I'm in love with Mamet the director and Mamet the philosopher of storytelling. (His politics are another matter, but I love lots of people whose politics I don't agree with--like my own father.) His books on theatre, moviemaking, and storytelling are great. He's like a polemicist on storytelling.
I adore his whole perspective on movie directing that Trey described. On the Criterion audio commentary for Homicide, he goes into it. He says that as a director you should never want to hear someone describe a shot you've composed as "interesting." "Interesting" is the worst word, he says. "Direct,"clear," "honest," those are the words you want to hear.
(IIRC, he illustrates the point by telling a funny story about Roger Deakins, who was the DP on Homicide. He makes it clear that he thinks RD is a genius before describing how Deakins wanted to ruin one of the best shots in the movie by making it more "interesting." In the finished film, there's a fantastic visual reveal that the audience doesn't see coming because it isn't being telegraphed with the camera in the way normal film grammar would telegraph it. Basically, Deakins wanted to telegraph it. And Mamet's like, Uh, no, the idea here is that I want the audience to be surprised, not feel the reveal coming. That story is Mamet's POV, obviously, but when you see how the reveal comes off in the finished film, it does look like something a seasoned DP would not be keen on--which is why the reveal works. It's such a badass little reveal that Mamet plagiarizes himself and does it the exact same way in Oleanna.)