THE perpetrators of these horrific killings fall along what one might call the Loughner-Klebold spectrum. Everyone seems to have known that Jared Loughner, who wounded Representative Gabrielle Giffords and killed six others at a meet-and-greet in Tucson in 2011, had something seriously wrong with him.

In an e-mail months before the shootout, a fellow student said: “We have a mentally unstable person in the class that scares the living crap out of me. He is one of those whose picture you see on the news, after he has come into class with an automatic weapon.” The problem was obvious, and no one did anything about it.

No one saw anything wrong with Dylan Klebold. After he was arrested for theft, Mr. Klebold was assigned to a diversion program that administered standardized psychological tests that his mother said found no indication that he was suicidal, homicidal or depressed. Some people who are obviously troubled receive no treatment, and others keep their inner lives completely secret; most murder-suicides are committed by people who fall someplace in the middle of that spectrum, as Adam Lanza appears to.

So what are we to do? I was in Newtown last week, one of the slew of commentators called in by the broadcast media. Driving into town, I felt as though the air were full of gelatin; you could hardly wade through the pain. As I hung out in the CNN and NBC trailers, eating doughnuts and exchanging sadnesses with other guests as we waited for our five minutes on camera, I was struck by a troubling dichotomy. People who are dealing with a loss of this scale require the dignity of knowing that the world cares. Public attention serves, like Victorian mourning dress, to acknowledge that nothing is normal, and that those who are not lost in grief should defer to those who are. When I stopped in a diner on Newtown’s main drag, I did not sense hostility between the locals and the rest of us but I did sense a palpable gulf between us. We need to but cannot know Adam Lanza; we wish to but cannot know his victims, either.

In a metaphoric blog post called “I Am Adam Lanza’s Mother,” a woman in Boise, Idaho, who clearly loves her son but is afraid of him worries that he will turn murderous. Many American families are in denial about who their children are; others see problems they don’t know how to stanch. Some argue that increasing mental health services for children would further burden an already bloated government budget. But it would cost us far less, in dollars and in anguish, than a system in which such events as Newtown take place.

Robbie Parker, the father of one of the victims, spoke out within 24 hours of the shooting and said to Adam Lanza’s family, “I can’t imagine how hard this experience must be for you, and I want you to know that our family and our love and our support goes out to you as well.” His spirit of building community instead of reciprocating hatred presents humbling evidence of a bright heart. It also serves a pragmatic purpose.

My experiences in Littleton suggest that those who saw the tragedy as embracing everyone, including the families of the killers, were able to move toward healing, while those who fought grief with anger tended to be more haunted by the events in the years that followed. Anger is a natural response, but trying to wreak vengeance by apportioning blame to others, including the killer’s family, is ultimately counterproductive. Those who make comprehension the precondition of acceptance destine themselves to unremitting misery.