After a history of how non-fiction prose has come to be taught--it comes partly from the renaisssance work of assimilating classical culture and partly from legal argument, he gives a description of essays--a sort of writing which begins with a question rather than a premise and which describes the discursive work of getting an answer.
(IIRC, I was never given any systematic explanation, good or bad, of how to write an essay, but I do remember having to write about who was the tragic hero of _Julius Caesar_ and wondering why anybody would care.)
The river's algorithm is simple. At each step, flow down. For the essayist this translates to: flow interesting. Of all the places to go next, choose the most interesting. One can't have quite as little foresight as a river. I always know generally what I want to write about. But not the specific conclusions I want to reach; from paragraph to paragraph I let the ideas take their course.
So, what's interesting?
Surprises are things that you not only didn't know, but that contradict things you thought you knew. And so they're the most valuable sort of fact you can get. They're like a food that's not merely healthy, but counteracts the unhealthy effects of things you've already eaten.
This at least starts to address one of the questions I've been chewing on for a while--how to be interesting. I'm at least decent at it, but the web and the net are plagued by people who are want attention but don't know any pleasant way of getting it. Telling them about surpise might help and is kinder than asking them to come back when they can pass a Turing test.