After nearly a year of answering questions, John Sorensen posed one of his own: “Do you know what you want to do when you get old?”

It was a day of frustration for Mr. Sorensen, whose 92nd birthday was the day after Christmas. He was in the kitchen of his Upper West Side apartment, holding pieces of a mop that he could not put back together. Gout had made his fingers almost useless, and his right arm hung limp from a torn rotator cuff. Just combing his hair that morning was a struggle.

“It makes me mad,” he said, speaking about what his life had come to. “I want to go.”

But flip the perspective, and it was another day in a long and rich life. Mr. Sorensen, who had made a career as a decorator, was living independently in his own home, amid the furniture and décor he had carefully chosen himself, and amid memories of the man who had shared his life there. He had music that could still take his breath away, and old movies that never failed to entertain. If his capacities had diminished, they had narrowed to activities that gave him satisfaction. Even in near blindness, he inhabited a mansion of visual memories.

“I’ve had a good life,” he said in the kitchen, retrieving a moment that was more vivid to him than the recent past. “I’ll never forget coming into the living room once and my dad had a canary on his hand. And my mother was looking at him, and I will never forget the smile on her face. It was like a young girl falling in love. I never saw such a smile on my mother. It was only an instant, because as soon as they saw me, it changed. But it was a beautiful memory that’s engraved in my mind.”

To live with a memory like that — was that life, and was it a life worth living?

Do you know what you want to do when you get old?

Since the start of the year, the photographer Nicole Bengiveno and I have been visiting Mr. Sorensen and five other New Yorkers over the age of 85 — in hospital rooms and at birthday parties, on family vacations and at readings in nightclubs — and through it all, some version of Mr. Sorensen’s question has lingered: What is reasonable to ask of old age? Beyond the assaults of poverty or illness, to what extent can people shape the quality of life in their late years?

In New York City, the population age 85 and up has been growing at five times the rate for the city as a whole, doubling since 1980 to about 150,000. For this often invisible population, the first of its size, what does an older life really look like? And can it be better?

Throughout the year, the six talked unflinchingly about death and loss, but also about love and connection, about accomplishment and meaning. A paradox of old age is that older people have a greater sense of well-being than younger ones — not because they’re unreservedly blissful, but because they accept a mixture of happiness and sadness in their lives, and leverage this mixture when events come their way. They waste less time on anger, stress and worry. As Ping Wong, 90, put it: “When you’re young, the future is so far away, and you don’t know what will happen to you and the world. So when you’re young, you have more worries than the elderly. But I don’t worry now.”

Each of the six survived the year, an accomplishment in itself. They nurtured plants, made jewelry, maintained websites and sang like Billy Eckstine on karaoke night at the rehabilitation center. For some, their age came as a surprise. “I don’t know, it just fell upon me,” said Helen Moses, who turned 91 in October. “Your life goes so quick, all of the sudden I’m 90 years old. I remember when I was 13. I used to come home for lunch every day. And I was going down the hill and I said, Hey, I’m 13 years old already. And here I am, 90. It’s all right.”

Life won out — and not just life, but a life that reflected the complicated individuals navigating it. Mr. Sorensen wanted to die, but he also wanted to mop the kitchen floor, and he did his exercises every morning. “So I’m still trying,” he said. “I don’t know why.”

In the Hebrew Home at Riverdale the other day, Ms. Moses took stock of the year that had just passed. It was early morning, and she was wearing fresh makeup and a new floral print sweater and Balinese pearl necklace given to her by her daughter.

She was up early, as she is every morning. “I don’t want to miss anything,” she said.

For Ms. Moses, the year is ending as it began — with talk of marrying Howie Zeimer, her neighbor down the hall, and with gale-force opposition from her daughter. The couple met in 2009, shortly after moving to the home, and have been together ever since. Tensions with Ms. Moses’ daughter began almost immediately.

