Figure 3. The moon near horizon looks larger than the moon when it appears at zenith. In addition, the presence of mountains below the moon near horizon subtend a larger visual angle than that subtended by the moon itself, while it also reduces the expanse of empty space below the moon. However, the presence of mountains, and its effect on the expanse of empty space surrounding the moon and as a referent for the size of the moon would be negligible when the observer looks at the moon high up at zenith.  

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Over centuries, this has been a puzzling phenomenon for psychologists, philosophers, and physicists to solve. In 1943, Boring, a distinguished psychologist at Harvard, published his illuminating contribution in the American Journal of Physics, where he has argued that the larger appearance of the moon near horizon is a perceptual phenomenon. Although the variable, the angle of regard, that he introduced to address the problem of moon illusion, explains part of the variance for the illusion, the dominant theory of moon illusion today is commonly accepted to be Rock’s and Kaufman’s (1962) theory in which the main role is played by the interpretation of 3D cues, mainly the distance implied by such cues between the observer and the moon near horizon. Another major theory, was developed by Baird et al. (1990) mainly based on size contrast. 

However, despite strong arguments, which are partly supported by experimental data, formulated in the abovementioned theories, there are questions to which there has been no satisfactory answers. For instance, Boring raised interesting questions such as “Why should (size) contrast make the moon seem large rather than small (near horizon)?" (Boring 1943, page 55), and went on by questioning the role of apparent distance between the observer and the horizon moon in explaining the moon illusion since the moon at zenith in fact seems farther away than the moon near horizon (Boring 1943, page 56). To address the puzzling problem of the moon illusion as well as providing an explanation for such questions (e.g., Boring 1943; Rock’s and Kaufman 2000), I have formulated a theory of moon illusion based on the function of 2D cues instead of 3D cues. This theory that is formulated based on the principle of interaction between the size contrast and empty space surrounding the target stimulus is inspired by my theory of geometric-optical illusions published in 2009. The size contrast between the size of the retinal image of the sun (Figure 1) or the size of retinal image of the moon (Figure 2) and the size of objects such as the mountains or buildings near the horizon in interaction with the size of the empty space surrounding these objects determine the magnitude and direction of the illusory representation of such heavenly bodies. 

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According to this theory, the horizon moon can be grouped with objects subtending smaller visual angles such as buildings (Figure 3) or with objects that can take geometrical (i.e., regular or irregular) shapes such as broken clouds (Figure 4) or be surrounded by overcast clouds with no geometrical shape.