Nancy Gibbs and Michael Duffy are editors at Time magazine and the authors of The Presidents Club: Inside the World's Most Exclusive Fraternity.

"You will be our president when you read this note," George Herbert Walker Bush wrote to Bill Clinton, the man who defeated him in the 1992 campaign, denying Bush the provisional vindication that reelection provides until history has its chance to judge from a distance. Nonetheless, in Oval Office tradition, Bush left a note for Clinton to read on taking office, and it echoed the message of transitions past, even between bitter political rivals: "I am rooting hard for you."

Note the pronoun: You will be our president. My president. In our interviews and research into the private relations among these most public men, the pronouns matter. At a time when Democrats and Republicans in Congress talk past each other and their supporters view collaboration as corrupt, presidents talk to, and about, one another in very particular ways.

"President Obama and I didn't talk much about politics when we played golf the other day," Clinton told us, as we discussed the distinctive code of the "Presidents Club." Clinton was exhausted that day, he recalled, but "when my president summons me, then I come and I would play golf in a driving snowstorm." Which suggests how far the two men had come since their proxy war in 2008.

The offers of help come, often across party lines, because former presidents know what incoming presidents only learn over time...