Thanks, this is a beautiful explanation
depressurize
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Thoughts on Zero Points
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 my mind are whether the hobby causes you to make friends and whether it keeps you in good shape, but those are pretty surface-level and obvious. There are lots of other ways a hobby can be helpful (e.g. it can advance your career, it can fulfill a desire in you to help others, it can make you money). But those all seem like saying “good books are ones with a relatable main character and narrative tension”, they will help filter out many bad (and a few good ones) but they’re to simplistic and general to be much help in finding a truly great one. Many great books are great because they did something unique no one else did, and probably many great ways to spend your time are great because they have some unique massive advantage that’s difficult to find anywhere else.
Some ways of spending your time are better than others
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 way to go directly from ¬¬P to P.
Proof of negation (allowed): Prove ¬P by assuming P and deriving a contradiction
Proof by contradiction (not allowed): Prove P by assuming ¬P and deriving a contradiction
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.