Considering that he invented Twitter and is about to launch another potential game changer with his new company, Square, Jack Dorsey has one of the lowest profiles in tech. But from his childhood obsession (city maps) to his dream job (mayor of New York City), Dorsey’s eclectic, ascetic vision has focused on the flow of human interaction. David Kirkpatrick gets the press-shy visionary talking about his taxicab inspiration, his ejection as Twitter’s C.E.O., and his ambition to make Square the payment network of the future.