The first thing to know, said Dr. Benjamin Levine, an exercise researcher and a cardiology professor at the University of Texas Southwestern Medical Center in Dallas, is that no one really knows what limits human performance. There’s the ability of the heart to pump blood to the muscles, there’s the ability of the muscles to contract and respond, there’s the question of muscle fuel, and then, of course, there is the mind.

“How does the brain interact with the skeletal muscles and the circulation?” Dr. Levine said. “How much of this is voluntary and how much is involuntary? We just don’t know.”

But since most people can do better, no matter how good their performance, the challenge is to find a safe way to push a little harder. Many ordinary athletes, as well as elites, use a technique known as dissociation.

Dr. Morgan, who tested the method in research studies, said he was inspired by a story, reported by an anthropologist that, he suspects, is apocryphal. It involves Tibetan monks who reportedly ran 300 miles in 30 hours, an average pace of six minutes a mile. Their mental trick was to fixate on a distant object, like a mountain peak, and put their breathing in synchrony with their locomotion. Every time a foot hit the ground they would also repeat a mantra.

So Dr. Morgan and his colleagues instructed runners to say “down” to themselves every time a foot went down. They were also to choose an object and stare at it while running on a treadmill and to breathe in sync with their steps. The result, Dr. Morgan said, was that the runners using the monks’ strategy had a statistically significant increase in endurance, doing much better than members of a control group who ran in their usual way.

That, in a sense, is the trick that Paula Radcliffe said she uses. Ms. Radcliffe, the winner of this year’s New York City Marathon, said in a recent interview that she counts her steps when she struggles in a race. “When I count to 100 three times, it’s a mile,” she said. “It helps me focus on the moment and not think about how many miles I have to go. I concentrate on breathing and striding, and I go within myself.”

Without realizing what I was doing, I dissociated a few months ago, in the middle of a long, fast bike ride. I’d become so tired that I could not hold the pace going up hills. Then I hit upon a method  I focused only on the seat of the rider in front of me and did not look at the hill or what was to come. And I concentrated on my cadence, counting pedal strokes, thinking of nothing else. It worked. Now I know why.