I personally find notes and visualizations kind of distracting while reading, the cue of trying to “visualize” something like the Schrodinger equation doesn’t help much, visualizing the symbols themselves won’t do anything for your understanding of it. So what I like to do is take a short break after every section in a chapter and ask myself “what does this knowledge imply?”, “What is the next logical step to take from here?”, basically trying to predict what the next pages in the book will contain. This makes it easier to see which leaps of logic in a book were easy and obvious, and which were much harder. It also provides immediate feedback and lots of “goddamnit, of course, how could I be so stupid?!” moments when I read the book take what is obviously the only possible next step.
Another idea for math study is to look at proofs and try to distinguish between steps that are just mechanical calculation vs steps that are leaps of insight.
With book-based arguments, like a work of philosophy, I find it helps to identify the point of a paragraph and then think beyond it. I like to do that with “Question Notes,” writing one question per paragraph where the paragraph in the text could be a valid answer to the question itself.
In an equation, I often start by imagining how the result changes as the variables change, or why the variables are as they are.
I wonder if this could be productive applied to strictly empirical findings, like the structure of RNA polymerase? Often I find that the textbook will present a structure, then point out the inferences from that structure to its function (and in biology, often the reverse—mRNA and genes were known to exist long before we identified their structure).
In any case, I agree that this is a whole other mode of relating with a text—one that I use, but haven’t focused on as a technique, perhaps because it’s not something that’s as easy to define and apply mechanically. Thanks.
I personally find notes and visualizations kind of distracting while reading, the cue of trying to “visualize” something like the Schrodinger equation doesn’t help much, visualizing the symbols themselves won’t do anything for your understanding of it. So what I like to do is take a short break after every section in a chapter and ask myself “what does this knowledge imply?”, “What is the next logical step to take from here?”, basically trying to predict what the next pages in the book will contain. This makes it easier to see which leaps of logic in a book were easy and obvious, and which were much harder. It also provides immediate feedback and lots of “goddamnit, of course, how could I be so stupid?!” moments when I read the book take what is obviously the only possible next step.
Another idea for math study is to look at proofs and try to distinguish between steps that are just mechanical calculation vs steps that are leaps of insight.
With book-based arguments, like a work of philosophy, I find it helps to identify the point of a paragraph and then think beyond it. I like to do that with “Question Notes,” writing one question per paragraph where the paragraph in the text could be a valid answer to the question itself.
In an equation, I often start by imagining how the result changes as the variables change, or why the variables are as they are.
I wonder if this could be productive applied to strictly empirical findings, like the structure of RNA polymerase? Often I find that the textbook will present a structure, then point out the inferences from that structure to its function (and in biology, often the reverse—mRNA and genes were known to exist long before we identified their structure).
In any case, I agree that this is a whole other mode of relating with a text—one that I use, but haven’t focused on as a technique, perhaps because it’s not something that’s as easy to define and apply mechanically. Thanks.