Stanford, Calif.

The woman sitting opposite me, dressed in a charcoal pantsuit and a duck-egg-blue turtleneck, can’t go anywhere, at any time of day, without a bodyguard. She is soft-spoken and irrepressibly sane, but also—in the eyes of those who would rather cut her throat than listen to what she says—the most dangerous foe of Islamist extremism in the Western world. We are in a secure room at a sprawling university, but the queasiness in my chest takes a while to go away. I’m talking to a woman with multiple fatwas on her head, someone who has a greater chance of meeting a violent end than anyone I’ve met (Salman Rushdie included). And yet she’s wholly poised, spectacles pushed back to rest atop her head like a crown, dignified and smiling under siege.

Ayaan Hirsi Ali, born in Somalia in 1969, is Islam’s most eloquent apostate. She has just published a slim book that seeks to add a new four-letter word—dawa—to the West’s vocabulary. It describes the ceaseless, world-wide ideological campaign waged by Islamists as a complement to jihad. It is, she says, the greatest threat facing the West and “could well bring about the end of the European Union as we know it.” America is far from immune, and her book, “The Challenge of Dawa,” is an explicit attempt to persuade the Trump administration to adopt “a comprehensive anti-dawa strategy before it is too late.”

Ms. Hirsi Ali has come a long way from the days when she—“then a bit of a hothead”—declared Islam to be incapable of reform, while also calling on Muslims to convert or abandon religion altogether. That was a contentious decade ago. Today she believes that Islam can indeed be reformed, that it must be reformed, and that it can be reformed only by Muslims themselves—by those whom she calls “Mecca Muslims.” These are the faithful who prefer the gentler version of Islam that she says was “originally promoted by Muhammad” before 622. That was the year he migrated to Medina and the religion took a militant and unlovely ideological turn.

At the same time, Ms. Hirsi Ali—now a research fellow at Stanford’s Hoover Institution, where I also work—is urging the West to look at Islam with new eyes. She says it must be viewed “not just as a religion, but also as a political ideology.” To regard Islam merely as a faith, “as we would Christianity or Buddhism, is to run the risk of ignoring dawa, the activities carried out by Islamists to keep Muslims energized by a campaign to impose Shariah law on all societies—including countries of the West.”

Dawa, Ms. Hirsi Ali explains, is “conducted right under our noses in Europe, and in America. It aims to convert non-Muslims to political Islam and also to push existing Muslims in a more extreme direction.” The ultimate goal is “to destroy the political institutions of a free society and replace them with Shariah.” It is a “never-ending process,” she says, and then checks herself: “It ends when an Islamic utopia is achieved. Shariah everywhere!”

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