Interesting. tl;dr -- we learn by experiencing things, not by being told things.
How to Understand Things
11–20 of 121 posts
Re: How to Understand Things
#12Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…
Did that realization at the eve of exams bring up a bout of anxiety ? (edit: I would have freaked out)
Re: How to Understand Things
#13Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…
>I suspect lots of people go through the entire education system like this.
+1. it took me a couple years after getting kicked out of college to get my head sorted out to the point where I felt like I could "think" again
I think one of the most harmful things about schooling is the way it imposes a tracked structure on learning. it demarcates knowledge into discrete subjects and sets up a linear progression through them and says you need to master each step on the track before moving onto the next one. this is poisonous and borderline evil, and I've encountered many people who are crippled for life by it. a lot of people never pursue things they're really interested in and could become extremely passionate about because school has convinced them they need to stack up prerequisite knowledge before they're even allowed to touch it
Re: How to Understand Things
#14Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…
What happened after this revelation? Did anything change? Did you try to intuitively understand the problems you were working on? I think this boils down to how you were taught (or self taught) to approach the subject and the set of tricks you learned along the way that became your toolset. Did you do a lot of exercises in school? They usually help build the intuitive part, the aha moment, that comes through repetiti…
Yup, definitely changed the game for me, and turned on my 'intuition' spidey sense, of whether I actually understood a concept.
We did do a lot of exercises in school, but they mostly just tested whether you can reliably apply a method that you were taught, rather than testing understanding.
Re: How to Understand Things
#15Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…
Did that realization at the eve of exams bring up a bout of anxiety ? (edit: I would have freaked out)
Haha, yeah. Thankfully, the Maths exams were set up such that you could always get 60% (the boundary for a "2:1" grade in the UK — an acceptable score for most people) by just knowing the 'bookwork', which you could do by memorising stuff without understanding it.
Re: How to Understand Things
#16Earlier quoted context omitted.
Agree on the aspect of time. As we have progressed, we now have many levels of abstraction that it is hard to think deeply about the problem. Almost à la like a code that has grown too deep to understand every "bit" of it. Moreover, I think people now work in teams rather than one individual thinking about the system holistically.
It’s possible. It just takes time; very few people are in a position to devote that time. This gives an advantage I haven’t seen discussed: when you put in the time, you make connections no one else thought of. It happens time and again, and it’s a clear pattern at this point. It takes months of daily study, often tedious, with no clear benefit. But the benefits sometimes come. (I wrote “usually” rather than “sometim…
I like to imagine that at some point we might collectively have a large enough software development population to solve most significant problems comprehensively enough -- and fairly and equitably enough -- for most people that we begin to see developers with increasing amounts of free time.
At that point I think we could collectively really begin digging into some of the huge backlog of software bugs and errors that we've built up over time and make everything more reliable, seamless and consistent.
It'd be a massive undertaking, especially to solve each issue thoroughly and without causing negative externalities elsewhere. But it'd also be a great puzzle-solving and social challenge, not to mention an educational and useful one.
Re: How to Understand Things
#17One of the things I remember quite vividly from my Psychology classes in college was the idea of a "satisficing" problem solver. Given a (reasonably solvable) problem to solve most people can come up with a satisfactory solution. The difficulty comes when you ask them to come up with a new solution. Many people struggle because their brains say "I already came up with a solution, and it was a pretty darn good solution too."
The really creative people are the ones who insist that their brains come up with another solution, and another one until they can be confident that they've found the best solution within a reasonable time investment.
Re: How to Understand Things
#18Great post. Personal anecdote: I don't think I really understood anything in school, but I was decent at going through the motions of carrying out certain methods and recalling certain facts when I needed to. I went on to study Maths at university, and for most of my first year, I had the same surface level "methods + facts" knowledge that got me through school. After some studying, I could recite definitions and the…
OP here -- that is a fantastic anecdote! Do you have an example of a "drawing" of a theorem, in this context? (I've seen these for fairly trivial theorems but not for more complex ones, so I'm curious.)
Ahh I did a bit of googling but couldn't find anything nice — sorry! Most of the time, the complex stuff is broken down into smaller "lemmas" with their own manageable proofs, and then the proof of the whole theorem will be something like "Follows from Lemma 2.1, Lemma 2.2, and a basic application of Theorem 1.4"
This is the theorem I was talking about: https://i.imgur.com/1xEH51Z.png (taken from https://taimur.me/posts/thinking-at-the-right-level-of-abstr... which touches on a similar topic to your post)
Re: How to Understand Things
#19> Understanding something really deeply is connected to our physical intuition
This rings true to me.
I think that I "understand" how to start a fire, which I do a couple dozen times a year, in a deeper more complete way than I understand any of the abstract software development that I spend 30 hours a week doing.
Re: How to Understand Things
#20> This quality of “not stopping at an unsatisfactory answer” deserves some examination.
> This requires a lot of intrinsic motivation, because it’s so hard; so most people simply don’t do it.
It also requires self-confidence, persuasiveness, and social power.
Without these traits, your attempts to really understand something will be dismissed as "overthinking things" or "trying to understand the universe". Those around you will urge you to "stop thinking just do the task" or "do the obvious thing" as they lose patience with you. If you don't resist them you'll end up moving forward despite feeling confused, sometimes completely. You'll then end up pissing people off when you execute too slowly or fail (in their eyes, intentionally).
> This is a habit. It’s easy to pick up.
Not if the people around you are exhausted by you.