Let’s say you’re trying to develop some novel true knowledge about some domain. For example, maybe you want to figure out what the effect of a maximum wage law would be, or whether AI takeoff will be continuous or discontinuous. How likely is it that your answer to the question is actually true?
(I’m assuming here that you can’t defer to other people on this claim; nobody else in the world has tried to seriously tackle the question, though they may have tackled somewhat related things, or developed more basic knowledge in the domain that you can leverage.)
First, you might think that the probability of your claims being true is linear in the number of insights you have, with some soft minimum needed before you really have any hope of being better than random (e.g. for maximum wage, you probably have ~no hope of doing better than random without Econ 101 knowledge), and some soft maximum where you almost certainly have the truth. This suggests that P(true) is a logistic function of the number of insights.
Further, you might expect that for every doubling of time you spend, you get a constant number of new insights (the logarithmic returns are because you have diminishing marginal returns on time, since you are always picking the low-hanging fruit first). So then P(true) is logistic in terms of log(time spent). And in particular, there is some soft minimum of time spent before you have much hope of doing better than random.
This soft minimum on time is going to depend on a bunch of things—how “hard” or “complex” or “high-dimensional” the domain is, how smart / knowledgeable you are, how much empirical data you have, etc. But mostly my point is that these soft minimums exist.
A common pattern in my experience on LessWrong is that people will take some domain that I think is hard / complex / high-dimensional, and will then make a claim about it based on some pretty simple argument. In this case my response is usually “idk, that argument seems directionally right, but who knows, I could see there being other things that have much stronger effects”, without being able to point to any such thing (because I also have spent barely any time thinking about the domain). Perhaps a better way of saying it would be “I think you need to have thought about this for more time than you have before I expect you to do better than random”.