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02/01/2000
How High the Moon
Today, January 20, 2000, is a day that will live in infamy in our
household. Would you believe that my wife wished me "Happy
Anniversary!" as we headed out to the mall for our morning
walk? From my opening remark, you''ve probably guessed - I
completely forgot! Please don''t let me forget next year''s, our
50th. If I''m not mistaken, I haven''t forgotten that there is another
memorable event scheduled for today, a total eclipse of the moon.
Unfortunately, we''re having a snowstorm that will probably
obscure the lunar event.
By the time you read this, I''ll hopefully be on Marco Island in
Florida. When there, I look forward to my daily six-mile walk on
the beach. Normally, here in New Jersey, I walk three miles a day
but my wife will tell you that she often has to prod me to get off
my butt and get moving. Not so in Florida, where I''m on the
beach way before sunrise finding my way by the lights of the
hotels and, for part of the month, by the light of the moon. The
most beautiful times are the few mornings when there is a full
moon setting in the west at the same time that the sun is rising in
the east. Somehow, it makes me feel very virtuous to get up early
enough to witness this celestial happening. Of course, as I watch
the moon at the horizon, the age-old question arises as to why the
moon is twice its size at the horizon compared to its smaller size
when it''s directly above me in the sky.
As a child, I thought there was no problem. The moon just got
bigger or smaller on a regular basis. Later, as I developed my
keen scientific mind, this explanation no longer seemed likely.
Just a minute ago, I looked up the explanation in our decades old
World Book Encyclopedia and the answer was simple. The
apparent size of the moon depends on the angle at which you
look at it and over the years, I''ve seen different explanations for
the effect, which has befuddled great minds over several
millennia.
A few weeks ago, I saw an article in the New York Times
Science Times section on this very subject. The article describes
some joint work by two fellows named Kaufman, one a
psychologist from New York, the other a physicist from
California. They claim to have conclusive proof that one theory
for the moon-size effect does indeed provide the correct
explanation. Appropriately enough, the answer lies in the brain, a
nice touch at the end of the official Decade of the Brain in the
1990s.
We have all seen many examples of optical illusions due to the
ways in which the brain tends to process data. Sometimes, it will
fill in missing features from a picture. Other times, you might
stare at a picture and see color that really isn''t there, etc. As for
the moon-size effect, the plausible explanations apparently have
narrowed down to two reasonable theories. But first, the size of
the moon that you see on the horizon is the "true" size. This
holds for both theories. In one theory, the apparent size of the
moon as it rises in the sky is postulated to be the cause of the
illusion. According to this theory, because the moon appears
smaller the higher it is in the sky, we sense the moon as being
farther away than it is at the horizon.
The second theory goes at it from the opposite point of view. In
this theory, the brain decides that the moon on the horizon is
humongous, but far away, thanks to the cues provided by
indications of distance such as trees, buildings, mountains, etc.
On the other hand, when the moon gets smaller as it ascends
higher in the sky, our brain actually is convinced that it''s closer.
If you think as I do, this second theory doesn''t make sense. It
should be just the other way around, right? Wrong!
To illustrate the second theory, the Times article shows a drawing
of the "Ponzo Illusion". You can draw it yourself very quickly.
Just draw a railroad track, the spacing between the rails wide at
the bottom of the page, narrowing towards the top of the page as
they would in a perspective drawing. (Even though I got a "D" in
art in junior high school, I did learn to give perspective to parallel
lines by converging them to a "distant" point.) (Hey, you didn''t
have to bring up the other "D" in shop!) But back to our railroad,
draw in a few ties lightly and parallel to the bottom of the sheet of
paper. Now we''re set. Draw in a heavy bar centered between the
rails (not touching them) near the bottom of the page and a bar
the same size centered between the rails near the top of the page.
In my crude attempt to duplicate this below, the smaller dashed
lines are the ties and the two solid lines are the aforementioned
bars, which in Office 97 I can make bold but this probably will not
"take" for this Web site. They should be thickened and/or
darkened to give the best effect.
-/-----------
/ _______
-/----------------
/
-/----------------------
/ _______
-/----------------------------
[Editor Note: I apologize that the drawing is askew. Picture
it all lined up like a pyramid. Unfortunately, when you transfer
documents onto the browser for this site, only text works as the
author may have intended.]
Ignoring my feeble artistic attempt (you see why I got that "D"),
if you''re a normal person with a normal brain you would say that
the bar at the bottom (closest to you) is smaller than the top bar
farthest from you. Yet you know they''re the same size! You''ve
just shown the validity of the second theory. That is, the object,
the bar (or the moon) appears smaller to you because you think
it''s closer to you!
Now, the two Kaufmans were much more sophisticated in their
proof of the second theory. They rigged up a computer setup in
which two moons the same size could be projected in a
stereoscopic manner and the subject could move one of the
moons in closer to himself or herself. In one experiment, the
subjects were told to move the moon halfway between themselves
and the other moon. When the stationary moon was on the
horizon, the halfway distance at which the subjects placed the
moon was about 100 feet. When the moons were projected
overhead, the halfway distance dropped to about 25 feet. In
other words, the subjects thought the smaller, overhead moon
was closer than when it was on the horizon.
The other experiment was simpler and surprising to the subjects.
The two moons were projected high overhead and the subjects
were told to press a key to bring the one moon closer to them.
We, being enlightened, are not at all surprised that they perceived
the moving moon to get smaller as it got closer.
Well, now that we''ve cleared that up, you may be wondering what
other tricks your brain is playing on you. If you''ve been reading
some of the medical type articles recently, you know that one
trick is the "placebo" effect. There is currently a heated debate
among physicians and ethicist types about doctors prescribing placebos,
which seem to be quite effective in relieving symptoms of certain
ailments in certain patients. But that could be a topic
for later perusal.
Now, I''ve got to finish and wish my wife a Happy Anniversary. I
love you, Honey!
Allen F. Bortrum
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