How High the Moon

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