China's new president, Xi Jinping, ventured abroad on the weekend to meet Barack Obama, the US president.
By all accounts the eight hours of face-to-face talks, on a whole range of topics, were cordial and ended well. "The vast Pacific Ocean," Mr Xi said, "has enough space for two large countries like the United States and China."
He also spoke in positive terms of building a "new model of major country relationships". In dealing with China, however, the Americans, and the rest of the world, must always recall a very old model of foreign policy, one that persists in Chinese thinking to this day: for millennia, the Chinese have perceived themselves as the "middle kingdom", the perennial centre of civilisation. Other realms paid tribute, or should have done so.
Other empires through history have had their own sense of grandeur. But even through the centuries when China's empire and its dynastic system of rule disintegrated under pressure from more dynamic western empires, the old idea held, deep in the Chinese psyche.
The proof of that is the speedy re-emergence of this exceptionalism in the demeanour and strategy of China under the Communist dynasty, so to speak, that emerged in the 1950s. China's self-imposed isolation in the time of Mao Zedong can be seen as part of a long tradition of superior disdain for the rest of the world.
Since the end of Mao's disastrous Great Leap Forward, China really has moved forward, so that today it rivals the US, a country with its own sense of exceptionalism and mission. From Tibet to the South China Sea, the Chinese today display little regard for their neighbours, and while they know how to bluster, they are more adept at projecting their power economically, both in their neighbourhood and by using state enterprises to invest in resource companies around the world.
China is no unstoppable juggernaut. Domestic problems - slowing economic growth, endemic corruption, unresponsive government, and an ageing population - are stirring enough dissent to give the lie to any notion of a monolith of 1.34 billion united people.
But in foreign affairs, the old notion holds. To be sure, China's leaders travel abroad more than their predecessors did, China's place in world trade is obvious, and China is more open to foreign visitors than ever in its history.
The modern world has changed China enormously, and self-perception, too, will change.
But until it does, understanding how the Chinese see the world is vital to all who deal with China.