We Americans are sometimes like the ancient Greek astronomer Ptolemy. That is, we see the United States as the fixed center of the universe, with other nations and events revolving around us. I think it's one of our endearing qualities, this ebullient national self-centeredness -- except when it leads to errors in geopolitical navigation.

President Bush gave a moving evocation of this American Ptolemaism in his acceptance speech last week. "Like generations before us, we have a calling from beyond the stars to stand for freedom," he said. Like his mentor Ronald Reagan, Bush conveyed his conviction that God has bestowed great blessings on the United States -- made it a "shining city on a hill" -- with corresponding responsibilities to lead the world.

The problem for the United States is the disconnect between this self-image and the way the rest of the world feels about us. Increasingly, people in other countries don't see America as that beacon of idealism but as something menacing. We can think they're wrong and we can choose to ignore them, but unfortunately, that won't change the way they feel.

This disconnect is clear in recent poll findings. A study released in March by the Pew Research Center found "somewhat" or "very" unfavorable views about the United States among 63 percent of those surveyed in Turkey, 61 percent in Pakistan, 93 percent in Jordan and 68 percent in Morocco. And these are our allies in the Islamic world.

The Pew study found that images of the United States were almost as negative among America's allies in "old Europe," with sharp deterioration from two years before -- 62 percent were unfavorable in France, compared with 34 percent in 2002, and 59 percent were unfavorable in Germany, compared with 35 percent before.

The same bleak trend was evident in a 2003 study co-sponsored by the German Marshall Fund of the United States, a group for which I serve as a trustee. Less than half the Europeans surveyed said they wanted to see a strong U.S. presence in the world, down from 64 percent the previous year.

The Ptolemaist in me wants to tell the rest of the world to go to hell. In economic, military and political terms, the United States is the center of the universe -- and it does have a historic mission to spread its ideals of liberty and democracy. You could hear a roar of approval for this view when Bush told the Republicans last week: "I believe that America is called to lead the cause of freedom in a new century."

But we should consider the need for a Copernican revolution in the way we think about America and the world. As students of history recall, the 16th century Polish astronomer Nicolaus Copernicus shattered conventional wisdom when he argued that Earth is not at the center of the solar system but is one of many planets revolving around the sun. This theory was a blow to the idea that God had set Earth at the center of his creation.

The importance of Copernicus was not simply that he got it right but that the truth he revealed allowed scientists to make accurate calculations at last about the Earth's orbit and the movement of other planets. Realizing that the Earth wasn't at the center of the universe didn't make earthlings any less important; it just allowed them to do their sums right.

One of John Kerry's strengths in this presidential campaign is that he's a Copernican. He understands that however powerful and important the United States may be, it isn't the fixed center of the world. There are other nations, traveling in their own orbits -- with their own cultures, traditions and values -- which must be taken into account. Kerry takes a lot of flak from Republicans for this view, but critics miss the point.

You can't wish away America's present unpopularity in the world. It's a fact, and a dangerous one. The task of leadership, especially in a time of war -- is to gather support among other nations for U.S. policies. That's a subtle process, but it begins with a recognition that however blessed America may be, it doesn't have a God-given right to tell everyone else what to do. When America tries this approach (and Bush is hardly the first president who's guilty of it), it tends to make enemies.

So in this political season, a little more Copernicus, please. Seeing America as a great nation in a system of nations, each spinning at its own speed, will help the United States navigate better in the long journey to create a stable world, where our terrorist enemies can be contained. Who knows, it could even win us more friends.