Father-son scientists confirm why horizon
moon appears larger
SAN JOSE, Calif. (2 p.m. PST Jan. 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* 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 at: http://www.research.ibm.com/news/detail/newmoon.html.
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 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 Itself 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.
Prof. Kaufman's earlier results were described in two articles
in Science Magazine (Science 136, 953-961 and 136, 1023-1031),
an article in the front page of the N.Y. Times (April 17, 1960,
copy attached) and the cover story of the July 1962 Scientific
American.
* Ponzo Illusions can be linked to at:
