Having spent two days getting to know each other in Sunnylands, California, in June, Presidents Xi Jinping of China and Barack Obama of the U.S. sent each other Christmas gifts this year. Obama sent a B-52 bomber through airspace that China claims as its own; Xi then sent a ship from his new carrier group to cut a dangerous 200 yards in front of an American cruiser. Cool war heating up much?

The U.S. and China have the most important bilateral relationship in the world. The rising global superpower and the status quo superpower are deeply cooperative and deeply competitive — at the same time. Hostile military gestures are part of that relationship, but so was the warm Sunnylands summit, to say nothing of separate trade negotiations each side is pursuing with the same Asian countries. In 2013, the year Xi called for “a new type of great-power relationship” between the countries, those contradictions deepened. The dangers of nationalism on both sides can be increasingly sensed. Hillary Clinton and other aspiring Democratic presidential candidates had better pay attention — you can be sure that Bobby Jindal and other smart, aspiring Republican candidates are.

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Written by Noah Feldman

Photograph by Pete Souza/Official White House Photo