Our doorman saw the crime scene when he came to work at 5 a.m.

It lay at one end of the nearby street that in its six-block length changes from high-end — a fenced private park that you need a key to enter — to the bustle of a typical crosstown avenue — many-story buildings, old and new, a college dorm, a grocery store, kid places, fast-food places. The crime had occurred on the avenue, where the victim, leaving her night shift at an IHOP, was heading to the subway that would take her home. Security cameras showed a man in a dark sweatshirt and face mask following her on the other side of the avenue, until he crossed it, came up behind her, and killed her with a single shot to the head.

The victim was identified as Imani Armstrong, 25. She had moved to the city from Virginia three years ago with a woman, from whom she was recently divorced. She had two children currently in foster care, and was reportedly taking anger-management classes in an effort to get them back. She worked two jobs, one as an exotic dancer, the other at the pancake house. One of her co-workers there told a reporter, “She was happy. She was greeting the customers and all that stuff. . . . She worked well. She got along with everybody. She knew a lot of people around here.”

The alleged killer, arrested two days later, was Clarkson Wilson, a 44-year-old with a long rap sheet. Early in the century he had done time for armed robbery. Anonymous police sources regaled reporters with accounts of arrests in cases that fell apart. Wilson was the father of one of Armstrong’s children. Cameras showed him waiting outside her place of employment on her last night alive for five hours.

An 18-year-old neuroscience major living in the college dorm (annual tuition: $54,880) said, “When I heard the shot, I was like, ‘Oh, sh**.’ . . . I never predicted something like this to happen, especially across the street from where I live.”

“I was here cooking when I heard a loud boom,” said a 56-year-old man working in a coffee cart on the avenue. “It’s a shame. You have these people killing one another. They kill somebody and the system lets them back out. . . . It’s crazy. The president, the politicians, they are not doing anything about it. All they think about is getting voted back in.”

An aunt of Armstrong in Virginia took a longer view. “To whoever did this, all I can say is, God have mercy on your soul. The thing is, we are hurt, but we do have to forgive. Hurt people hurt people, so this person is hurt. The one that is gonna judge them is God, and when God judges you, it’s the worst judgment. God said ‘Vengeance is mine,’ so I’ll leave it up to God.” She also spoke of what might have been with her niece. “You went out of state, it didn’t work, you come back home. We are going to help you. It’s sad she didn’t reach out.”

We meet with things dying every day. As we age, death finds the range of family and friends, those we know by fate or by choice; outside that circle he culls neighbors, those we know by chance. Living in the same building for decades one acquires city acquaintances, seen every week in the elevator or the laundry room, recognized by sight, not by name, who are at last seen in walkers or wheelchairs, then are seen no more. A few years ago, a single woman living on our floor contracted an aggressive cancer. The management tried to get her out of her apartment (perhaps, what with medical expenses, she had gone into arrears on rent). The super told us he had asked his bosses, in indignation and amazement, “Do you believe in God?” Maybe, maybe not, but city-dwellers, landlords and tenants alike, believe in the Hundred Years’ Rent War.

Murder, however, differs from attrition. Man speeds up the process. We know that murders take place in the city more often than rainy days; students of urban policy will give you charts tracking the ebb and flow of annual rates. But no more than the 18-year-old neuroscience major do I expect to have one occur two blocks from my doorstep. Cities think of themselves as melting pots, bringing everything and everyone cheek by jowl. “Sir, when a man is tired of London, he is tired of life; for there is in London all that life can afford.” Yet cities have many mechanisms of segregation: neighborhoods (meaning differential rents or, at the heights, purchase prices); modes of transportation (the hierarchy of safety is probably chauffeured cars, cabs, buses, subways); men (police-, fire-, door-) who stand on guard for thee. These are the barriers behind which we cook or, when the mood takes us, order in; see patients or winkle out the details of two-hundred-year-old lives via JSTOR; hear music of our own choosing, not ours plus whatever leaks out of somebody else’s headset; read the paper of record (on paper) and the novels of Jane Austen (bound).

Not that I romanticize the sticks. They are not always places of happy camaraderie. The grieving aunt induces our sympathy, but the niece took off years ago, so maybe there were reasons. But here is where her journey ended. Mr. Wilson will have his day in court. Ms. Armstrong has no more days in this world.

Memo to the mayor, elaborating on the remarks of the coffee vendor. Your heart is in the right place. Its being there is the reason you were elected, on the heels of the feckless ideologue who preceded you. But to justify your victory you will have to bring crime down. That will require you to take on those — the district attorneys, the state legislators, the governor — whose misguided policies keep it high. It will take a little aggression, a little mania, a lot of work. Your city needs it.