The Moon Illusion: A Mystery in Your Head? By Dr John Jensen

     This one is a real puzzler, that perplexed the ancient Greek and Chinese scientists. The moon appears to be larger in size when it is near the horizon than when it is higher in the sky. The moon does not increase its size, nor does it get closer nor is there any atmospheric effect generating this, such a refraction. One can take a photo of the full moon on one’s mobile phone when the moon is full, and see that the object which seems so large and close that one could touch it, is really the same size as before. Thus, the effect is an illusion, but what causes it?

     This puzzle has resisted explanation from scientists for over 2,500 years, and according to one frequently cited review, is still unexplained: F. Egan, “The Moon Illusion,” Philosophy of Science, vol. 65, 1998, pp. 604-623; S. Nanavati, “A History and Experimental Analysis of the Moon Illusion,” The New School Psychology Bulletin, vol. 6, 2009, pp. 15-25. The later paper gives a good historical overview of proposed solutions, but my article will focus upon modern attempts since it is generally agreed that the ancients failed to solve the problem.

     The modern explanations of the moon illusion begin with Bishop George  Berkeley (1685-1753), who attempted to explain the moon illusion from his theory of vision: An Essay Toward a New Theory of Vision (1709). Berkeley objected to the view of size perception held by theorists of the time, such as Kepler and Descartes, that the visual system derives an estimation of the size of an object from a prior determination of the distance, and then calculates the size. Berkeley disagreed with this, believing that there is no good reason to think that the visual system does this because distance cues are also cues about the size of objects in the visual field as well. Berkeley objected to the assumption of innate knowledge based upon internal mathematical calculation, and favoured instead, an empiricist model where the ideas of size and shape are acquired from touching an interacting with objects.

     Although rejecting the notion that atmospheric factors cause the moon illusion, Berkeley gave one explanation based on the proposition that the atmosphere did produce a fainter image of the horizon moon than the zenith moon, and faint objects are correlated with the visual perception of larger objects, or so he said. But, this is doubtful as many full moons appear exceptionally clear, and in any case the Apollo astronauts reported seeing an “Earth illusion” where the moon has no atmosphere at all. (Egan, p. 609) It is known that intervening objects has an impact upon perception of the moon, with the moon appearing very large when viewed from skyscrapers. The horizon moon also looks big when viewed in scenes where there are no intervening objects such as across a lake.

     However, when the full moon is viewed from an airplane, there is no moon illusion, nor was the “Earth  illusion” seen when the Apollo 10 astronauts viewed the rising Earth from orbit around the moon, but the rising Earth seen from the moon’s surface did generate the Earth illusion. However as Egan argues, while the horizon moon may appear larger when there are cues increasing its apparent distance, the horizon moon seems large even when there is not and the visual system may perceive greater size where there are no cues indicating greater distance. The moon illusion occurs while standing on a flat stoneless desert, in ditch darkness. Egan has concluded: “So the moon illusion remains unexplained. While we have a fairly good understanding of the cue for the illusion roughly, the filled space between the observer and the horizon moon-we are still in the dark about the underlying mechanism.

     What are the prospects for a solution to the puzzle? There is no reason to think that a general theory of visual space perception would yield, in any straightforward way, an explanation of the mechanism underlying the moon illusion. Illusions typically arise from complex interactions among various levels of visual processing involving both fixed or structural features of the visual system as well as “higher-level” or “cognitive” processes (see Coren 1989). Explaining an illusion requires disentangling and independently specifying each contributing factor.

     This will be especially difficult for the moon illusion, because we do not even have a clear specification of the explanandum. When observers judge that the horizon moon looks larger than the zenith moon, are they reporting that it appears to be a larger object, or that it fills more of one’s visual field?28 It simply is not clear. Even more problematic, as we have seen, are distance judgments. We have no way of measuring or specifying the apparent distance of the moon. How far away does the zenith moon look? Of course, nothing can look 250,000 miles away. How much further does the zenith moon look than the horizon moon? The question has no sensible answer. Given these difficulties, the moon illusion’s status as our longest standing scientific puzzle seems to be secure.” (pp. 620-621)
  https://www.mnn.com/earth-matters/space/blogs/why-nobody-can-explain-the-moon-illusion 
  https://www.youtube.com/watch?v=RXkYjL_7jME
  https://www.researchgate.net/publication/265108374_The_Moon_Illusion_An_Unsolved_Mystery 

     The moon illusion is thus an outstanding scientific problem. It is interesting that such a puzzle, which can be seen each month, has resisted solution. Perhaps this illustrates some fundamental limitation of the human brain; it certainly shows that the human perceptual system can be systematically deceived.