And there is no reason to exclude China from co-operation in space.
Yet for both leaders, there is more to be gained from co-operation than conflict.
He said that in the past four decades China-US relations had gone through "wind and rain" and reaped huge benefits from co-operation.
If the gains from co-operation are great, there is a big incentive to be a free rider: to take the gains without paying the cost.
But America and China are not just rivals for global influence, they are also mutually dependent economies with everything to gain from co-operation.
China has been making substantial efforts on its own to curb such excesses, and these might well benefit from co-operation with outsiders.On another level, China knows it can score valuable political points by agreeing to such human-rights initiatives.
There is nothing to be gained from co-operation in zero-sum games, but participants in non-zero-sum games typically stand to do better by co-operating with each other than by singly pursuing their individual interests.
Mr Dawkins suggests the source is a combination of genetic instincts, which evolved because morals allowed humans to benefit more efficiently from co-operation, and a cultural Zeitgeist.For some people consolation and inspiration are genuine benefits of religion, as even Mr Dawkins will allow.
It seems willing to accept Russia as a partner in diplomacy; for its part, Russia may have been persuaded that it has more to gain from co-operation than from wrecking.Meanwhile, the Kremlin has begun to repair relations with Azerbaijan, which had, until recently, been among the most Russophobic of ex-Soviet republics.
Russia may get a generous serving of the post-Saddam oil and reconstruction contracts as a reward for keeping quiet or America may decide that other, more useful, friends deserve a bigger share.The argument in Washington seems to be between those who regard Russia as too weak to matter and those who think that there are big benefits to be won from co-operation and respect.
Mr Xi said the two countries' interests were now "more than ever interconnected", with much to gain from co-operation.