“She says if I marry Howie she’ll never visit me again,” Ms. Moses said. Yet day to day, being with Mr. Zeimer gave her life purpose and romance. She was not lonely, as so many in the home are, and she felt valuable in his presence. “He has nobody,” she said. “I tried to be everything to him. I think I am.”

She complained often about her life in the nursing home: about the food, the other people, the lack of privacy, even the songs they sang in glee club. “That’s a song for old people,” she said. She missed walking in spring or raking autumn leaves, or working at the Gap, where she was a sales clerk until she had a stroke at age 85.

Yet she did not dwell on the things she could no longer do.

“When I was 50 years old, it was the worst day in my life,” she said. “’Cause I was getting old. But now it’s not so bad. ’Cause I met Howie.” She mimed kisses in Mr. Zeimer’s direction. “And nobody tells me what to do.”

What can society gain from people like Ms. Moses, who no longer pay income taxes or raise families?

Plenty, said Monika Ardelt, an associate professor of sociology at the University of Florida, one of a group of researchers who have begun to study whether older really is wiser. Their answer is a qualified yes: that even as the brain slows down or memory deteriorates, older people are often better decision-makers, recognizing patterns or being more attuned to the effects of their decisions.

Interactive Feature | Over 85 in New York: A Demographic Profile

Ms. Moses’ approach to her conflict with her daughter is a case in point. By keeping the question of marriage unresolved — making plans one day, dropping them another — she gets almost all of what she wants from both Mr. Zeimer and her daughter, without risk of alienating either.

“If I was younger, I’d say, the hell with you, I’m doing what I want,” Ms. Moses said of her daughter. “But she’s all I got.” With age, she said, “I listen a little more — I listen to what she says and I do what I want.”

Was she wise, then? “No one ever called me that,” she said.

In surveys of people in nursing homes and hospices, Dr. Ardelt found that wisdom was positively related to their sense of well-being, even after the researchers controlled for factors like physical health, financial status and social engagement. The frailer or closer to death people became, the greater the role wisdom played in their feelings of well-being. Wisdom may not necessarily increase with old age — other researchers have found that it does not — but it becomes more central to people’s lives as they age, and compensates for much of the decline.

“We have this idea of ‘successful aging,’ that it should be a prolongation of middle age: Don’t get sick, stay active, keep in touch with your friends,” Dr. Ardelt said. “But eventually that’s not always possible. For many people, the argument is that if I cannot be like I was in middle age, I don’t want to enter old age. But you take something away from the last stage of life. Older people still have a lot to offer to us, even if only how to die and age gracefully.”

Frederick Jones, 88, is a man of elderly wisdom, and if you don’t believe it, just ask him. “Oh, no, I wouldn’t say that,” he said. “Because I’m still making the same mistakes I made when I was young.”

The first time I met Mr. Jones, on a snowy afternoon last winter, he described how he had picked up a woman 30 years younger than he in a department store. We were in a supermarket near his apartment in Crown Heights, Brooklyn, and he was surveying the checkout lines to see which had the most attractive cashier.

He had a badly infected big toe, a can of Pringles and some ham hocks, and two flights of stairs between him and his apartment. He could not have been much happier.

“I really appreciate all these days, because I’ve already set my goal on living to be 110, 115,” he said. “But I don’t want to be a vegetable, sitting in the corner, not doing anything. If I can get around like I am now, that’d be fine.”

Mr. Jones began the year finishing two months in a nursing home, recovering from complications related to low blood pressure, and he is ending it back home in his rent-controlled apartment, after a second stint in a nursing home, this time after having parts of two toes amputated because of gangrene. In midyear, after surgery, he could not walk to use the bathroom, but he never doubted that he would return to his walk-up apartment. By late fall he was making the slow climb up and down with minimal complaint.

In between climbs, he delighted in the wonders of his lifetime.

“I remember the ‘21’ Club,” he said one afternoon. “This woman got out of a limousine, looked like it was as long as this room. She had a fur. I don’t know what it cost but it looked good. And she had it partially dragging on the ground. She was already tanked up from wherever she came from, and she’s going into ‘21.’ It was two women and one man. I said, boy, you really got troubles on your hands. Two half-drunk women? That’s too much.”

