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When the glorious waves of Barack Obama's rhetoric have washed over us, leaving us warm, tingling and refreshed like a Hawaiian surfer, we should remember King Canute.

On the day Mr. Obama finally won the primaries, he declared that "generations from now, we will be able to look back" (those of us lucky enough still to be alive generations from now) and tell our children (as, presumably, they lean on their walkers) that "this was the moment when the rise of the oceans began to slow and our planet began to heal." That set an Olympic record for hyperbole. The 11th-century Canute, by contrast, had his throne placed on the beach, commanded the ocean to stop coming in - and got his feet wet. He did this (the legend has it) precisely to show his supporters the limits of his power. But then Canute wasn't running for president.

For the next 10 weeks, Mr. Obama must say whatever it takes to get elected, while not giving too many hostages to fortune. At this, he's brilliant: a genius of the inspirationally unspecific. On the morning after, Canute will be called for. I suspect Mr. Obama knows this. His books and policy documents show a nuanced understanding of the world as it is. We may trust that he does not make the mistake of confusing his own rhetoric with reality, so nor should we.

Hailing the Democrats' messiah as "a clear-eyed pragmatist," his newfound running mate, Joe Biden, says a president Obama has a chance "not just to change America but to change the world." That's what a lot of the world hopes, too. Here's the true score: With a good deal of luck and a massive turnout of volunteers and younger voters, Mr. Obama can be elected president, overcoming the electoral obstacles of being black, inexperienced, liberal (in the peculiar contemporary American sense) and intellectual. By just being elected, and being who he is, he would change both America and how the world sees America. Changing the world is another matter.

Schmaltz is a staple ingredient of U.S. politics, and there's no schmaltzfest more buttery than a Democratic convention. Yet, what his wife, Michelle, said in an ur-schmaltzy speech still contains a moving element of truth. That "a girl from the South Side of Chicago and the son of a single mother from Hawaii" could make it this far represents everything good and hopeful about America. After West Side Story, a world suffused with American popular culture thrills to South Side Story.

Actually, it's two stories. Story No. 1 is how the descendants of slaves might occupy the White House; after Colin Powell and Condoleezza Rice at the State Department, this is the final frontier. Story No. 2 is Mr. Obama's own: the offspring of a mobile Kenyan father and white American mother, with family ties in many cultures. A child of our increasingly mixed-up world now standing to become the most powerful man in it.

The most powerful - but less so, relatively, than most of his predecessors since 1945. For this, too, defines the Obama moment: that the relative power of the U.S. president has diminished. Consider what's been happening outside the U.S. election bubble: In Georgia, Russia has cocked a snook at Washington and torn up the terms of the post-Cold War settlement. In Afghanistan and Pakistan, Islamic extremists are growing stronger as we pay the price for George Bush's wild goose chase in Iraq.

At the Beijing Olympics, China has trumpeted its peaceful re-emergence as a world power in spectacular fashion. Those massed acrobats, drummers and dancers sent a message more powerful than any Russian tanks. The world is getting the message, too. Even before the Olympic demonstration, the Pew Global Attitudes Project produced the remarkable results of an opinion poll asking respondents in 24 countries whether China will replace or has already replaced the U.S. as the world's leading superpower. Few thought it already has, but roughly half the French, Germans, British, Spanish and Australians said it will. So did one in three Americans. And in foreign affairs, as in financial markets, perception is a large part of reality.

World trade talks, meanwhile, have collapsed. The steps needed to reduce carbon emissions are not being taken. The ice caps go on melting. It's unclear how even a radical shift in U.S. policy would change this. Michelle Obama spoke of her husband's desire to shift "the world as it is" toward "the world as it should be." But U.S. capacity to do that is far less than it was in the 1940s, or even in the 1990s, when Bill Clinton was lucky enough to walk with history.

The domestic strengths of the U.S. are also not what they were. In the credit crisis of turbo-capitalism, flagship U.S. banks run to the sovereign wealth funds of the Middle and Far East for help. East bails out West. The U.S. housing market teeters on the verge of collapse. Jobs are hard to find. Middle-class Americans slide out of health care and into poverty.

While hundreds of billions of dollars have been squandered in Iraq, and on Terminator IV hardware for the mightiest military the world has seen, anyone who spends time in America can see how civil infrastructure is crumbling. This is not a country that can afford to "pay any price, bear any burden" - to recall the soaring rhetoric with which Senator Ted Kennedy's elder brother once thrilled the world.

America still has extraordinary strengths. Among the greatest of them is its ability to attract the brightest, most energetic and enterprising men and women from across the world, and then to give them the freedom and opportunity to use their talents to maximum effect. People like Barack Obama. As a man, Mr. Obama personifies his country's continued strengths. As a president, he will have to confront its growing weaknesses.