Ironically, for many older Okinawans this diet was born of hardship. Ushi Okushima grew up barefoot and poor. Her family scratched a living out of Ogimi's rocky terrain, growing sweet potatoes, which formed the core of every meal. To celebrate the New Year, her village butchered a pig, and everyone got a morsel of pork.

During World War II, when U.S. warships shelled Okinawa, Ushi and Setsuko, whose husbands had been conscripted into the Japanese Army, fled to the mountains with their children. "We experienced terrible hunger," Setsuko recalls.

Ushi now wakes every morning at six and eats a small breakfast of milk, bananas, and tomatoes. Until very recently she grew most of her food (she gave up gardening when she took a job). But her tradition-honored daily rituals haven't changed: morning prayers to her ancestors, tea with friends, lunch with family, an afternoon nap, a sunset social hour with friends, and before bed a cup of sake infused with the herb mugwort. "It helps me sleep," she says.

Back in Ushi's house we're finishing our tea. Outside, dusk is falling; rain patters on the roof. Ushi's daughter, Kikue, who is 78 and finds little amusement in the attention her mother draws, shoots me a glare that I take to mean "you've overstayed your welcome." (When Ushi ran away from home, she was actually fleeing an argument with Kikue. She packed a bag and boarded a bus without telling her daughter. A relative caught up with her in a town 40 miles (64.4 kilometers) away.)

Ushi, Setsuko, and Matsu take the cue and fall silent in unison. These women have shared each other's fortunes and endured each other's sorrows for nearly a century and now seem to communicate wordlessly.

What is Ushi's ikigai, I ask—that powerful sense of purpose that older Okinawans are said to possess?

"It's her longevity itself," answers her daughter. "She brings pride to our family and this village, and now feels she must keep living even though she is often tired."

I look to Ushi for her own answer.

"My ikigai is right here," she says with a slow sweep of her hand that takes in Setsuko and Matsu. "If they die, I will wonder why I am still living."