I’ve had the opposite experience (though restricted to problems that someone at all has solved/understood). There are multiple fields (such as AI/ML, cryptocurrency, and zero-knowledge proofs) that I at some point thought were mysteriously difficult. In each case, there is a finite set of important concepts (less than 30) to learn, and it is possible to do cutting-edge research from there.
As far as I can tell, nothing is magic. Nothing that anyone can do is mysteriously difficult. Complicated things that anyone understands decompose into a finite number of interacting parts, each of which (as well as their interactions) can be modeled. Skills people have (even ones they don’t understand) can be learned through experience and guides; getting great can take years, but getting adequate usually only takes months. Actually doing any of these requires willingness to understand and think for yourself. If you don’t know if you can understand a field, you can set aside an amount of time, such as one month, to intensively study it, and see what happens.
(Of course, some things can be so hard that no one knows how to do them, and these actually can be mysteriously difficult, though won’t be with the benefit of hindsight if someone actually does them. And all of this is based on my own personal experience.)
Glad that this approach worked out for you! It’s an amazing feeling when you finally solve or get something that looked so hard initially. I would not deny that this has happened to me, too, but mostly in the cases I knew for sure I could handle with enough effort. I did my PhD in General Relativity, and had to go through a few proofs that required significantly more background than I had at the time. I was able to master the necessary basics of Algebraic Topology enough to add my own small theorem on top of what was already in my research area, yet it was excruciatingly slow and painful to get to that point, and not a lot of fun. I had to abandon any larger ambitions in the area. Similarly, I was used to getting A and A+ in almost all my undergrad and grad classes, yet when I hit advanced grad classes, like String theory and topics in QFT, I was lucky I could get through them, even though other grad students seemed to have had little difficulties there.
In general, I have found that in many areas, especially in math, everyone has their threshold of abilities. Below the threshold the effort required scales basically linearly with the amount of material, Past that threshold any extra learning becomes exponentially more difficult. I mean “exponentially” in the mathematical sense, not in the colloquial one. Gotta know your limits.
Have you tried tackling them during a full blown-psychotic break? In Europe I figured out the solution to the P=NP problem and the hard problem of consciousness during a psychotic episode, but I subsequently forgot them due to a psychotic episode.
[I think that in general, comments with less than −10 karma should have at least one comment explaining why.]
I downvoted you because I believe you to be strongly false: either lying or deluded. This is due to my prior for “somebody solves two Hard Problems in a matter of days” being much lower than my prior for “somebody claims to have solved two Hard Problems in a matter of days”. In particular, people in altered mental states are often much more susceptible to false feelings of enlightenment. (See “Mysticism and Pattern-Matching” by Scott Alexander for related ideas and support for this argument.)
[I originally wrote this as a description of my beliefs about why people in general downvoted the parent, before remembering the LW comment rules (describe your ideas, not your idea of the consensus). This is one data point for the rules being effective.]
I downvoted this explanation because it’s uncharitable to claim that someone is either lying or deluded when it seems plausible that they were instead making a joke. Perhaps you have other reasons to think that Alephywr isn’t joking, but if so it’s worth explaining that.
Humor is hard. After seeing a bunch of Alephywr’s comments I do indeed think it was probably a joke, but delivery via text is hard and I think it’s understandable for someone to not consider that as a hypothesis.
In general it’s understandable not to consider that hypothesis. But when you are specifically making a pointed and insulting comment about another person, I think the bar should be higher.
I did not write the grandparent to insult Alephwyr. For instance, I wrote “I downvoted you” because I felt an obligation to prevent scenarios where somebody is strongly downvoted and doesn’t know why. You began your reply in the same way, but the grandfather has positive karma, so you can’t have meant the same thing. Either there is a misunderstanding, or you are mocking me, or you consider “I downvoted you because” to be purely antagonistic and are retaliating in kind, etc.
I agree with you, now, that Alephwyr could be joking. (Or insane or trolling. “He is either mad or writing poetry.”) I had taken the post at face value, and my comment was an accurate description of my reasoning. I appreciate your contribution to the discussion of “what is Alephwyr’s purpose?”, and I admit that you revealed an oversight in my thinking, but I think that you are being somewhat uncharitable to see something direct and assume that it is “specifically.… pointed and insulting.”
(I am straightforward, you are to the point, he is insensitive.)
Have tried to tackle hard-seeming problems. They turned out even harder than they seemed.
