Down the hall from Mark Zuckerberg's desk sits a virtual reality studio. Foreign heads of state and other dignitaries have been known to lose themselves here in games of zero-gravity Ping-Pong and the real-seeming experience of firing virtual fireworks at each other. Such are their number, and frequency, that on an early summer morning Zuckerberg is at a loss to remember—or perhaps too diplomatic to divulge—one of their names. He does, however, recall the anecdotal nugget of the man's visit.

"He wouldn't leave," says Zuckerberg, sitting in a glass-walled conference room in Facebook's cavernous and almost factorylike headquarters in Menlo Park, California. "His aide was like, 'Mr. Prime Minister, you have to take off…you're two hours late for your flight.'"