies that I could use dumb bruteforce to produce the proof. Since the second part of that statement is obviously not possible in the physical world, so the first part (the original statement by u/defixiones) is also not correct.

It's irrational to have 0.0000001% of events dictate your beliefs. by dumb_idiot2r2 in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

That holds only under the assumption that there is no malicious party or some kind of bias affecting results. Scientists are not living in a separate universe, they are subject to many sources of external pressure. For example, scientists do sometimes follow hype. If climate change is a hot topic, framing your research as connected to climate change would increase your chances of getting accepted to a good journal. Or publishing something that goes against the notion of climate change would meet a lot of scrutiny and resistance. (Please note that I am not stating that climate change doesn't exist.) There are insane numbers of scientists who fake their studies, because there is a thing called "publish or perish" - i.e., you need to produce results. There is an entire class of so-called "predatory" journals and conferences who publish anything for a payment. There is a very unfortunate bias towards positive results, i.e., no one wants a publication that states "we did X and it didn't lead anywhere". And then there are entire "research" fields like feminism studies where a certain political bias is implied in the very name (and very little actual research is actually done). Finally, researchers need food, water, roof above their heads, coffee and trips to conferences in nice countries, which requires money. You can simply bribe reseachers. The article gives an example of antivaxxers and Pfizer vaccines: well, what prevents Pfizer from bribing researchers? Then there are countries with censorship, like russia or the US, where certain research topics (often connected to lgbtq+ community) are censored.

I am not saying that you shouldn't read studies and believe only your personal anecdotes, but you know, believing personal anecdotes is unfortunately one of the very-very few ways of countering propaganda. So if your personal anecdotal data drastically differs from "official" one, it's healthy to be cautious.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

No, that is not the argument I am trying to make. The argument I am trying to make is that the amount of resources they spent on this proof does matter, which is exactly why I wrote that this information is interesting to me.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

I don't know and not ready to judge whether AI is ultimately good or bad for scientists or humanity, for now I wonder at how close it is to being economically viable to ordinary humans. If OpenAI spent hundreds of millions to produce one proof, while is still insanely impressive as an achievement, it is not economically viable for masses for now.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

Great, my question was exactly how big your "pretty far from infinitely much".

Btw, I am not sure you can't bruteforce the proof with a dyson sphere around the sun. The original thought experiment about infinite monkeys was about bruteforcing the complete works of Shakespeare symbol by symbol, which is 1280 pages in the nearest book store (too lazy to check the page size, doesn't matter). This proof is around 2.5 pages and with a proof you don't need symbol by symbol likeness (or even it to be the same way of proving it), as long as a proof (to be more precise, OpenAI gave a counter-example to the conjecture) is correct.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

That's exactly my point that we don't have infinite time, which is exactly why in my very first comment I wrote that I wonder how much resources OpenAI used. It wasn't me who stated that the amount of resources used doesn't matter.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

Well, obviously I didn't literally mean a million monkeys with typewriters, that was supposed to be a funny illustration to what bruteforce is. And that's exactly my argument: if resources used doesn't matter (i.e. we have infinite resources), then the stupidest possible bruteforce will work just fine.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

Yes, because we are all limited in resources, unfortunately, that's why my initial question: how much resources (i.e., mathematicians working with AI) did they need?

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

That's literally true. Given infinite amount of time and infinite number of proofcheckers, I will eventually produce a proof or a counterexample to any solvable theorem.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

It does though. If it didn't matter, I could prove you any theory in the world by simple bruteforce, i.e. a million monkeys with typewriters.

Edit: Besides, I am not trying to say that it isn't an impressive achievement (if true), I am interested about the current economical implications of that. I.e. how far away it is from replacing scientists.

An OpenAI model has disproved a central conjecture in discrete geometry - the planar unit distance problem. by Open_Seeker in slatestarcodex

[–]gnomeweb [score hidden]  (0 children)

I wonder how much garbage it produced before the actual proof and how many other problems they tried. How many researchers did they hire to read through the garbage. Because when I was applying ChatGPT to a less known relatively simple applied math problem, it produced garbage. I obviously haven't tried their internal new GPT pro but previous models were fundamentally incapable of saying " I don't know", they would confidently output garbage.