But, Dr. Levy wondered, were there long-term effects of believing the stereotypes of aging? She found a study that could provide answers, the Ohio Longitudinal Study of Aging and Retirement. The two-decade-long study included 1,157 people, nearly every resident of Oxford, Ohio, who was 50 or older and was not suffering from dementia. And it had questions about beliefs about aging.

It turned out that people who had more positive views about aging were healthier over time. They lived an average of 7.6 years longer than those of a similar age who did not hold such views, and even had less hearing loss when their hearing was tested three years after the study began. The result persisted when the investigators took in account the participants’ health at the start of the study, as well as their age, gender, and socioeconomic status.

Some like Dr. Suzman were swayed, but Dr. Hodes urges caution. As provocative as the data may be, he notes, the studies cannot tell for sure what is cause and what is effect. It may be that people who had negative attitudes about aging somehow knew that they were not really well.

Dr. Hodes confesses that in this case indirect studies may be the best that can be done. To obtain direct evidence would require randomly assigning some participants to keep hearing negative comments about themselves as they age and others to hear positive things. “How ethical would that be?” he asks.

If it is true that perceptions of aging affect memory, behavior and health — and many researchers are betting that they do — that may bode well for today’s middle-age people, Dr. Levy says. They may not be quite so willing to declare themselves old when they reach their 60’s and beyond and they may be less likely to believe the stereotypes of old age.

Still, Dr. Levy and others say, it can be difficult to resist the pervasive stereotypes of aging. Many people may accept them without realizing it.

“Then they become a self-fulfilling prophecy,” Dr. Levy said.

But not for people like Dr. Butler or Mr. Bialokur, who managed to escape that trap. Others, too, say they have thrived simply by ignoring the stereotypes.