For the first year and a half of Beatlemania, the Stones were No. 2 only in publicity—their sales lagged beyond the Dave Clark Five's and barely stayed ahead of the Kinks' and the Animals'. Then came "Satisfaction." It was the perfect Stones paradox—the lyrics denied what the music delivered—and it dominated the summer of 1965. Driving home from rainy retreats, vacationing parents and their children shouted out "I can't get no" in unison, while older brothers and sisters decided that the middle verse was about a girl who won't put out because it's her period. A whole country was brought together, sort of, by Mick and Keith's anthem of frustration.

Suddenly, the Stones' project of radical self-definition was becoming a mass movement—against everything that kept the world within our reach and out of our grasp, everything that stopped us from making felt possibilities real. Mick and...