The Rockefeller researchers explained their observations in one of their papers: “It is entirely possible that weight reduction, instead of resulting in a normal state for obese patients, results in an abnormal state resembling that of starved nonobese individuals.”

Eventually, more than 50 people lived at the hospital and lost weight, and every one had physical and psychological signs of starvation. There were a very few who did not get fat again, but they made staying thin their life’s work, becoming Weight Watchers lecturers, for example, and, always, counting calories and maintaining themselves in a permanent state of starvation.

“Did those who stayed thin simply have more willpower?” Dr. Hirsch asked. “In a funny way, they did.”

One way to interpret Dr. Hirsch and Dr. Leibel’s studies would be to propose that once a person got fat, the body would adjust, making it hopeless to lose weight and keep it off. The issue was important, because if getting fat was the problem, there might be a solution to the obesity epidemic: convince people that any weight gain was a step toward an irreversible condition that they most definitely did not want to have.

But another group of studies showed that that hypothesis, too, was wrong.

It began with studies that were the inspiration of Dr. Ethan Sims at the University of Vermont, who asked what would happen if thin people who had never had a weight problem deliberately got fat.

His subjects were prisoners at a nearby state prison who volunteered to gain weight. With great difficulty, they succeeded, increasing their weight by 20 percent to 25 percent. But it took them four to six months, eating as much as they could every day. Some consumed 10,000 calories a day, an amount so incredible that it would be hard to believe, were it not for the fact that there were attendants present at each meal who dutifully recorded everything the men ate.

Image Jules Hirsch, a research physician at Rockefeller University, conducted a simple but groundbreaking experiment on obesity nearly 50 years ago, changing the way scientists think about fat. Credit... Fred R. Conrad/The New York Times

Once the men were fat, their metabolisms increased by 50 percent. They needed more than 2,700 calories per square meter of their body surface to stay fat but needed just 1,800 calories per square meter to maintain their normal weight.