But what is true of the British is also true of most other world cultures. The world is turning bicultural. From Pakistan to Paris, everyone has a local culture–language, history, food, religion, buildings. But almost everyone has some American culture, too, a secondary culture nudging the first. Thanks to American hyper-power, some 4 percent of the world’s population, the Americans, now dominate the other 96 percent. Compared with this, Rome was just a village with attitude.

So what does the rest of the world think of America? The BBC commissioned polls across a spread of countries to try to find out. The good news for Americans is that our basket of countries regarded them as friendly, united, religious and free. The bad news is that they are also seen as arrogant and are disliked over a wide range of policies, from Israel-Palestine to world poverty and global warming. Overall, 30 percent agreed that “America is reaping the thorns planted by its rulers in the world,” including 56 percent of the French, 48 percent of South Koreans and 46 percent of Indonesians. The quote, by the way, comes from Saddam Hussein.

President George W. Bush has a terrible global image. It’s also clear that many people have only the haziest idea of America, just as many Americans know very little about the rest of the world. To teeming millions, America means only its brands–its burgers, fizzy drinks and a few trite, aging TV series. The deeper United States of Jefferson, Twain, the Constitution, the War Between the States, the New Deal and desegregation… none of that registers at all.

Class makes a difference, self-evidently: there is a global ruling class, and it tends to speak American English, wear chinos on the weekend and know its U.S. culture. American legal ideas have been spread through multinational business. The speaking of English, from India to Canada, makes countries vastly more porous to U.S. influence, but also more sophisticated about it. Bollywood and British tabloids are different from Hollywood and U.S. newspapers by defiant design.

In my country, Americanism now transcends class. The high-income political obsessives of Westminster hoover up the latest books on Clinton and Bush, watch “The West Wing” and speculate about Ari Fleischer’s future. The posh schools of west London are crammed with the voices of Americans, who return to the United States only for the mandatory few weeks on Cape Cod or the Vineyard. Writers I know who cross the Atlantic like frantic petrels wryly describe themselves as “Nylons” (New Yorker-Londoners) or, more poetically, Atlanticans. But the working-class and lower-middle-class British are the ones buying Big Macs and dreaming of family holidays at Disneyland. Among poorer British blacks, U.S.-style evangelical Christian churches are making headway, while the kids rejecting that mimic street culture in Chicago and Los Angeles.

The British experience is relevant around the world because of the intensity of America’s effect on our culture, and how we react. We have become internally divided–partly overseas Americans but also determined to put up barriers. At first glance they seem random ones: Radio 4 is perhaps the most un-American daily act in Europe; baseball will never eclipse cricket, no matter how badly we now play it; in Britain no issue is deader than the death penalty. The point is not where the barriers fall. It’s the need to have them.

Americans, I conclude, need to think harder about how they want to be known in the rest of the world. Religion is more a barrier than a bridge; in once Roman Catholic France or Muslim Indonesia, President Bush’s Protestant certainties grate. Brands are fine, but they are shallow and somehow callous. Nor is America’s awesome military power enough, in itself, for genuine security.

These questions are just going to get bigger. With half the world’s R&D and a young population that will outstrip Europe’s, America is likely to dominate more in the decades ahead, not less. Everyone has to come to terms with that fact–the 96 percent by becoming culturally bilingual, and Americans by realizing, as the British had to, that no superpower is an island. They cannot touch so far beyond their borders without being touched, and changed–perhaps more than they know.