What you think you know about them is likely wrong and that's dangerous.

Winning hearts and minds - the Bush administration, foreign policy wonks, even the U.S. military agree that this is the key to any victory over global terrorism. Yet our public diplomacy program has made little progress on improving America's image. Few seem to recognize that American ignorance of Islam and Muslims has been the fatal flaw.

How much do Americans know about the views and beliefs of Muslims around the world? According to polls, not much. Perhaps not surprising, the majority of Americans (66%) admit to having at least some prejudice against Muslims; one in five say they have "a great deal" of prejudice. Almost half do not believe American Muslims are "loyal" to this country, and one in four do not want a Muslim as a neighbor.

Why should such anti-Muslim bias concern us? First, it undermines the war on terrorism: Situations are misdiagnosed, root causes are misidentified and bad prescriptions do more harm than good. Second, it makes our public diplomacy sound like double-talk. U.S. diplomats are trying to convince Muslims around the world that the United States respects them and that the war on terrorism is not out to destroy Islam. Their task is made infinitely more difficult by the frequent airing of anti-Muslim sentiment on right-wing call-in radio, which is then heard around the world on the Internet.

Finally, public ignorance weakens our democracy at election time. Instead of a well-informed citizenry choosing our representatives, we are rendered vulnerable to manipulative fear tactics. We need look no further than the political attacks on Barack Obama. Any implied connection to Islam - attending a Muslim school in Indonesia, the middle name Hussein - is wielded to suggest that he is unfit for the presidency and used as fuel for baseless rumors.

Anti-Muslim sentiment fuels misinformation, and is fueled by it - misinformation that is squarely contradicted by evidence.

Starting in 2001, the research firm Gallup embarked on the largest, most comprehensive survey of its kind, spending more than six years polling a population that represented more than 90% of the world's 1.3 billion Muslims. The results showed plainly that much of the conventional wisdom about Muslims - views touted by U.S. policymakers and pundits and accepted by voters - is simply false.

For instance, Gallup found that 72% of Americans disagreed with this statement: "The majority of those living in Muslim countries thought men and women should have equal rights." In fact, majorities in even some of the most conservative Muslim societies directly refute this assessment: 73% of Saudis, 89% of Iranians and 94% of Indonesians say that men and women should have equal legal rights. Majorities of Muslim men and women in dozens of countries around the world also believe that a woman should have the right to work outside the home at any job for which she is qualified (88% in Indonesia, 72% in Egypt and even 78% in Saudi Arabia), and to vote without interference from family members (87% in Indonesia, 91% in Egypt, 98% in Lebanon).

What about Muslim sympathy for terrorism? Many charge that Islam encourages violence more than other faiths, but studies show that Muslims around the world are at least as likely as Americans to condemn attacks on civilians. Polls show that 6% of the American public thinks attacks in which civilians are targets are "completely justified." In Saudi Arabia, this figure is 4%. In Lebanon and Iran, it's 2%.

Moreover, it's politics, not piety, that drives the small minority - just 7% - of Muslims to anti-Americanism at the level of condoning the attacks of 9/11. Looking across majority-Muslim countries, Gallup found no statistical difference in self-reported religiosity between those who sympathized with the attackers and those who did not. When respondents in select countries were asked in an open-ended question to explain their views of 9/11, those who condemned it cited humanitarian as well as religious reasons. For example, 20% of Kuwaitis who called the attacks "completely unjustified" explained this position by saying that terrorism was against the teachings of Islam. A respondent in Indonesia went so far as to quote a direct verse from the Koran prohibiting killing innocents. On the other hand, not a single respondent who condoned the attacks used the Koran as justification. Instead, they relied on political rationalizations, calling the U.S. an imperialist power or accusing it of wanting to control the world.

If most Muslims truly reject terrorism, why does it continue to flourish in Muslim lands? What these results indicate is that terrorism is much like other violent crime. Violent crimes occur throughout U.S. cities, but that is no indication of Americans' general acceptance of murder or assault. Likewise, continued terrorist violence is not proof that Muslims tolerate it. Indeed, they are its primary victims.

Still, the typical American cannot be blamed for these misperceptions. Media-content analyses show that the majority of U.S. TV news coverage of Islam is sharply negative. Americans are bombarded every day with news stories about Muslims and majority-Muslim countries in which vocal extremists, not evidence, drive perceptions.

Rather than allow extremists on either side to dictate how we discuss Islam and the West, we need to listen carefully to the voices of ordinary people. Our victory in the war on terrorism depends on it.

John L. Esposito is an Islamic studies professor at Georgetown University. Dalia Mogahed is executive director of the Center for Muslim Studies at Gallup. They co-wrote "Who Speaks for Islam? What a Billion Muslims Really Think."