By now, many know the legend of Eric Schmidt—how, back in 2001, Google’s young co-founders, Larry Page and Sergey Brin, brought him into the company in its critical early years to be “the adult in the room” and instill discipline in their unruly, fast-growing start-up.

The boys—28 and 27 years old at the time—had first hoped Steve Jobs might take the gig. Not to be. Later they were introduced to Schmidt, a seemingly mild-mannered 46-year-old in a baggy suit who was C.E.O. of Novell, a software company that was losing ground to Microsoft. On the surface the three didn’t seem to have much in common. Until, that is, the conversation turned to Burning Man, the quasi-apocalyptic, sometimes druggy, often free-swinging sex-fest in the Nevada desert, of which Sergey and Larry were big, big fans.