I’ve had the opposite experience (though restricted to problems that someone at all has solved/understood). There are multiple fields (such as AI/ML, cryptocurrency, and zero-knowledge proofs) that I at some point thought were mysteriously difficult. In each case, there is a finite set of important concepts (less than 30) to learn, and it is possible to do cutting-edge research from there.
As far as I can tell, nothing is magic. Nothing that anyone can do is mysteriously difficult. Complicated things that anyone understands decompose into a finite number of interacting parts, each of which (as well as their interactions) can be modeled. Skills people have (even ones they don’t understand) can be learned through experience and guides; getting great can take years, but getting adequate usually only takes months. Actually doing any of these requires willingness to understand and think for yourself. If you don’t know if you can understand a field, you can set aside an amount of time, such as one month, to intensively study it, and see what happens.
(Of course, some things can be so hard that no one knows how to do them, and these actually can be mysteriously difficult, though won’t be with the benefit of hindsight if someone actually does them. And all of this is based on my own personal experience.)
Glad that this approach worked out for you! It’s an amazing feeling when you finally solve or get something that looked so hard initially. I would not deny that this has happened to me, too, but mostly in the cases I knew for sure I could handle with enough effort. I did my PhD in General Relativity, and had to go through a few proofs that required significantly more background than I had at the time. I was able to master the necessary basics of Algebraic Topology enough to add my own small theorem on top of what was already in my research area, yet it was excruciatingly slow and painful to get to that point, and not a lot of fun. I had to abandon any larger ambitions in the area. Similarly, I was used to getting A and A+ in almost all my undergrad and grad classes, yet when I hit advanced grad classes, like String theory and topics in QFT, I was lucky I could get through them, even though other grad students seemed to have had little difficulties there.
In general, I have found that in many areas, especially in math, everyone has their threshold of abilities. Below the threshold the effort required scales basically linearly with the amount of material, Past that threshold any extra learning becomes exponentially more difficult. I mean “exponentially” in the mathematical sense, not in the colloquial one. Gotta know your limits.
Have you tried tackling them during a full blown-psychotic break? In Europe I figured out the solution to the P=NP problem and the hard problem of consciousness during a psychotic episode, but I subsequently forgot them due to a psychotic episode.
[I think that in general, comments with less than −10 karma should have at least one comment explaining why.]
I downvoted you because I believe you to be strongly false: either lying or deluded. This is due to my prior for “somebody solves two Hard Problems in a matter of days” being much lower than my prior for “somebody claims to have solved two Hard Problems in a matter of days”. In particular, people in altered mental states are often much more susceptible to false feelings of enlightenment. (See “Mysticism and Pattern-Matching” by Scott Alexander for related ideas and support for this argument.)
[I originally wrote this as a description of my beliefs about why people in general downvoted the parent, before remembering the LW comment rules (describe your ideas, not your idea of the consensus). This is one data point for the rules being effective.]
I downvoted this explanation because it’s uncharitable to claim that someone is either lying or deluded when it seems plausible that they were instead making a joke. Perhaps you have other reasons to think that Alephywr isn’t joking, but if so it’s worth explaining that.
Humor is hard. After seeing a bunch of Alephywr’s comments I do indeed think it was probably a joke, but delivery via text is hard and I think it’s understandable for someone to not consider that as a hypothesis.
In general it’s understandable not to consider that hypothesis. But when you are specifically making a pointed and insulting comment about another person, I think the bar should be higher.
I did not write the grandparent to insult Alephwyr. For instance, I wrote “I downvoted you” because I felt an obligation to prevent scenarios where somebody is strongly downvoted and doesn’t know why. You began your reply in the same way, but the grandfather has positive karma, so you can’t have meant the same thing. Either there is a misunderstanding, or you are mocking me, or you consider “I downvoted you because” to be purely antagonistic and are retaliating in kind, etc.
I agree with you, now, that Alephwyr could be joking. (Or insane or trolling. “He is either mad or writing poetry.”) I had taken the post at face value, and my comment was an accurate description of my reasoning. I appreciate your contribution to the discussion of “what is Alephwyr’s purpose?”, and I admit that you revealed an oversight in my thinking, but I think that you are being somewhat uncharitable to see something direct and assume that it is “specifically.… pointed and insulting.”
(I am straightforward, you are to the point, he is insensitive.)
I second this. (It would also be nice if that was visible though, but comments with karma that low are hidden, along with comments on them.)
I’m familiar with psychosis and your reply seems totally believable to me.