I think the most common failure mode is neuroticism; getting stressed and frustrated with the lack of progress, thinking about the progress toward the outcome rather than the problem to be solved. Stress in particular is extremely poisonous to thinking. The expectation should be that it takes as long as it takes, and you need to be calm and well rested.
If you find yourself choosing between working on the problem and taking a nap, always take the nap. (Given the choice between remaining in bed, and taking another peek at the problem, usually take a peek at the problem, after which you should do what feels best.)
Some experimentation should convince you that this is how human minds work (well, most of 'em, and yours is probably one of them), after which you can employ this strategy without guilt during a crisis.
A lack of necessary prior knowledge is often a major reason for struggling with a problem. As a relatable example, suppose you're taking an exam. There's a problem near the end that you don't know how to solve—and the reason is that you haven't studied that topic enough. No matter how smart (as in, fast at learning) you are, you need to practice with similar or related problems to solve that issue.
But suppose you're outside of an exam environment and have time to look up the relevant material. I've known a PhD candidate in a non-mathematics field who had to find a mathematical solution to a certain research problem. That person is smart but still needed a few months to learn the mathematical fundamentals to understand and solve the problem. In contrast, someone with a math background could have solved this far more quickly. But that person would have taken at least some months to get up to speed on the research literature for the non-mathematics part of the research problem, in order to properly understand its constraints and bigger-picture significance.
Lara Alcock's book "How to Study as a Mathematics Major" touches upon this topic more directly. She encourages readers not to be too intimidated if other students in a course seem really smart: much of the time, the reason is not due to an innate difference in smartness, but rather prior exposure by other students to concepts in the course. Students who seem to find the material effortless often have already studied many of the topics in another course or could even be retaking the course after a previous attempt.
When you plant a seed in a garden, there's many factors at play - is the season right? Is the climate right for that seed? Is the soil the right type? Are there pests or varmints roaming that might eat it prematurely? Etc.
The garden of thought has analogous factors: Is this a question your brain actually cares about right now? Do you have the background knowledge necessary to work it out? Is your brain calm enough to process that question? Are there distractions or anxieties that disturb the process?
That said, some people truly are stupid. I recently read John Cleese's autobiography, and he tells a story from when he was a Geography teacher...
There was a lad who he was teaching countries and their capitals. Even when given direct attention, the kid simply wasn't able to name any capitals whatsoever. He would smile and nod, giving no indication of difficulties... But he couldn't recall the info even after being told it 8 seconds previously. This particular type of data slid off his brain.
At the end of the term, the kid got one question right on the final exam, probably by accident. Cleese posted the paper in the teacher's room, attracting the comment from one teacher "The sad thing about true stupidity is that you can do absolutely nothing about it".
Perhaps that kid had a genius for engines or something, but he was never going to be able to understand geopolitics. He lacked even the awareness to know that he was stupid (at least about countries and capitals). He would never have asked if he was stupid, because he was truly stupid.
If your friend is ever curious about their intelligence, they're probably ok and can develop the skill of thinking like this.
This is a difficult fact to accept. We have all been told that people are generally equal, especially in intelligence, if given the same opportunities, but it becomes more clear in time that some problems are intractable to some people and no amount of training or exposure can change that. However, it's a better answer to the problem of why some people like Cleese's example do not absorb information. The alternative is to apply malice and laziness to them when it just isn't so.
We all have these intelligence holes that gives some insight into the mechanism. Eg. I'm bad at remembering names. As in the example, if you tell me someone's name, I'm likely to forget it 5 minutes later. I just spent 3 years reading Douglas Hofstadter's book and had to look up his name to type it here. This seems to happen because I don't see an application to remembering the name. I'm never going to meet Doug and rarely will anyone need to be told about the book, so why remember it? There's definitely a parallel to state capitals in that example.
While thinking is somewhat of a background process, our brains don't just solve the mysteries of the universe while we eat a ham sandwich. We tell our brains which problems are of high importance and it focuses on them. If you've ever laid down to go to sleep and told yourself to wake up at 6:30 and it worked, you've witnessed an obvious application of this.
The problem comes when we fail to point out the importance of a problem, or when we do so reflexively which means that we tell our brain that everything is important and it simply cannot process all of the requests.
