When supporters of the "Vote Leave" campaign sketch out a future for Britain outside the European Union (EU), they often point to the "Anglosphere" of English-speaking nations - bequeathed by Britain's imperial past. So Mr Barack Obama's intervention in Britain's EU referendum last week was a potentially devastating moment for the Brexit campaign. Here was the President of the US - the most powerful member of the Anglosphere - arguing forcefully for Britain to stay inside the EU.
In desperation, some members of the Leave campaign have suggested that Mr Obama might harbour a special animus against Britain. London Mayor Boris Johnson flirted with the theory that the "part-Kenyan President's ancestry" might explain his views.
In reality, no special explanation is needed for Mr Obama's remarks. It has long been US policy to support British membership of the EU.
Yet the Brexiters are on to something in a broader sense. For all the ritualistic tributes to the enduring nature of the "special relationship", something has changed during the Obama years. That change is a growing awareness in both Washington and London of the rise of Asia, which has made both the US and Britain reconsider their approaches to the world - and each other.
President Obama's personal background does indeed matter here. But the significant point is not that he is the first African-American President, but that he is the first Pacific President. Mr Obama was brought up in Hawaii, in the middle of the Pacific Ocean, and spent several years of his childhood in Indonesia. Like no other president before him, he really grasps the vital and growing importance of the Asia-Pacific region.
The signature foreign policy initiative of the Obama years has been America's "pivot to Asia". Amid all the turmoil in the Middle East and Ukraine, the US President has remained grimly, stubbornly, determined to devote more of his country's diplomatic, military and economic resources to Asia.
There was much talk, during Mr Obama's London visit, about whether the US might strike a separate trade deal with a post-Brexit Britain, or whether it would focus more on the US-EU Transatlantic Trade and Investment Partnership (TTIP). Mr Obama controversially suggested that Britain would be at the "back of the queue" in any quest for a separate trade deal.
But the reality is that America's biggest trade priority is neither Britain nor the EU - it is Asia. While negotiations on TTIP are still years from conclusion, the Trans-Pacific Partnership deal has already been agreed between the US and 11 other nations in the Asia-Pacific region, and now awaits ratification.
Some Brits and Europeans hope that the departure of President Obama might mean that the US places less emphasis on Asia and pivots back to the Atlantic.
That is unlikely. Any US president who looks at America's strategic priorities is likely to come to conclusions similar to Mr Obama's. Mrs Hillary Clinton, his likeliest successor, is a firm believer in the "pivot" to Asia, as she made clear in a 2011 article entitled America's Pacific Century.
The British, in particular, have few grounds to complain about America's current preoccupation with Asia and the Pacific, since the Cameron government has been conducting its own pivot to Asia - even at the expense of ties to the US.
Prime Minister David Cameron has led a succession of high-profile trade delegations to Asia and signed Britain up as a founder member of the Beijing-based Asian Infrastructure Investment Bank, against the express wishes of the American government. One member of the Obama administration complained (to the Financial Times) about Britain's "constant accommodation" of China.
Of course, there are still deep ties linking Britain and the US. Anybody who doubts that should consider the number of leading members of the American foreign policy establishment who once studied at Oxford. Ms Susan Rice, Mr Obama's national security adviser, Mr Bill Burns, who was Mrs Clinton's deputy at the State Department, and Mr Jake Sullivan, one of her closest advisers, are all Oxford alumni.
These kinds of links help give Britain easy access in Washington. But, in future, even elite educational ties may be thinner. Mr Stephen Schwarzman, an American financier, has just set up a major scholarship scheme, inspired by the Rhodes scholarships to Oxford, to take high-achieving Americans and others to study at Tsinghua University in Beijing. Mr Schwarzman's not-unreasonable assumption is that, in future it might be more important for aspiring American leaders to understand China.
The rise of Asia is also changing the nature of Canada and Australia, two other key members of the historic Anglosphere. Australia does 10 times as much trade, by value, with China and Japan as it does with Britain. The population of Toronto, Canada's largest city, is now around 35 per cent ethnic Asian, and the figure is well over 40 per cent for Vancouver on the Pacific coast.
Still, any Brits who feel nostalgic for the Anglosphere, and a little resentful about Mr Obama's "back of the queue" comments, might reflect how much they still benefit from the cultural power of the US. The traditional Anglosphere may be in disrepair. But a different sort of Anglosphere has emerged in Brussels, with English now the common language of the EU institutions.
THE FINANCIAL TIMES