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copying is essentially a very slow kind of reading. back when the literary language was often very different from the spoken language, comprehension wasn't some immediate thing that could be taken for granted. even the surface grammatical meaning of a sentence might not be obvious. struggling with all of that leads not just to the thoughts the author intended, but all sorts of other alternate possibilities
the same thing happens when i read mathematics (esp. research papers). for close readings, you treat the written proofs as a "cookbook recipe" for reproducing the argument in your own brain. often there are steps that are unclear at first and which require deep thought, but in the course of trying to understand those, you learn other things the author perhaps didn't intend, or didn't find worth writing
e.g. many of the developments in algebraic geometry up to the 80s or so could essentially be characterized as ideas people had while reading EGA and SGA.
I guess what I'm trying to say is simply that reading is a much slower and more complicated process than we might give it credit for, so rote methods of learning like copying and memorizing are ways to trick ourselves into slowing. of course this only works when one is doing it willingly. when forced to memorize or copy by a teacher, many people manage to learn to do so without actually paying attention to the text
(sorry for writing so much -- in retrospect this probably should have been an email...)
Also, rereading these now, I realize I was basically doing some version of "redoing" by writing these: taking the ideas you wrote about and reworking them into my own words. I guess this is the particular sort of "copying" that a modern university education generally trains it's students with (as you noted with your reference to "the last few hundred years of scholasticism")
Thank you for the thoughtful comments and no need to apologize, these are all great. What is interesting to me is how pointless (close) reading is if you don't apply yourself to it 100%, yet how useful it is in learning something. And there's no external way to tell the two apart; it's even difficult for the learner themselves to tell if they are in fact learning something. The "inefficiency" of rote learning (1/2)
and how easy it is to make it an utter waste of time, plus the fact that the yields aren't immediate or quantifiable, might all be part of the reason why it's looked at so negatively in American schools nowadays, but we lose a lot if we banish it entirely. (2/2)