At 88, Mr. Jones looked back on his life so far as one of romantic impulsiveness, producing six children by four women, and leaving him alone, with only television and his own rich singing voice to keep him regular company. Sometimes he talks to a photograph of his mother, thanking her for the life she provided him and his older brother. “It’s good I live alone, because somebody would think I’m crazy,” he said.

Did he miss the amatory adventures? He did not, he said — though it surprised him when, a decade ago, he lost his interest in sex, except as a conversational sweetener. “I feel like I had more than my share,” he said. “I don’t like to brag.”

When Mr. Jones was born in 1927, the American life expectancy at birth was under 60; for African-Americans it was under 50. (It rose for people who survived childhood.) A lifetime later, changes in longevity have produced a cohort of elder “pioneers, carving a path in an open field,” said Laura L. Carstensen, founding director of the Stanford Center on Longevity. People like Mr. Jones, who had paced their lives according to an old timetable — when to study, when to retire — were left with decades of life off the map.

Mr. Jones retired from Civil Service at 63, meaning that the current phase of his life now totals more than one quarter of his years, longer than the time between his birth and the end of his service in World War II, plus his four years of college.

The good news is that this extended period is better than young people think, Dr. Carstensen said. Levels of gratitude, forgiveness, calm and appreciation all rise through midlife to a peak around age 70, and remain relatively high through later years, she said. Anger and stress, on the other hand, recede.

“The older people get, the more positive they are about aging and the more adaptive they are to their limitations,” Dr. Carstensen said. “Social science tends to define old people by their disabilities. But people don’t define themselves that way.”

This is part of the wisdom of elders, even if they do not always call it such. For Mr. Jones, it surfaced as a steady expression of gratitude.

One afternoon in the nursing home, when he could barely walk across the cafeteria, and the staff had given him the wrong lunch, I asked him what was the best part of his day. He was wearing a shirt given to him by the home, perhaps after the previous owner died.

He beamed. “My favorite part of the day is waking up in the morning and thanking God for another day. That’s my favorite part of the day.”

How much of people’s experience of old age is within their control? Some, like Mr. Jones, seem to look past their daily aches and losses.

Recent research suggests that people’s attitude toward aging, even in their younger years, may affect their bodies as well.

In 2002, researchers from Harvard and Yale Universities found that people 50 and older who had positive images of old age, measured by whether they agreed with statements like “As you get older, you are less useful,” lived an average of 7.5 years longer. Other studies have found that people with negative perceptions of aging had greater memory loss and higher rates of heart disease. Of course, it may be that people in better health simply have brighter views of aging.

Ping Wong believes that she has some influence over her old age, even if she cannot slow the constant pain in her joints. Ms. Wong, who lives in a subsidized building for low-income older people near Gramercy Park, became nearly homebound during the year, and her conversation seemed to become more disjointed and less responsive.

But she played mah-jongg with friends every day, and read newspapers and books to keep her mind occupied. She avoided complaining about her problems as some of her peers did.

“Time is short, I know,” she said the other day. “No matter how much time I have I will laugh. The everyday activities I do will make myself happier. I prolong it by myself.”

Her former priorities — raising children, making a home, saving money — all aimed toward future payoffs. Now, like Mr. Jones, she sought satisfaction in the moment at hand.

“At my age I’m not thinking about what can be better,” she said. “I have a house to live in and a government to take care of me. So I have nothing to worry about.”

In Sheepshead Bay, Brooklyn, Ruth Willig lamented the dark season at year’s end. On an afternoon before Thanksgiving, Ms. Willig, 92, held out an old photograph of seven friends, taken after her husband’s death in 1994. Earlier that week, one of the women in the photograph had died, leaving only four. “So this is what happens when you’re old,” she said. “I remember when my mother was in her 80s, she would always go to funerals. I said, ‘Ma, how do you deal with it?’ She said, ‘You know, it happens. You have to accept it.’ And now I know.”

