Thanks, this is a beautiful explanation
For math I'd like to submit this series: "A hard problem in elementary geometry" by fields medalist
Timothy Gowers. It's a 6 part series where each part is about an hour long, of him trying to solve this easy-seeming-but-actually-very-difficult problem.
"It's the only thing that satisfies my compulsion" is a good reason to do something IMO. Certainly not useless for you (even if it would be for most people), assuming it actually is the best thing you could be doing with your time that satisfies your compulsion. I definitely relate though, I find it very difficult to prevent myself from writing.
what are the actual criteria you're using to evaluate them right now?
What I'm trying to get at is "how much does this hobby make my life better outside of me finding it fun". I think the two that come most to ...
The way I think of it, is that constructivist logic allows "proof of negation" via contradiction which is often conflated with "proof by contradiction". So if you want to prove ¬P, it's enough to assume P and then derive a contradiction. And if you want to prove ¬¬P, it's enough to assume ¬P and then derive a contradiction. But if you want to prove P, it's not enough to assume ¬P and then derive a contradiction. This makes sense I think - if you assume ¬P and then derive a contradiction, you get ¬¬P, but in constructivist logic there's no...
An anvil problem reminds me of a cotrap in a petri net context. A petri net is a kind of diagram that looks like a graph, with little tokens moving around between nodes of the graph according to certain tiles. A cotrap is a graph node that, once a token leaves that node, it can never renter. (There are also traps, which are nodes that tokens can’t leave once they enter.) My analogy: “having at least one anvil” is a cotrap, because once you leave that state, you can’t get back into it. So if you’re looking for a new term, cotrap is what I would suggest.