Third, these scholars have found that religious and factual beliefs play different roles in interpreting the same events. Religious beliefs explain why, rather than how. People who understand readily that diseases are caused by natural processes might still attribute sickness at a particular time to demons, or healing to an act of God. The psychologist Cristine H. Legare and her colleagues recently demonstrated that people use both natural and supernatural explanations in this interdependent way across many cultures. They tell a story, as recounted by Tracy Kidder’s book on the anthropologist and physician Paul Farmer, about a woman who had taken her tuberculosis medication and been cured — and who then told Dr. Farmer that she was going to get back at the person who had used sorcery to make her ill. “But if you believe that,” he cried, “why did you take your medicines?” In response to the great doctor she replied, in essence, “Honey, are you incapable of complexity?”

Moreover, people’s reliance on supernatural explanations increases as they age. It may be tempting to think that children are more likely than adults to reach out to magic to explain something, and that they increasingly put that mind-set to the side as they grow up, but the reverse is true. It’s the young kids who seem skeptical when researchers ask them about gods and ancestors, and the adults who seem clear and firm. It seems that supernatural ideas do things for adults they do not yet do for children.

Finally, scholars have determined that people don’t use rational, instrumental reasoning when they deal with religious beliefs. The anthropologist Scott Atran and his colleagues have shown that sacred values are immune to the normal cost-benefit trade-offs that govern other dimensions of our lives. Sacred values are insensitive to quantity (one cartoon can be a profound insult). They don’t respond to material incentives (if you offer people money to give up something that represents their sacred value, and they often become more intractable in their refusal). Sacred values may even have different neural signatures in the brain.

The danger point seems to be when people feel themselves to be completely fused with a group defined by its sacred value. When Mr. Atran and his colleagues surveyed young men in two Moroccan neighborhoods associated with militant jihad (one of them home to five men who helped plot the 2004 Madrid train bombings, and then blew themselves up), they found that those who described themselves as closest to their friends and who upheld Shariah law were also more likely to say that they would suffer grievous harm to defend Shariah law. These people become what Mr. Atran calls “devoted actors” who are unconditionally committed to their sacred value, and they are willing to die for it.

One of the interesting things about sacred values, however, is that they are both general (“I am a true Christian”) and particular (“I believe that abortion is murder”). It is possible that this is the key to effective negotiation, because the ambiguity allows the sacred value to be reframed without losing its essential truth. Mr. Atran and his colleague Jeremy Ginges argued in a 2012 essay in Science that Jerusalem could be reimagined not as a place but as a portal to heaven. If it were, they suggested, just getting access to the portal, rather than owning it, might suffice.