We are going to assume that there is little transfer of knowledge between attempts, so that each attempt succeeds iff the amount of effort you spend on the problem is greater than its difficulty rating e>d.
This hypothesis is plain false for research. Like, most of the time, you find the solution between attempts, not while investing the maximum amount of effort that you ever did. What I find true is that there is usually a minimal amount of total effort to invest before your intuition can kick in when you’re doing something else, but you can do it in multiple times. It might even be more productive to do so.
You do mention my issue at the end of your post:
Real life is not as harsh in our assumptions—usually part of the effort spent carries over between attempts and we have information about the expected difficulty of a problem. But in general I think this is a good heuristic to live by.
But having an assumption that is so blatantly false makes me very dubious that this model has any use, at least in the context of research.
This hypothesis is plain false for research. Like, most of the time, you find the solution between attempts, not while investing the maximum amount of effort that you ever did. What I find true is that there is usually a minimal amount of total effort to invest before your intuition can kick in when you’re doing something else, but you can do it in multiple times. It might even be more productive to do so.
You do mention my issue at the end of your post:
But having an assumption that is so blatantly false makes me very dubious that this model has any use, at least in the context of research.