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Lloyd Kaufman, a psychologist at Long Island University, and his son, James H. Kaufman, a physicist at IBM, reported their findings in the January 4th issue of Proceedings of the National Academy of Sciences. They performed two experiments in which subjects adjusted the distance of a simulated Moon near a horizon and high in the sky. In both cases, the observers acted as if the Moon appeared farther when near the horizon. The elder Kaufman explains, "Our latest results leave no doubt that perceived distance information plays a primary role in creating the moon illusion." The nature of the Moon itself plays no role; the "Moon illusion" also makes constellations seem to loom larger when they are near the horizon.
IBM Almaden Research Center
San Jose, California
This "moon illusion" is a genuinely mind-baffling illusion, since the horizon and elevated moons are actually the same size and distance away from earthly viewers. Possible explanations have been discussed and debated for centuries. Now a father-son pair of scientists have teamed up to show decisively that the moon illusion occurs because the brain interprets the horizon moon as being much farther away than the elevated moon. Thus, the "apparent distance" to the moon -- rather than the real distance -- determines its perceived size.
Dr. Lloyd Kaufman and his son, Dr. James H. Kaufman, presented their findings in cover story of the Jan. 4, 2000 issue of the Proceedings of the National Academy of Sciences. The elder Kaufman is Professor Emeritus at New York University, where for many years he was Professor of Psychology and Neural Science. He is now Senior Research Scientist at the C.W. Post Campus of Long Island University. James Kaufman is a physicist and Manager of Advanced Materials for Technology and Storage at IBM's Almaden Research Center in San Jose, California.
"Understanding such a pervasive and historic phenomenon as the moon illusion is central to scientists' quest to understand how our brains perceive space and distance." said Professor Kaufman. "Our latest results leave no doubt that perceived distance information plays a primary role in creating the moon illusion."
In 1960 as a young graduate student, the elder Kaufman and his mentor, Irvin Rock, first presented experimental results supporting the apparent-distance theory to explain the moon illusion. This theory says that the brain "computes" perceived distances to objects. When the moon is just above the horizon, the information presented by the intervening terrain affects the "computation" by indicating that the moon is at a vast distance. By contrast, a view of the elevated moon contains weaker cues to distance, so the brain responds as if the moon were closer. Since information regarding an object's apparent distance determines its perceived size, the more distant horizon moon is perceived as being up to twice as large as the elevated moon. This is similar to the classic Ponzo prespective illusion dating from 1913 in which two same-length lines are drawn between or across a pair of converging lines resembling railroad tracks going off into the distance. The upper line appears much larger because it spans a greater apparent distance between the rails, which our mind assumes are parallel.
A class of alternative explanations for the moon illusion based on an "apparent-size" theory was first described in 1965. According to this theory, since the elevated moon is perceived as being smaller, it must also be perceived as being farther away than the apparently larger horizon moon. In general, this theory holds that the apparent size of an object governs its apparent distance -- diametrically opposed to the apparent-distance theory. In the case of the moon, most apparent-size proponents believe that other cues to distance, such as terrain, are irrelevant. Some proponents also hold that when we view the elevated moon our eyes focus and converge to a different distance than when we view the horizon moon, and that this difference leads directly to the reduced apparent size of the elevated moon.
"For many years, my father and I discussed the causes of the moon illusion, and we looked at many moons," recalled James Kaufman. "While considering the details of both theories a few years ago, we realized that one reason for the continued controversy was that virtually all experimental studies measured or manipulated the perceived size of the moon but made only inferences about its perceived distance from the viewer. I asked why we couldn't measure the apparent distance directly rather than just deduce it."
The Kaufmans then designed two experiments to measure directly the perceived distance to the moon. Both tests used an apparatus built at IBM Research to project stereoscopic images of artificial moons from an IBM ThinkPad computer display to optical infinity so viewers could see them against an actual sky. Professor Kaufman then took people to a Long Island hilltop, where he made hundreds of measurements of their perceptions of the distance to the moon.
Each person was first asked to position an artificial moon so it appeared to be halfway between themselves and a fixed moon that was either near the horizon or elevated. In every case, the viewers placed the halfway point to the horizon moon as being much farther away -- on average four times more distant -- than the halfway point to the elevated moon. This is entirely consistent with the apparent-distance theory.
In their second test, the viewer used the ThinkPad to adjust the apparent
distance to a moon projected either on the horizon or elevated sky. In all
cases, as the subjects moved the projected moon closer, they reported that
it appeared to become smaller, not larger -- a direct contradiction of the
apparent-size theory. An animated simulation of this surprising but
convincing second experiment can be viewed on the Web
Before the tests, each of Kaufman's subjects said they thought that the apparently larger moon would appear closer. But the opposite occurred. "A key element of a true illusion is that our conscious deductions and preconceptions do not necessarily reflect how our brains actually respond to the outside world," Professor Kaufman said.
"Humans can accurately perceive an object's size regardless of its distance," Professor Kaufman says. "This effect -- known as size constancy -- is why we can discern the real size of a distant automobile, tree or building despite its small image size. Our brain automatically takes the apparent distance into account and compensates for the geometrical reality that the image we see of a distant object is smaller than the image of that same object nearby."
In most cases, the terrain provides a rich set of cues that enable us to accurately perceive the sizes of objects at different distances, Professor Kaufman added. But apparently such large distances as those to the moon are beyond our brain's capability. As an example, Professor Kaufman recommends viewing the moon through an aperture, such as pinching it between your thumb and forefinger or viewing it through a tube, which hides the the terrain leading up to the moon. The moon suddenly appears to be small because our brain locates it at the nearby distance of the edges of the aperture. Removing the aperture restores the terrain's distance cues and the moon springs back to its large, illusory size.
Others who have written about the moon illusion over the years include such notable scientists as: Aristotle, Roger Bacon, Leonardo da Vinci, Johann Kepler, Rene Descartes, Marin Mersenne, Christiaan Huygens, Leonard Euler, Alexander von Humboldt, Hermann von Helmholtz and Thomas Huxley II.