For baseball games, Yankee Stadium seats 50,287. If all the homeless people who now live in New York City used the stadium for a gathering, several thousand of them would have to stand. More people in the city lack homes than at any time since . . . It’s hard to say exactly. The Coalition for the Homeless, a leading advocate for homeless people in the city and the state, says that these numbers have not been seen in New York since the Great Depression. The Bloomberg administration replies that bringing the Depression into it is wildly unfair, because those times were much worse, and, besides, for complicated reasons, you’re comparing apples and oranges. The C.F.H. routinely disagrees with Mayor Bloomberg, and vice versa; of the many disputes the two sides have had, this is among the milder. In any case, it’s inescapably true that there are far more homeless people in the city today than there have been since “modern homelessness” (as experts refer to it) began, back in the nineteen-seventies.

Most New Yorkers I talk to do not know this. They say they thought there were fewer homeless people than before, because they see fewer of them. In fact, during the twelve years of the Bloomberg administration, the number of homeless people has gone through the roof they do not have. There are now two hundred and thirty-six homeless shelters in the city. Imagine Yankee Stadium almost four-fifths full of homeless families; about eighteen thousand adults in families in New York City were homeless as of January, 2013, and more than twenty-one thousand children. The C.F.H. says that during Bloomberg’s twelve years the number of homeless families went up by seventy-three per cent. One child out of every hundred children in the city is homeless.

The number of homeless single adults is up, too, but more of them are in programs than used to be, and some have taken to living underground, in subway tunnels and other places out of sight. Homeless individuals who do frequent the streets may have a philosophical streak they share with passersby, and of course they sometimes panhandle. Homeless families, by contrast, have fewer problems of mental illness and substance abuse, and they mostly stay off the street. If you are living on the street and you have children, they are more likely to be taken away and put in foster care. When homeless families are on the street or on public transportation, they are usually trying to get somewhere. If you see a young woman with big, wheeled suitcases and several children wearing backpacks on a train bound for some far subway stop, they could be homeless. Homeless families usually don’t engage with other passengers, and they seldom panhandle.

One Saturday afternoon, I was standing at the corner of Manor and Watson Avenues, in a southeastern part of the Bronx, waiting for a woman named Christina Mateo. I had met her and her then partner on the street the day before. She had said she would show me what a shelter was like—I had never been in one. They were living in a nearby shelter for homeless families. No shelters say “Shelter” on them in big letters. This one looked like an ordinary shabby apartment building, with a narrow entry yard behind a tall black iron grate whose heavy iron door did not lock. People were going in and out. Two young men, one in a hoodie despite the heat and the other in a clean, tight white T-shirt and a black do-rag with the tie ends dangling, leaned into the open windows of cars that pulled up. In between doing that, they looked at me. I am past the age of being a prospect or a threat. I nodded back, genially.

Christina came down the sidewalk pushing a stroller. With her were her nineteen-year-old daughter, her seventeen-year-old son, her fifteen-year-old daughter, and two grandchildren. They had just picked up the younger grandchild from a shelter where she was living with her other grandmother. We all went in, lifting the strollers, and crowded into the small elevator. The security person at the desk asked Christina if I was with her and she said I was. At the door to her fourth-floor apartment, she took out a single key, unattached to any chain, key ring, or other keys, and opened the door.

Uncheerful interior, and an air of many people having recently passed through; the floors were like the insides of old suitcases, with forgotten small things in the corners. Bent window blinds; tragic, drooping, bright-green shower curtain; dark hallway opening onto two bare bedrooms. Christina is forty-one and has pained, empathic dark-brown eyes. She wore blue denim cutoffs, a white blouse, sandals, ivory polish on her fingernails and toenails, and her hair in a bun. Sitting on the only chair in the larger bedroom while I perched on the bed, she told me how she came to be here. She was a home health aide. After the deaths of patients whom she had grown close to—one of them a four-year-old girl with AIDS—she had a breakdown and was given a diagnosis of P.T.S.D. In shelters, out of shelters; for a while she enjoyed her own apartment, with a rent subsidy from a program established by Mayor Bloomberg. The program was cut. She lost the apartment, complicatedly, somehow without being evicted right away, although if she had been, she said, she would have qualified for other, preferable housing.

“Please read back that last remark in a more murdery voice.” Facebook

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An accordion file of documents leaned at her ankle. Everybody has documents, but the homeless must keep theirs always close by. She showed me letters with letterheads and foxings and pencil underlinings, and a sheaf of certificates attesting to her success in various programs: Parenting Skills, Anger Management, Women’s Group, Basic Relapse Prevention (“I was smoking a lot of marijuana, and this course taught me how to recognize my triggers. Boredom was one of my triggers”), Advanced Relapse Prevention, and My Change Plan. “What I’m waiting for is the paper saying that we have been declared eligible to stay in this shelter. Right now my case is under review. This place is adequate, but it’s not hygienic—but I don’t want to move. Stability is very important. They will decide if we can stay or not, and then they’ll slide the paper under the door.” She pointed to the end of the dim hallway as if this paper might appear at any moment, sliding in silently like the checkout bill in a hotel room.

As it happened, the news Christina was expecting arrived late that same night, in the form of a shelter employee who knocked on the door and presented the paper by hand. It said that she had been declared ineligible for shelter and would have to go to the PATH center before eight-thirty the next morning to reapply.

Some of the things people have said to me outside the PATH center:

“I came here first when I was eighteen, when foster care maxed me out. I been in the system for fourteen years, and I don’t know how many times I’ve had to come back here. When you go to PATH, they always want to deny you. They don’t believe you really homeless.”