In one of those happy coincidences of presidential scheduling, just as Barack Obama was receiving a private tour of the Forbidden City in Beijing on Tuesday afternoon following three hours of meetings with Chinese President Hu Jintao, residents of the Czech Republic were celebrating the 20th anniversary of the student protest that started the Velvet Revolution.

If the fall of the Berlin Wall in 1989 and the end of communism in eastern Europe ushered in an era of unparalleled US dominance, Mr Obama's first visit to China 20 years later arguably marks another once-in-a-generation revolution in global power politics – the moment when the shift to a genuinely multipolar world became undeniable.

To the annoyance of the White House, the US media have focused on the conciliatory tone that Mr Obama adopted in his nine days in Asia – including the now notorious deep bow he gave Emperor Akihito of Japan last weekend. Mr Obama's overtures to China were seen as a new “diplomacy of deference” in the words of a relatively polite outlet, while a less polite one described the shift from George W. Bush's brash unilateralism to Mr Obama's polite engagement as a move from “cowboy to kowtow”.

Ten years from now, however, it is the substance and not the tone of the trip that will interest historians. Mr Obama in effect invited Beijing to form a two-nation committee in which the countries would aim for common ground in tackling the world's largest problems. No other country has received such an offer – and none is likely to. In Beijing this week, Mr Obama formally conceded that in today's world the US can get only so far without China's help.

“We know that more is to be gained when great powers co-operate than when they collide,” he said. “The United States welcomes China's efforts in playing a greater role on the world stage – a role in which a growing economy is joined by growing responsibilities.”

US officials put it more bluntly: “There are really only two countries in the world that can solve certain issues,” says Jon Huntsman, the US ambassador to China and former Republican governor of Utah. “So the meetings really have been aimed at co-ordinating like never before on the key global issues.”

The reality of China's ascendance and the shifting global balance of power is not in itself a revelation. But by framing the issues so boldly, Mr Obama has started this week to try to answer the big questions about how this new international order will function.

Those include how the US will seek to assert leadership in a world where it is the strongest but not the dominant power; whether China is really willing to play the sort of global leadership role that Mr Obama desires; and how much importance the two countries will place on the big differences in values and political ideas that separate them.

Mr Obama's controversial overture to China marks two sharp changes in America's stance towards the world. The first, which he repeatedly acknowledged during his election campaign, is the general acceptance that the US now finds itself in a multipolar era.

“I believe that our world is now fundamentally interconnected,” Mr Obama told a hand-picked audience of 400 Chinese students in Shanghai on Monday. “The jobs we do, the prosperity we build, the environment we protect, the security that we seek – all of these things are shared. And given that interconnection, power in the 21st century is no longer a zero-sum game.”