This week, Barack Obama will welcome Xi Jinping to Rancho Mirage in California. For the first time in a century, one could debate whether the US or the Chinese president is the more important of the two. Mr Obama has less than four years left to serve while Mr Xi is at the start of an expected 10-year term. By the time he steps down, China may be the world’s biggest economy.

The US and China disagree on a range of issues, from Iran and North Korea to cyber warfare and the extent of the US presence in the Pacific. Pessimists see a real danger of war as the two powers butt up against each other’s interests. The US pivot, seen by Washington as a necessary “hedge” against China, looks like raw containment to Beijing. As He Yafei, a senior Chinese diplomat, wrote recently, there is a severe “trust deficit” between the two sides.

Yet things are not as bad as the pessimists would have it. Outside the military realm, the two have built a formidably broad-ranging dialogue. That at least provides an opportunity to build the trust that is lacking and to move gradually to what amounts to a new world order.