(or: How to Read Knuth)

The ancient masters are deep and obscure, subtle and comprehensive.
Well, if they are deep beyond comprehension, I can still describe them:
Careful as if crossing thin ice.
Alert as if surrounded by rivals.
Courteous as a guest.
Yielding as melting ice.
Simple as an uncarved block.
Opaque as muddy water.

When the water is stilled, it gradually becomes clear;
when the sleeper is moved, he gradually awakens.

Who holds to the Way does not seek completion:
it is only because he is incomplete
that he can grow.

 


chapter notes:

One of the most useful skills I learned in school was how to read math books (and, by extension, any dense technical literature):

  • First, skim it: the chapter, the section, whatever unit of the text is most convenient. Pay some attention to structure and essential definitions, but don’t worry if you don’t understand everything the first time through — skip over the tough bits.
  • Take a break, then go through it again in more depth. Again, you won’t get everything, but you will now be primed to understand the content, in ways you weren’t the first time around.
  • Take a break. Let the material settle in your head. Meditate and/or sleep on it.
  • Read through it again, in detail. This time, you can skim the bits you understand thoroughly, and focus on anything else that isn’t perfectly clear.

You may need to repeat the last two steps a few times, but eventually you will be enlightened.

Of course, this assumes you understand the prerequisites, and leaves out looking up other sources, discussions with teachers and peers, working out problems assigned or otherwise, and so on. But the primary points are these:

  • It is an iterative process. Dense, unfamiliar abstract material is difficult to learn, and the most effective route is to familiarize yourself with it in stages.
  • The meditation bit is important, and it really works. It helps to have a mixture of detachment from and engagement with the material, without frustration, anger, or forced focus. Although this kind of mental attitude is difficult to describe, it does seem very much a Daoist sort of attitude.
  • However, note that the meditation is not the *only* thing. I have suggested alternating between active reading and meditative consideration (although in fact you should do whatever gets the job done, and ignore any suggestions to the contrary…).

At any rate, to me this chapter seems the very image of this process, and the attributes of the ancient masters seem like a description of the virtues of a well-written paper — with simplicity at its core, care in its composition, and opacity only as a consequence of the fundamental concepts to be grasped.