President Bush made a strong case at the U.N. for why the world community should not allow Iraq to go on flouting U.N. weapons inspections. But what struck me most about the scene was how intently the U.N. delegates were waiting for, and listening to, the president's speech. We should listen to their listening — because it is telling us some important things about our world.

First, for all the noise out there about rising anti-Americanism, America remains the unrivaled leader of the world — the big power, which makes its share of mistakes, but without which nothing good happens.

But, second, while our leadership requires American valor, it is ultimately based on American values. That is, what gives America its unprecedented power and influence today is the fact that, more than at any time in history, the world has come to accept the Western values of peace, democracy and free markets — around which American society is organized. That is the truly significant trend in the world today — not terrorism or anti-Americanism.

Third, while terrorists like Osama and rogues like Saddam can unleash lethal events against us, they do not represent an alternative trend with any global appeal. Indeed, the reason the terrorists unleash huge events like 9/11 is precisely because they have no mass following and must substitute sound and fury for compelling ideas, enduring achievements and popular support.

Hitler's Germany, Stalin's Soviet Union and Mao's China not only represented powerful alternatives to U.S. leadership in their day but also powerful, and popular, alternative ideologies to peace, democracy and free markets. With Hitler's, Stalin's and Mao's downfalls in the last century, there is no longer any serious military or ideological rival to these ideas. That global trend is enormously favorable to us — but its sustainability depends on America's health and the wisdom with which it leads this world, particularly now.

I wish I could say I had thought of all these concepts on my own. But I didn't. They come from reading an important and compelling new book, "The Ideas That Conquered the World: Peace, Democracy and Free Markets in the Twenty-first Century," by Michael Mandelbaum of Johns Hopkins and the Council on Foreign Relations.

Mr. Mandelbaum's thesis is that all the powerful ideological rivals to America and its democratic allies have been vanquished and that three big ideas now dominate global politics: The first is peace as a way of organizing international relations. By that he means the core idea that has finally stabilized a fractious Europe, namely arms control — the notion that armies should be configured primarily for defense, with a high degree of transparency so everyone knows what everyone else is doing. The second idea that has triumphed is the notion that free markets are the best way for nations to grow from poverty to prosperity. And the third is that democracy is the ideal form of political organization.

"To be sure, these ideas are not practiced everywhere," Mr. Mandelbaum said, "but they are far more powerful and attractive than any other ideas and have no serious rivals today. Bin Laden and Saddam pose a threat to the personal safety of people living in our world, but they do not pose the kind of existential threat that Hitler, Stalin or Mao did. Neither man controls a major country with large, attractive ideas."

And that brings us to today. It is crucial that as we confront Iraq, or other terrorist events, that we do it in a way that reinforces the positive global trends already in our favor.

"That means," Mr. Mandelbaum said, "dealing with Iraq with as many allies as possible, with as broad an international endorsement as possible, so that confronting Iraq is seen as enforcing what are now widely accepted norms — rather than the policy of one particular country. We must act vis-à-vis Iraq in a way that persuades people that this is an international imperative, not an American preference."

Never forget: We are winning. The terrorists and the rogues do not have the power to dislodge our world, or reverse the broad positive trends. Only we, the trendsetters, can do that — by acting in ways that would upset the trend toward peace, disrupt global markets and put the democracies at odds with one another. Do that, and we really would create a dangerous world — a world where the best Western ideals would be mismanaged and the country most important for sustaining those ideals — America — despised, weakened or discredited.