The overestimation of the size of the moon on the horizon compared with the estimated size of the moon positioned higher in the sky, is known as the moon illusion. This illusion has been recognized for thousands of years and many theories have been developed in order to explain it. Second-century astronomer Ptolemy, proposed that an object that is seen through filled space will appear to be farther away than an object seen through empty space. This is known as the apparent distance theory. In 1962, Kaufman and Rock concluded that the moon illusion was in fact dependent on the presence or absence of terrain. Kaufman and Rock (1962) also tested the angular size-contrast theory which states that the moon will appear to be smaller when it is surrounded by larger objects. Photographs of the moon transform a three-dimensional world into a two-dimensional representation. Although few studies have been done in this area, Coren and Aks (1990) concluded that the moon illusion does exist in pictures. This implies that the moon illusion contains mechanisms similar to that of traditional, two-dimensional visual illusions. The results also provided support for the size-constancy theory, finding that the presence of depth cues causes constancy scaling, resulting in the appearance of a larger moon. The objective of our study is to show the effect that rotating and inverting pictures of the moon will have on the magnitude of the moon illusion. If the size-constancy theory is a component, then an inverted and vertical picture of a moon scene, with the moon the same distance away from the horizon as the original picture, should produce an illusion of the same magnitude.
Methods
Subjects
Twenty-two Alma College students, eleven males and eleven females participated as subjects. All were naive to the purpose of the study.
Stimuli
Stimuli were twelve computer generated scenes, each representing a different displacement of the moon. The pictures were created and shown on a Macintosh computer using Eye Lines software. The diameter of the moon in each of the pictures measured 17.7 mm. Two types of scenes were used, one containing scenery (an outline of the sky) and on without scenery (plain background). The horizon for both was placed at 59 mm. Each of these scenes were presented using three different views: the first in a normal, upright position; the second with the horizon tilted 90 degrees, creating a vertical line with the horizon; the third with the horizon tilted 180 degrees, creating an inverse picture of the horizon. These six scenes were then duplicated, creating twelve scenes. In half of these, the moon was centered 132.75 mm. above the horizon, representing a zenith moon. In order to create a scene that represented night, the following colors were used: shade 171, a medium blue for the ground, shade 177, a dark blue for the sky; shade 217, a yellow for the moon; and shade 129, a gray for the buildings in the skyline.
Procedure
Stimuli were presented in random order with the restriction that the horizon and elevated moon for the same picture could not follow one another. Subjects were then presented with a "Matching Moon" which was an adjustable circular figure also programmed under Eye Lines. The figure was placed on an adjacent computer screen. Subjects were then asked to adjust this figure to measure the same size they percieved the moon in the picture to be.
Results
As Figure 1 shows, the magnitude of the moon illusion was greatest in the pictures with a normal orientation with a difference of .156mm between low and high moon. Participants consistently judged the moon in vertically oriented scenes to be larger regardless of moon placement. There was little difference (.18 mm) in perceived moon size in pictures that were inverted.
Figure 2 shows that pictures with no scenery in the background shows the greatest difference (.168 mm) in perceptual size between the high and low moon. Pictures with a sky line in the background show a .3 mm difference, actually judging a high moon to be larger.
Discussion
Our results showed that the perceived size of the moon in normally oriented and inverted pictures were not the same. This finding does not agree with the size-constancy theory. A possible explanation for the fact that the illusion is lost in inverse pictures is because of our body's upright orientation. Because our bodies are not oriented to view things upside down, the illusion is lost when we are presented with such stimuli. The apparent distance theory and angular size contrast theories were partially supported by our experiment, because subjects judged the size of the moon to be larger through filled space than through empty space. Although this was true, the perceived size of the moon was not dependent on the location of the moon. One possible explanation for this is that the computer screen used was not a perfect square, and was shorter in height than width. The presence of the buildings made it difficult to make a great difference between a moon on the horizon and a moon in the sky. The explanation behind the fact that the vertically oriented moon was consistently judged to be larger regardless of its position cannot be explained by the given theories. Overall, our experiment did show that the moon illusion is to some degree present in two-dimensional pictures. This leads us to believe that the properties of the moon illusion are similar to traditional, two-dimensional, visual illusions.
Coren, S. & Aks, D. (1990). Moon illusion in pictures: a multimechanism approach. Journal of Experimental Psychology: Human Perception & Performance, 16, 365-380.
Kaufman, L. & Rock, I. (1962). The moon illusion. Scientific American, 207, 120-132.
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