Setting your thinking requests before doing a non-thinking activity is a good way to start. Think about the problem consciously and then specifically ask for an answer to a question. Then go do something physical or mechanical: take a walk, sleep, mow the lawn, watch a non-challenging movie, etc. Be prepared to accept whatever result you get. A common response is: non enough information, but it should point you toward what that additional info looks like.
marginalia_nu|1 year ago
wizzwizz4|1 year ago
Some experimentation should convince you that this is how human minds work (well, most of 'em, and yours is probably one of them), after which you can employ this strategy without guilt during a crisis.
jyunwai|1 year ago
But suppose you're outside of an exam environment and have time to look up the relevant material. I've known a PhD candidate in a non-mathematics field who had to find a mathematical solution to a certain research problem. That person is smart but still needed a few months to learn the mathematical fundamentals to understand and solve the problem. In contrast, someone with a math background could have solved this far more quickly. But that person would have taken at least some months to get up to speed on the research literature for the non-mathematics part of the research problem, in order to properly understand its constraints and bigger-picture significance.
Lara Alcock's book "How to Study as a Mathematics Major" touches upon this topic more directly. She encourages readers not to be too intimidated if other students in a course seem really smart: much of the time, the reason is not due to an innate difference in smartness, but rather prior exposure by other students to concepts in the course. Students who seem to find the material effortless often have already studied many of the topics in another course or could even be retaking the course after a previous attempt.
mandmandam|1 year ago
When you plant a seed in a garden, there's many factors at play - is the season right? Is the climate right for that seed? Is the soil the right type? Are there pests or varmints roaming that might eat it prematurely? Etc.
The garden of thought has analogous factors: Is this a question your brain actually cares about right now? Do you have the background knowledge necessary to work it out? Is your brain calm enough to process that question? Are there distractions or anxieties that disturb the process?
That said, some people truly are stupid. I recently read John Cleese's autobiography, and he tells a story from when he was a Geography teacher...
There was a lad who he was teaching countries and their capitals. Even when given direct attention, the kid simply wasn't able to name any capitals whatsoever. He would smile and nod, giving no indication of difficulties... But he couldn't recall the info even after being told it 8 seconds previously. This particular type of data slid off his brain.
At the end of the term, the kid got one question right on the final exam, probably by accident. Cleese posted the paper in the teacher's room, attracting the comment from one teacher "The sad thing about true stupidity is that you can do absolutely nothing about it".
Perhaps that kid had a genius for engines or something, but he was never going to be able to understand geopolitics. He lacked even the awareness to know that he was stupid (at least about countries and capitals). He would never have asked if he was stupid, because he was truly stupid.
If your friend is ever curious about their intelligence, they're probably ok and can develop the skill of thinking like this.
mortify|1 year ago
This is a difficult fact to accept. We have all been told that people are generally equal, especially in intelligence, if given the same opportunities, but it becomes more clear in time that some problems are intractable to some people and no amount of training or exposure can change that. However, it's a better answer to the problem of why some people like Cleese's example do not absorb information. The alternative is to apply malice and laziness to them when it just isn't so.
We all have these intelligence holes that gives some insight into the mechanism. Eg. I'm bad at remembering names. As in the example, if you tell me someone's name, I'm likely to forget it 5 minutes later. I just spent 3 years reading Douglas Hofstadter's book and had to look up his name to type it here. This seems to happen because I don't see an application to remembering the name. I'm never going to meet Doug and rarely will anyone need to be told about the book, so why remember it? There's definitely a parallel to state capitals in that example.
mortify|1 year ago
The problem comes when we fail to point out the importance of a problem, or when we do so reflexively which means that we tell our brain that everything is important and it simply cannot process all of the requests.
Setting your thinking requests before doing a non-thinking activity is a good way to start. Think about the problem consciously and then specifically ask for an answer to a question. Then go do something physical or mechanical: take a walk, sleep, mow the lawn, watch a non-challenging movie, etc. Be prepared to accept whatever result you get. A common response is: non enough information, but it should point you toward what that additional info looks like.
lordgrenville|1 year ago
ajkjk|1 year ago
marginalia_nu|1 year ago