Over the year, Ms. Willig sometimes seemed consumed by her losses, including her diminished mobility. She hated using a walker, she said often, because it “puts me in a class that I don’t want to be in.”

“People look at you like you’re dependent,” she said.

To the question of whether old people were happier, she said, “Not me. Not I.”

Yet Ms. Willig, too, found satisfaction in her immediate activities, including her flowers and the email message she writes every morning to let her children and grandchildren know she is still alive.

The last survivor of four siblings, she has become the connecting point for the family’s many branches. It is a role she never expected, because she was the youngest, but one that makes her essential to the people she loves. “I’m the matriarch, the last one,” she said. “I feel proud in a way. Maybe I have done something right.”

In another part of Brooklyn, Jonas Mekas wondered what he was doing in an article with all those old people. Mr. Mekas, who turned 93 on Christmas Eve, finished the year with an exhibition of his films and photographs in Brescia, Italy, and the publication of an anthology of his writings, “Scrapbook of the Sixties: Writings 1954–2000” (Spector). He spent days in his Clinton Hill loft working with people who were not yet born when he made his name in avant-garde film and criticism.

For Mr. Mekas, old age was like younger age: an imperative to pay attention to the moment and do good in it. Toward the end the year, after he returned from giving a lecture in Berlin on the theme of “100 Years of Now,” he spoke of his filmmaking in words that could apply to his life.

“My contribution is focusing my camera on the present moment,” he said. “That’s the reality in front of the lens now. If I don’t do what I’m doing now, and become distracted by political events around me, that is not going to help humanity to develop and become more subtle and better.”

This focus gave him guidance, he said, and kept him from wasting time on far-off eventualities that might never bear out. “I know we are all limited, and at some point our work ends, but you don’t think about it,” he said. “I don’t think about it. I just do, and I know if I do something that is good for humanity, there will be somebody else who will pick up from the point where I leave it. That’s normal. If we give up the possibility of paradise, then that would be very bad.”

Oliver Sacks, in the final weeks of his life, wrote that his mind was focused on life rather than death, and on a fullness that transcended his pains. He gave up the hopes of dying “in harness” that he had written about just a few years before. “And now,” he wrote, “weak, short of breath, my once-firm muscles melted away by cancer, I find my thoughts, increasingly, not on the supernatural or spiritual but on what is meant by living a good and worthwhile life — achieving a sense of peace within oneself.”

Interactive Feature | 85 and Up Articles in this series looked at the lives of a group of New Yorkers age 85 and older, and how they navigate life at the upper end of old age in this city.

Maybe this is a gift of old age: that in its assault on the present moment, it also elevates it as the thing worthy of our concentration.

Ms. Moses found love; Mr. Jones found gratitude and a victory over stairs; Ms. Wong had mah-jongg; Ms. Willig filled a role as matriarch.

As for Mr. Mekas, at year’s end I asked him whether having experienced the Soviet invasion of Lithuania as a child and having been put in a Nazi forced labor camp, he was an optimist. He took a few stabs at an answer before giving up, then sent an email message the next day.

“I would say, that I am applying the ‘butterfly wing’ theory to my everyday life,” he wrote. “It’s a kind of moral dictum, moral responsibility to keep in mind that whatever I do this second affects what the next second will be. So I try not to do anything negative, which is my best insurance that the world will be better next second, or at least not worse. But of course, my positive action may be undermined by l00 negative actions of others and so it may mean nothing. But I still have to follow that dictum. You can call it optimism.”

Even Mr. Sorensen, who rued the prospect of living through another year, ended the year with a small victory. When we first met last winter, he said that the only thing he looked forward to was Thanksgiving at an old friend’s. Then in midyear he gave up hope: His digestion embarrassed him too much to be in public, and his hands could no longer hold a fork. But in the end he went. To his surprise, he said, “I felt good and I was even able to eat a little of it.”

He seemed to lighten briefly.

“I have moments of great pleasure,” he said. “But day to day it’s pretty rough.”