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Article by Carl Wenning - 1985
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New Thoughts on Understanding the Moon Illusion

Carl J. Wenning
Physics Department
Illinois State University
Normal, Illinois 61761

Planetarian, December 1985

Over the years I have been fascinated by illusions, whether they be optical or sleight-of-hand. Illusions hold a very special place for almost everyone. If you have ever gone to a science center which has a display of optical illusions, you might have watched people spending large amounts of time staring at and attempting to understand why they were perceiving the illusions that they were.

One optical illusion that holds an interest for me is the kind that uses background objects, lines, or other features to alter the appearance of foreground objects. For example the two illusions pictured here (Figures 1 and 2) cause otherwise straight lines to appear to "bend." If you don't believe that the lines are truly straight, turn this page edgewise and look down on them.

Figure 1

Figure 2

There is one special illusion that has held my interest since childhood, and that is the illusion of the apparent increased size of the moon when seen near the horizon. When the full moon is rising or setting, it appears larger than it does when viewed much higher in the sky. By sighting through a cardboard tube or whatever, you can measure the angular size of the moon under both circumstances and find that the two results are identically the same. That the moon's apparent diameter changes as a function of its "surrounding'' has been titled the "Moon Illusion."

I have heard many purported explanations of the "Moon Illusion" and have found most all of them wanting. Some authors have argued that the illusion is due to differential refraction that occurs near the horizon. But this (in the author's opinion) can be ruled out for the following reasons. Differential refraction would tend to flatten the moon and thus shorten, not enlarge it. Others have argued that the moon's apparent increased size was due to the orientation of the eye in its socket. if this were indeed the case, then one should be able to view the rising or setting moon in such a manner as to make the illusion disappear. It has been suggested that one could look upside down at it, for instance. But, this explanation doesn't work either. A third idea has been proffered, that foreground objects near to the observer affect (in some mysterious way) the perception of the moon watcher. This solution also fails, however, because the Moon Illusion is seen even by airplane pilots flying at very high altitudes.

I was especially happy to learn about another possible solution to the Moon Illusion (reference 1.) This solution dealt with two seemingly unrelated concepts.

The first is one of the most memorable illusions ever put forward and is named after its discoverer-the Ponzo Illusion (first presented by Mario Ponzo in 1913). The second deals with our perception of the sky itself.

The Ponzo Illusion, more commonly known as the "Railroad Track Illusion," is a set of "parallel" tracks that converge in the distance due to perspective (see Figure 3). Two blocks of exactly the same size are inserted between the tracks. Just as in the preceding examples, this "background" influences our perception of the "foreground" objects-the two blocks. The farther of the two blocks appears significantly larger than its nearer companion. Why is this so?

Since the two objects both exist in the plane of the paper, distance determination depends upon perspective and not on parallax or any other measurable clue. (We don't know how "big" the blocks really are.) Due to the apparent convergence of the "parallel" lines, we accept the narrowing, upper part of the picture as being farther away when compared to the more widely separated, lower portion of the picture. Now, according to the intuitive brain, the top block is farther away than the bottom block. Since the more distant block appears the same angular size as the closer block, the brain accepts that the more distant block is therefore much larger. But this is clearly impossible to the analytical brain, and hence, the illusion. Simply put, the intuitive brain does not agree with the analytical brain. You might wonder what the Ponzo Illusion has to do with the Moon Illusion. The connection indeed seems tenuous until you consider how we perceive the sky. Perhaps you haven't noticed it yet, but the "distance to the sky" appears to be a function of where we direct our attention toward it. The sky nearer the horizon appears much more distant, say, than the point directly overhead. Why we perceive the sky in this way, I don't know, but it seems to be so for me and everyone else I've queried regarding it. It is "against" this changing background that we see the moon. If backgrounds can influence our perception of the size and nature of foreground objects, why can't the sight of the moon be influenced in a similar manner?

Figure 3

Just like the blocks in the Ponzo Illusion, our perception of the moon appears to be influenced by the background. The moon has the same true angular size whether seen near the horizon or when it is much higher in the sky. When we see the moon "against" a more "distant" horizon it appears larger than when we see it 'against" a much "closer" one. The explanation of the Moon Illusion, then, is that it is nothing more than the Ponzo Illusion inverted! (You might want to view Figure 3 turned upside down for a very convincing illustration of this argument.)

Some time ago, I was rambling through Minnaert's The Nature of Light and Color in the Open Air (reference 2) when I came across a very interesting section dealing with afterimages. The text related that afterimages of a constant size could be impressed upon the human eye by staring at a light bulb for a few minutes. Noted among the amazing variety of effects which would soon appear was that the afterimage could be made to change apparent size by "projecting" it onto a piece of white paper and varying the eye-to-paper distance. As I moved the paper toward my eye the image size would seemingly shrink, and in the opposite manner, when the paper was moved farther away the image seemed to enlarge. Because I knew that the image sizes created were really the same, it was the changing background that affected the perceived size of the afterimage!

During the summer of 1984, when presenting an evening program at one of our local parks, I was reminded again of the afterimages when a bright projector was suddenly shone in my eyes. I then wondered whether this could be related back to the Moon Illusion. Could the sky act like the paper held at varying distances? After creating an intentional afterimage on my eyes with a bright flashlight, I began to "project" the afterimage onto the sky. Once again, I was surprised to find that the background of sky did indeed produce the same illusion as with the moon. When the afterimages were close to the horizon, they appeared large. The same afterimages appeared small, however, when projected at the zenith. Thus, much to my satisfaction, the Moon Illusion seems to have been explained.

Over the years, many visitors to the l.S.U. Planetarium have asked me why the constellations appear so much larger when viewed outdoors than they do in the planetarium sky. I think that I now have the answer to that question also. Constellations appear very large when they are viewed near the horizon. For example, Orion appears larger when it is rising or setting than at any other time. When bright constellations are found near the horizon they are more likely to be noticed by the casual observer. They can thus appear larger for the same reason the moon does when it is viewed near the horizon. Under the "finite" planetarium dome the same perceptions of the nighttime sky do not creep in. As a result, the constellations, and the planetarium sun and moon, do not exhibit this illusory effect.

Perhaps future planetariums could be constructed in such a way as to include the audience's perceptions of form and structure in the nighttime sky. Not only might this alteration produce a version of the Moon Illusion indoors, it might also help cure the problem of the stars in the planetarium sky appearing too close. I leave that as a suggestion for future workers in this area.

References

Walker, B., "The Moon Illusion: A Review," Parts 1 and 2, Optical Spectra, January, February, 1978.
Minnaert, M., The Nature of Light and Color in the Open Air, Dover Publications, New York, 1954.


Reprinted from the Planetarian, Vol 14, #4, December 1985. Copyright 1985 International Planetarium Society. For permission to reproduce please contact Executive Editor, Sharon Shanks.

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