Lloyd Kaufman, a leading figure in the study of a phenomenon called the moon illusion, an optical trick puzzled over for millenniums by the likes of Aristotle and Kepler, died on Aug. 20 at his home in the Floral Park neighborhood of Queens. He was 97.

His death was confirmed by his daughter Robin Sellier.

Professor Kaufman, a cognitive psychologist with appointments at New York University and Long Island University, spent nearly half a century studying the mental mechanics that help produce human vision, becoming an eminent figure in that academic field.

In the popular press, he was known for his attempts to solve an age-old paradox: Why does the moon look so much bigger rising over the horizon than it does high in the sky late at night, even though in each position the moon is the same size and roughly the same distance from Earth?

“The moon illusion might be the world’s most widely known optical illusion,” Vox wrote in 2015.

Some say the earliest record of humanity’s awareness of the moon illusion is a Mesopotamian clay tablet from about the 7th century B.C. bearing cuneiform script that describes the changing sizes of the moon.

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The earliest known scientific inquirer into the phenomenon was Aristotle, who ascribed the effect to qualities of the atmosphere, according to “The Mystery of the Moon Illusion: Exploring Size Perception” (2002), a survey of the subject written by the psychologists Helen Elizabeth Ross and Cornelius Plug.

In later centuries, the problem drew the attention of the Egyptian astronomer Ptolemy, the medieval Arab physicist Ibn al-Haytham and figures like Leonardo da Vinci, Johannes Kepler and René Descartes.

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Easily performed experiments to test the moon illusion confirm that something funny is going on. If you look at the moon through a rolled-up piece of paper, say, or if you look at it while doubled over and peering at it behind you between your legs, the moon will appear to shrink.

The moon illusion is not particular to the moon, however. The same effects may be observed with the sun and the constellations. The association of the illusion with the moon comes from the simple fact that, of the three, the moon is the easiest to see.

Professor Kaufman first gained wide attention when The New York Times ran a front-page article about his work on the moon illusion in 1960.

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With help from his mentor and academic adviser, Irvin Rock, he had invented a viewing device that projected images of the horizon moon and the moon at its zenith onto changing backgrounds. Strikingly, subjects participating in experiments with the device did not notice if the moons and their backgrounds were flipped. Any moon projected onto the horizon line looked larger than any moon in the night sky.

The experiments were able to measure the size of the illusion: A moon on the horizon consistently appeared about one-third larger than a moon in the night sky. They also ruled out previous hypotheses suggesting that the cause of the illusion lay in the composition of the atmosphere or the shape of the sky. And they showed that the moon illusion had to do with human perception itself.

But the notion that Professor Kaufman and Professor Rock had “solved” the age-old problem, as The Times reported in 1960, struck other scientists as overstated. Experts began debating what aspect of perception, exactly, generated the illusion: Had it to do with humans’ apprehension of distance or apprehension of size?

Working with his son, James, Professor Kaufman tried to answer that question by inventing a new device. It involved a laptop computer, a mirror and two lenses that projected two artificial moons at different sizes and distances. Subjects enlisted for the experiments using the instrument were asked to match those qualities between the two moons.

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The results, published in 2000 and also covered by The Times, showed that the brain’s struggle to accurately register distance in the empty night sky causes the moon illusion, the Kaufmans argued.

To this day, there is no consensus on what exactly causes the illusion. But Professor Kaufman’s impact on the debate was clear.

“His books popularized the subject and his interpretations of the illusion were the standard others built upon,” Donald Simanek, a physicist and moon watcher, wrote in an email.

When asked in 2014 by the science magazine Nautilus why he had dedicated so much time to the moon illusion, Dr. Kaufman replied, “It’s the challenge of solving a problem the likes of Galileo and Newton couldn’t handle.”

Lloyd Kaufman was born on June 9, 1927, in the Bronx. His parents were Samuel, a shoe salesman, and Mildred (Lewis) Kaufman.

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He earned a bachelor’s degree in psychology from San Diego State University in 1950 and a Ph.D. in the subject from the New School for Social Research in Manhattan in 1961. He wrote and contributed to several books on the science of perception.

In addition to Ms. Sellier, Professor Kaufman is survived by his son; another daughter, Laura Forman; a brother, Maurice; six grandchildren; three great-grandchildren; and two great-great grandchildren.

In a eulogy he delivered at Professor Kaufman’s memorial service, Aries Arditi, a fellow scientist of perception, observed that the night before his friend had died, the moon appeared larger and more luminous than usual — not because of an illusion, but because it was closest to Earth in its orbit. Dr. Arditi called it a “celestial salute.”

Richard Sandomir contributed reporting.1xbet

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