I've read Villehardouin's chronicle of the Fourth Crusade at least two times, maybe three. And yet if I had to write down everything I remember from it, I doubt it would amount to much more than a page. Multiply this times several hundred, and I get an uneasy feeling when I look at my bookshelves. What use is it to read all these books if I remember so little from them?
A few months ago, as I was reading Constance Reid's excellent biography of Hilbert, I figured out if not the answer to this question, at least something that made me feel better about it. She writes:
Hilbert had no patience with mathematical lectures which filled the students with facts but did not teach them how to frame a problem and solve it. He often used to tell them that "a perfect formulation of a problem is already half its solution."
That has always seemed to me an important point, and I was even more convinced of it after hearing it confirmed by Hilbert.
我一直深以为然。看到希尔伯特也这么想，我就更加确信了。
But how had I come to believe in this idea in the first place? A combination of my own experience and other things I'd read. None of which I could at that moment remember! And eventually I'd forget that Hilbert had confirmed it too. But my increased belief in the importance of this idea would remain something I'd learned from this book, even after I'd forgotten I'd learned it.
Reading and experience train your model of the world. And even if you forget the experience or what you read, its effect on your model of the world persists. Your mind is like a compiled program you've lost the source of. It works, but you don't know why.
The place to look for what I learned from Villehardouin's chronicle is not what I remember from it, but my mental models of the crusades, Venice, medieval culture, siege warfare, and so on. Which doesn't mean I couldn't have read more attentively, but at least the harvest of reading is not so miserably small as it might seem.
