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
I think, that sharing is like testing that your Idea is good and new.
In programming, we have a concept named “Fail Fast strategy”. That means, that after some mistake program should fail as fast as possible. In ideal case—not even compile. Because the far your mistake stepping by “deploy ladder”—the more it costs. If your program does not compile then you set the wrong value to some variable—you’ll pay seconds for correcting. If it was found during QA tests—you’ll pay for switching from your current task to this one, because it’s high-priority. If it’s in production—you start losing clients.
In my opinion, the same stuff is working for Ideas. If your idea is junk—you should know about it before you’ve spent half of your life on it.
The situation looks like this: You have an Idea. You have Hypotheses that it’s “good” and it’s “new”
You have two strategies:
1) Start work on your Idea only based on evidence of that you have hypotheses about “good” and “new”
2) Collect additional evidence to falsify or prove your hypotheses that the Idea is good and new.
Sometimes 1st strategy is worth the risk. For example, if you want to incredibly improve balance on your bank account. OR if your idea is a really dangerous one. OR “continuous list, there you lose something because your idea shared”. In this situation, the second strategy increases the risks that someone else will implement your Idea, and that will decrease your chances of winning.
But if you don’t want to make money on your idea AND your idea won’t destroy the world if someone else will know about it AND “the other items of “loose if sharing” list”—I’d prefer the second strategy, because:
1. Your opinion on your Idea is biased. Communication is one of the power tools to improve your model of expectations from your idea.
2. Your Idea can be good overall, but you can be wrong in detail. Someone else will look at it from another point of view and can notice weak points, that you can fix.
3. While working on your Idea and improving it you will go far from the point where you had Insight about the idea. And the more that distance the more will be troubles about explaining that idea to other people because you will compress your long path to simple: “oh, I’ve been taking a shower and then realized...” The idea came not only because you’ve been taking a shower, but you also had a problem, you had observations, you had a path to your solution. And the more you live with your idea, the more chances that you will forget details about it. You already have a picture, there is no need for you to store data about how you’ve been solving the puzzle. But showing this picture to other people doesn’t explain to them what problem have you been solving, and why, and how. Give your auditory THE ANSWER—and they won’t get it. Giving them THE QUESTION and THE ANSWER is better but works only with some of them. But if you will give them QUESTION, and enough hints to make the path to the answer—you’ll have chances to be understood. The more time from Insight—the fewer hints that helped you you’ll remember.
4. As I mentioned, the more you wait—the more “Wrong Idea” costs. And most times better to look like a person that created the wrong idea than be a person who uses it. That’s why I sharing my ideas about this question)
So, my algorithm is:
1) Testing my Idea for weaknesses and “the wheel inventing” by myself.
2) If it passed step before—share it.
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.