Each attempt succeeds iff the amount of effort you spend on the problem is greater than its difficulty rating e>d.
Do you have any reasons to believe that this models real-world problems well? I think factors other than effort matter a great deal, and to some extent, effort can be conserved or expended based on learning DURING the effort. You don’t have to pre-commit, you can re-allocate as your knowledge and success criteria change. Importantly, the vast majority of worthwhile problems are not binary in success—there’s lots of different ways to get/contribute value.
In this situation, before committing to a three year PhD, you better make sure you spend three months trying out research in an internship to try out research. And before that, it seems a wise use of your time to allocate three days to try out research on your own. And you better spend three minutes beforehand thinking about whether you like research.
That’s ridiculous, or at least misleading. You should be researching and considering that DURING your previous training, and it’s nowhere near exactly logarithmic.
Do you have any reasons to believe that this models real-world problems well? I think factors other than effort matter a great deal, and to some extent, effort can be conserved or expended based on learning DURING the effort. You don’t have to pre-commit, you can re-allocate as your knowledge and success criteria change. Importantly, the vast majority of worthwhile problems are not binary in success—there’s lots of different ways to get/contribute value.
That’s ridiculous, or at least misleading. You should be researching and considering that DURING your previous training, and it’s nowhere near exactly logarithmic.