Thank you for the kind words.
It’s directionally opposed indeed. In my opinion, this website, which once started with the analogy of Map and Territory, forgot that the analogy is not a Territory, but a Map. And thus it should be challenged by evidence. It was a very interesting finding that the people who made a genuine discovery don’t report their process as incrementally becoming less wrong and instead talk about taking a wild leap which turned out to be correct.
Thank you for very relevant references—diving into posts and papers.
the question is how you’d get the idea for the theorem in the first place.
This is the question indeed. I was also thinking about examples where it would be hard to make the deduction within the framework itself. The classical one is probably the solution to cubics, where it was proven that you cannot reach the closed form solution using operations over reals. But it is trivial in complex numbers, and the formula will return a triplet of reals you can easily substitute and verify.
I suspect this could be actually quite a common case, but haven’t found the general formalization yet—incompleteness is somewhat analogous, but it says the statement is unverifiable. With cubics we have a way to check the correctness of the solution, which arrived through an “inexpressible” channel detour.
I was experimenting with exactly the same thing using GPT-4. Only 20 top questions, result—more or less equal to community.
But then it came to numeric estimations like “how much people will die due to covid”—it was outperforming humans giving highly accurate predictions (i was asking not for values but for ranges with quartiles, and results of humans had much higher dispersion comparing to GPT)
Also I was comparing only results of community predictions for January 2022 since gpt-4 was trained on sept 2021, and its unfair to compare predictions if people had a lot of additional evidence which gpt doesnt have.
if it’s interesting I can share methodology, results and dataset.
My wife was working in a BSL-3 facility with COVID and other viruses that were causing serious health issues in humans and were relatively easy to spread. This is the type of lab where you wear positive pressure suits.
To have access to such a facility, you need to take training in safety measures, which takes about a month, and successfully pass the exam—only after that can you enter. People who were working there, of course, were both intelligent and had master’s or doctoral degrees in some field related to biology or virology.
So, in essence, we have highly intelligent people who know that they are working with very dangerous stuff and passed the training and exam on safety measures. The atmosphere itself motivates you to be accurate—you’re wearing the positive pressure suit in the COVID lab.
What it was like in reality: Suit indicates that filter/battery replacement needed—oh, it’s okay, it can wait. The same with UV lamps replacement in the lab. Staying all night in a lab without sleeping properly—yeah, a regular case if someone is trying to finish their experiments. There were rumors that once someone even took a mobile phone with them. A mobile phone. In BSL-3.
It seems to me that after some time of work with dangerous stuff people just become overconfident because their observations are something like: “previously nothing bad happened, so it’s ok to relax a bit and be less careful about safety measures”.
Hello. I’ve created it. It’s more about information processing, but useful to understand some communication-related stuff too. It’s not finished because LW doesn’t allow me to add more than five posts a day, but the main part is here:
https://www.lesswrong.com/s/JsGa9AHEG3EgEq45s
Hi Mitchell,
I’ve actually solved the puzzle of cubics being “non-findable.” There was no formal definition, so I needed to make one myself. In case you’d be interested, here is a link: https://www.lesswrong.com/posts/TbMedZDimwc5TRnu7/the-two-board-problem-training-environment-for-research
It also discusses why, for some math problems, it’s hard to arrive at the idea in the first place.