Lars Hedegaard is a Danish journalist who has made his name denouncing Islam, which he describes as "a totalitarian system of thought" whose adherents "rape their own children." Last month, someone showed up at his door with a gun and fired a shot that missed him.

It's just what you would expect of those crazy Muslims, isn't it? Except that in the aftermath, Hedegaard found Muslims across Denmark were conspicuously un-crazy. They did not applaud the assailant or excuse his motives. Instead, they condemned the attack and upheld Hedegaard's freedom to preach unhinged bigotry.

One group even rallied in Copenhagen to disavow such violence. A Dane whose family came from Afghanistan told The New York Times, "We don't defend Hedegaard's views but do defend his right to speak."

Oh, but consider what happened last year when a far-right group marched in front of Berlin mosques carrying signs with caricatures of Mohammed, which Muslims consider forbidden. Sure enough, a subsequent bombing was blamed on Muslims -- a bombing in Sudan. In Germany, however, imams asked the faithful to ignore the provocation, and they did.

These episodes raise the possibility that European (and American) Muslims are not as rabid as they are commonly portrayed by their most vehement critics. Remember the uproar in 2006 after a Danish newspaper published cartoons of Mohammed? There were riots by Muslims -- but in the Middle East and Africa, not Europe. When a German paper published the images, local Muslims responded with a shocking display of restraint.

This is the rule, not the exception. Muslim terrorism, which was expected to explode after 9/11, is slightly less common on the continent than kangaroos. In 2010, Europe had 249 documented terrorist attacks or plots, of which only three involved Muslims. In 2011, there were 174 such episodes -- with Muslims accounting for zero.

Same story on this side of the pond. A new report from the Triangle Center on Terrorism and Homeland Security at Duke University, the University of North Carolina-Chapel Hill and RTI International says, "For the second year in a row, there were no fatalities or injuries from Muslim-American terrorism." Since 9/11, it said, such terrorists have killed 33 people in the United States -- a poor showing compared to the 200-plus slain by right-wing extremists.

Of course, a group can be extreme and intolerant without engaging in outright slaughter of those it hates. Daniel Pipes, director of the Middle East Forum, claims, "A vast number of Muslims, those living in Europe and the Americas no less than those elsewhere, harbor an intense hostility to the West."

You can reach that conclusion only if you pay no attention to what ordinary Muslims say. Most bear as much resemblance to Pipes' lurid portrait as they do to Dolly Parton.

Muslim immigrants in France say they have more in common with French people in general than with people of their own religion or national origin. American Muslims are more likely than their neighbors to express contentment with the state of the country and with their own lives. "Muslims appear to be among the least disenchanted and most satisfied people in the West," concludes journalist Doug Saunders in his 2012 book, "The Myth of the Muslim Tide."

"Intense hostility," you would think, would breed support for terrorism. But with intense hostility scarce, so is sympathy for militants. Among Muslims in Germany, only 1 percent say "attacks on civilians are morally justified." Same with those in France.

Some 8 percent of American Muslims approve of such attacks in some cases -- which sounds high until you recall that 24 percent of all Americans say such attacks are "often or sometimes justified."

If you hear someone in this country preaching violent resistance to the federal government or law enforcement, it's more likely to be a Texas secessionist than a fanatical follower of Islam. Across Western nations, writes Saunders, "support for violence and terrorism among Muslims is no higher than that of the general population, and in some cases it is lower."

The assumption among Islamophobes is that there is something intrinsically alien and incompatible about the presence of Muslims in free countries. In truth, they are not visibly different from other groups that have arrived with the mindset of the past and found themselves transformed into tolerant, loyal and law-abiding souls who value democracy and liberty.

Free societies have a way of doing that.