When two planes smashed into the World Trade Center towers in New York City and another crashed into the Pentagon outside of Washington, D.C., on September 11, 2001, most Americans saw the attacks as an act of war. But to those who interpret the teachings of the Koran, the holy book of Islam, in extreme ways, the destruction and damage wreaked on the financial and military centers of the United States was seen as an act ordained by Allah, the God of Islam.

Similarly, the continuing conflict in the Middle East between Israelis and Palestinians over territory and government is rooted in deeply held religious and ideological beliefs that span...