To me it helps to imagine that I am explaining the topic to someone else. If I had enough time, I would never copy the textbook; I would rewrite it using my own words, and probably change the entire structure. (In other words, instead of “paper1 → paper2”, it would go “paper1 → internal model → paper2″.) Unfortunately, doing things the way I wish takes a lot of time.
For example, if I make notes about programming, I am trying to write the simplest code that illustrates the concept in isolation from other concepts. (Most examples I find online are introducing multiple concepts at the same time. Okay, I suppose in reality, you usually use X and Y and Z together in the same project. But I still want to see X used separately, and Y separately, and Z separately. And then an example of how X and Y and Z go together.)
I would suggest to explore the concept in unusual ways. For example, when you learn about commutative operators, don’t just use “addition” and “multiplication” as obvious examples, but also think about ones like “least common multiple” or even “these words have the same amount of strokes in Chinese”. (Ultimately coming to “there is an arbitrary undirected graph, where the nodes are the possible inputs, and each edge contains an arbitrary output as a label”.)
Also, when you learn things, the value is not merely in the individual things, but also (mostly?) in their connections to other things. That is the difference between a newbie who can recite the facts but cannot apply them, and an expert who can immediately take three abstract concepts and chain them together to solve a problem. (Not sure what exactly this imples for note-taking and zettelkasten method. My preferred way to make notes would be like making wiki pages, so I would mention these connections at the bottom of the page.) For example, there are many proofs that there are infinitely many primes, but I enjoyed reading an argument how having finitely many primes would allow us to create an insane compression algorithm. (You take the input as a binary number, factorize it, and save the factors. If your input is much larger than the hypothetical largest prime, the output file size will be a logarithm of the input file size.)
To me it helps to imagine that I am explaining the topic to someone else. If I had enough time, I would never copy the textbook; I would rewrite it using my own words, and probably change the entire structure. (In other words, instead of “paper1 → paper2”, it would go “paper1 → internal model → paper2″.) Unfortunately, doing things the way I wish takes a lot of time.
For example, if I make notes about programming, I am trying to write the simplest code that illustrates the concept in isolation from other concepts. (Most examples I find online are introducing multiple concepts at the same time. Okay, I suppose in reality, you usually use X and Y and Z together in the same project. But I still want to see X used separately, and Y separately, and Z separately. And then an example of how X and Y and Z go together.)
I would suggest to explore the concept in unusual ways. For example, when you learn about commutative operators, don’t just use “addition” and “multiplication” as obvious examples, but also think about ones like “least common multiple” or even “these words have the same amount of strokes in Chinese”. (Ultimately coming to “there is an arbitrary undirected graph, where the nodes are the possible inputs, and each edge contains an arbitrary output as a label”.)
Also, when you learn things, the value is not merely in the individual things, but also (mostly?) in their connections to other things. That is the difference between a newbie who can recite the facts but cannot apply them, and an expert who can immediately take three abstract concepts and chain them together to solve a problem. (Not sure what exactly this imples for note-taking and zettelkasten method. My preferred way to make notes would be like making wiki pages, so I would mention these connections at the bottom of the page.) For example, there are many proofs that there are infinitely many primes, but I enjoyed reading an argument how having finitely many primes would allow us to create an insane compression algorithm. (You take the input as a binary number, factorize it, and save the factors. If your input is much larger than the hypothetical largest prime, the output file size will be a logarithm of the input file size.)