Is the woman pictured on the right more attractive than the woman on the left? Do her wider-set eyes, the longer distance between her hairline and the bridge of the nose, and the rounder shape of her face make her more beautiful?
The photograph on the right was doctored by the "beautification engine" of a new computer program that uses a mathematical formula to alter the original form into a theoretically more attractive version, while maintaining what programmers call an "unmistakable similarity" to the original.
Studies have shown that there is surprising agreement about what makes a face attractive. Symmetry is at the core, along with youthfulness; clarity or smoothness of skin; and vivid color, say, in the eyes and hair. There is little dissent among people of different cultures, ethnicities, races, ages and gender.
Yet, like the many other attempts to use objective principles or even mathematical formulas to define beauty, this software program raises what psychologists, philosophers and feminists say are complex, even disturbing, questions about the perception of beauty and a beauty ideal.
To what extent is beauty quantifiable? Does a supposedly scientific definition merely reflect the ideal of the moment, built from the images of pop culture and the news media?
Mr. Leyvand suggested there were practical applications for his software, including advertisements, films and animation. He also said he had heard from plastic surgeons interested in the software. That did not surprise those who have studied the history of beauty.
"We have always had a huge industry to make people look better," Dr. Etcoff said. "Everyone wants to look better. And we keep taking it further and further to all these images that have been doctored. There is a whole generation of girls growing up who think it's normal not to look the way they really look."