Prepared by John Melville Harris



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Observe in FIGURE 1 that the horizon moon may appear slightly larger than the moon at its zenith, even though the physical measurements of both moons are exactly the same.



Horizon Moon


Zenith Moon


The real moon illusion is an extremely strong one. It depends for its effect on our perception that the sky is like a flat-topped dome the rim of which appears further away than the top of the dome because of terrestrial distance cues such as fields, roads and trees (sketched schematically in the HORIZON MOON figure). The effect of this error in perspective is for the moon overhead (its zenith) to appear smaller than the horizon moon. The strength of the effect is difficult to produce on paper, or on a computer terminal, due to the absence of a perceptual error of an all-encompassing flat-topped dome. Even in three dimensions, if all points of the perceived dome were equidistant from the observer, there would be no moon illusion. The small extent that FIGURES 1 and 2 successfully express the moon illusion is owing to the degree to which the clouds in FIGURE 2 substitute for the flat-headed dome by making the zenith moon appear closer to the foreground without changing the actual size of the moon disc.

Normally , two objects of different distances from an observer will still appear to be the same size, even though their retinal sizes differ, a principle called SIZE CONSTANCY. Applying size constancy to objects of the same size means the two moons, measuring the same distance (having the same retinal size) should still appear equal in size to an observer. However, all points of the flat-topped dome are NOT at an equal, perceived distance from the observer. FIGURE 2 depicts the essential principle: There are two logs of identical size, but the one which appears more distant looks larger.

FIGURE 2 below permits an intuitive appreciation of how an observer can interpret an apparently near object to be smaller than another object of the same size which is apparently more distant. Because of size constancy, we interpret the log in the foreground to be a smaller size than the log in the background, even though both logs are exactly the same physical size and thus cause the same size retinal image. In the real world, the logs could cast the same size image on the retina only if the more distant log was larger. Thus perceived distance is the variable of interest in FIGURE 2 and in the moon illusion. Retinal size x perceived distance = perceived size. There are experiments which measure observers' subjective estimation of a target's distance from them. Knowledge of perceived distance while holding retinal size constant (actual distance) would make the perceived size of the moon at zenith and on the horizon predictable.


Log Illusion

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