“In the October 1950 Issue of La Gazette du cinema, a young Jean-Luc Godard, writing pseudonymously, penned a sentence that serves, for biographer Richard Brody, as a skeleton key to the legendary director’s often-inscrutable inner workings: ‘At the cinema, we do not think, we are thought.’ Brody, a film critic and editor at the New Yorker, uses this key throughout his rigorous yet readable biographical study, as dauntingly massive as it is helpfully clarifying, to unlock the intensely personal and political influences that shaped the work of an artist as pivotal to the evolution of his chosen medium as Picasso and Bob Dylan were to theirs. Like Picasso, Godard is an artist of many phases, each with enough revolutionary singularity to have sustained the reputation of any other director; like Dylan, he was a meteoric phenomenon of the 1960s who suffered a motorcycle accident and retreated to domestic…