Monday, January 3, 2000 — Last month’s winter-solstice full moon may have been the biggest and
brightest in decades, but throughout human history every rising or setting moon near the horizon has
appeared to be much larger than the same moon when it is higher in the sky.

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 perspective illusion
[http://www.sandlotscience.com/Distortions/Ponzo_java.htm] 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
[http://www.research.ibm.com/news/detail/newmoon.html
or
http://www.pnas.org/cgi/content/full/97/1/500/DC1] .

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.

The Moon Illusion is Ancient History

The moon illusion has been known since antiquity.In the second century A.D., the Greek-Egyptian
astronomer Ptolemy was essentially correct in suggesting that any object viewed across “filled space”
— such as the horizon moon — would seem to be more distant than objects the same distance away
but viewed over empty space, such as the moon at its zenith. An 11th century Arab astronomer
(Al-Hazan) seems to have been the first to develop the “apparent distance” theory in some detail.

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.