ed 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 view

---