There is a class of super-hard problems (AI alignment, a lot of social change) which are hard because they’re adversarial (at least partly). If different agents value different results, there can be no single preferred outcome (there may be a negotiated agreeable outcome, or there may not, but it won’t be “best” for everyone).
I don’t think that’s what you’re talking about though. I think part of the explanation is that we don’t have a model for distance from success. We have no clue if the researchers who’ve made serious attempts on these problems got us closer to an answer/proof, or if they just spun their wheels. In other words, these problems are hard because we haven’t found an incremental way to solve them.
Note that this is related to the reasons that colonizing Mars or mining asteroids is hard—there’s a lot of problems that need to be solved, many of which we don’t know a feasible/economical approach to, and as long as any of them is unsolved, the end-result remains impossible. Also similarly, there are discoveries about the sub-problems that are valuable in themselves, even if they don’t get us to the stated goal.
I think part of the explanation is that we don’t have a model for distance from success. We have no clue if the researchers who’ve made serious attempts on these problems got us closer to an answer/proof, or if they just spun their wheels.
This post is about experts in the fields of number theory and complexity theory claiming to have a clue about this. If you think “We have no clue”, you likely think they are wrong, and I would be interested in knowing why.
I added more details on this comment, given that someone else already shared a similar thought
There is a class of super-hard problems (AI alignment, a lot of social change) which are hard because they’re adversarial (at least partly). If different agents value different results, there can be no single preferred outcome (there may be a negotiated agreeable outcome, or there may not, but it won’t be “best” for everyone).
I don’t think that’s what you’re talking about though. I think part of the explanation is that we don’t have a model for distance from success. We have no clue if the researchers who’ve made serious attempts on these problems got us closer to an answer/proof, or if they just spun their wheels. In other words, these problems are hard because we haven’t found an incremental way to solve them.
Note that this is related to the reasons that colonizing Mars or mining asteroids is hard—there’s a lot of problems that need to be solved, many of which we don’t know a feasible/economical approach to, and as long as any of them is unsolved, the end-result remains impossible. Also similarly, there are discoveries about the sub-problems that are valuable in themselves, even if they don’t get us to the stated goal.
This post is about experts in the fields of number theory and complexity theory claiming to have a clue about this.
If you think “We have no clue”, you likely think they are wrong, and I would be interested in knowing why.
I added more details on this comment, given that someone else already shared a similar thought