Do this and similar exercises hundreds of times over multiple sessions weekly; continue for months; and, gradually, presbyopia lessens, a number of studies show.

One study also examined functions of the eye itself and found none of these improvements were because of changes in the eye. They’re all in the brain.

Various smartphone apps say they offer this kind of vision-improving training; I used one called GlassesOff, the only one I found that was backed by scientific studies.

Perceptual learning can improve the vision of people who already see quite well and those with other conditions. For example, a study tested the approach in 23 young adults, around age 24. Compared with a control group of 20 young adults, the treatment group increased letter recognition speed. Similar training is an effective component in treating amblyopia, also called “lazy eye,” which is the most frequent cause of vision loss in infants and children, affecting 3 percent of the population. It may also improve vision in those with mild myopia (nearsightedness).

It should be acknowledged that some researchers involved in many of these studies have financial ties to GlassesOff. However, other studies with no commercial links obtained similar results, and several scientists I spoke to, including those without ties to GlassesOff, thought the science behind the app was credible. One study published in Psychological Science trained 16 college-aged adults and 16 older adults (around age 71) with Gabor patch exercises for 1.5 hours per day for seven days. After training, the older adults’ ability to see low-contrast images improved to the level that the college-age ones had before training.

Scientists don’t know exactly how perceptual learning relieves presbyopia, but they have some clues based on how our brain processes visual information.