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The Moon Illusion

By Grant Ocean

The Resting Focus

        The smaller-looking zenith moon is due to the resting focus according to the proponents of oculomotor micropsia. When viewing the full moon directly overhead, in a clear sky, there are no other distance cues, and the eye adjusts to its resting focus a distance of 1 or 2 meters. Further support offered for this hypothesis is the effect of dark surroundings, which bias the eyes to adjust to the dark focus distance of about one meter.
        To test this hypothesis, measure the moon or sun at a close distance from your eye using a ruler or similar instrument, or pinch the moon or sun with your thumb and index finger at a close position. The moon or sun looks small and has a small measured size. If you move the ruler or the pinching thumb and index finger aside and focus on the moon or sun, now the moon or sun looks much bigger. Measure the moon or sun at arm's length, which is about one meter away from your eye, with the ruler or pinch the moon or sun with your thumb and index finger at arm's length. Then move the ruler or the pinching thumb and index finger aside. The moon or sun looks about the same size as the measurement on the ruler and the space between the thumb and index finger. This experiment proves that we do focus on a distance of approximately one meter while viewing the zenith moon or sun. However, I do not think that this focusing distance of one meter is the resting focus as hypothesized.
        It is suggested that we adjust our eyes to a resting focus when no distance cues are available. But there are no distance cues available at sea and we still perceive the horizon moon as larger over the ocean. Additionally, viewing the moons through a tube effectively removes all the distance cues. Yet we do not adjust our eyes to the resting focus; rather we focus on the opening of the tube. When the tube is shorter, we focus on a shorter distance; when the tube is longer, we focus on a longer distance. The situation of no distance cues created by the tube viewing does not make our eyes to focus on a specific spot, i.e., one meter from our eye. Finally, the resting focus should be achieved when we are not actively focusing on any object; so our eyes are at rest, not doing any thing such as converging, accommodating, viewing, and perceiving. Instead, we are trying very hard and actively to focus on the zenith moon when the resting focus occurs.
        The resting focus, in fact, is the converging point. The reason why it is approximately one meter from our eye is that it is the focusing distance allowed by the minimum converging angle when we look at an object as faraway as the moon or sun and have such a perceived size. As discussed in the previous article, the converging point cannot be moved forwards anymore when the minimum converging angle has been reached. At this point, an object that moves further away will be out of focus and appear smaller. All in all, the one meter converging point is the furthest position we can focus on when we view the zenith moon, which is regulated by the minimum converging angle. I would expect that any object casting the same perceived size as the zenith moon will have the same converging point no matter where it is located. Therefore, the so-called resting focus is not caused by lacking of distance cues, but by the perceived size and minimum converging angle. Likewise, the dark focus is the converging point set for viewing an infinitely far distance.
        Nonetheless, how far we can place the converging point depends on the size of the objects we are focusing on. For a small object such as an ant the minimum converging angle can be reached at a very close distance; thus we can hardly focus on an ant at one meter. On the other hand, for a large object such as the horizon, which is probably the largest object on Earth, the minimum converging angle will be reached at a very long distance. This is the main point of my proposal: the horizon moon looks larger because we can bring the converging point closer to the largest object on Earth, the horizon, in comparison to the zenith moon which is viewed through a much closer converging point to the viewing eye and farther away from the viewed object. This effect can be likened to the telescope. When you focus your telescope on an object, all those other objects in the view field will be enlarged as well. We can also use the paper tube to simulate this effect. If you view both the horizon moon and the zenith moon through one paper tube, they look the same size. Now view the zenith moon through two paper tubes and view the horizon moon through one tube. As a result, the zenith moon looks larger than the horizon moon because the converging point is closer to the viewed object while viewing it through two paper tubes. Similarly, both moons look the same on the photograph taken with the same focal length; but the zenith or horizon moon would look larger if taken with a longer focal length lens. Converging our eyes on the horizon is like viewing objects through a longer tube or longer focal length lens. Consequently, the larger-looking horizon moon is due to the fact that we can physically converge our eyes closer to the moon thanks to the horizon nearby which is the largest object in this world; as a result, the horizon moon also looks nearer like being viewed through a telescope. There is no need for subjective interpretation, taking into account, computing, compensating, calculating, inference (conscious or unconscious), guessing, expecting, processing, cuing, reasoning, and whatsoever.
        There is one aspect of the Moon illusion that has been neglected by all the researchers. It is that people perceive the horizon moon as larger and at the same time perceive the sky as smaller. So there are two aspects regarding the Moon illusion: one is the recognized larger-looking horizon moon and another is the overlooked smaller-looking sky. For instance, when people claim they perceive the horizon moon as 10 times larger, at the same time they also claim the horizon moon seems to occupy almost half of the sky. I think that the negligence is due to the fact that they did not have a proper concept to account for this second aspect of the Moon illusion. The researchers have had enough troubles already to deal with the larger-looking horizon moon; the second phenomenon would confound the explaining efforts even more. Fortunately, the concepts of the converging point and the visual field volume can help explain this phenomenon. Take a look at the diagram below, which we have seen many times before. If we move the converging point from the Focus1 to the Focus2 position, the sub-visual field is getting narrower around the far object. This illustrates why the sky appears to be smaller when we focus on the horizon. The two aspects of the Moon illusion are essentially represented in this single diagram.



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References


     Nanavati, S. (2009). A history and experimental analysis of the moon illusion. The New School Psychology Bulletin, Vol. 6, No. 1.
     Trehub, A. (1991). The Cognitive Brain. MIT Press.     

Related Information on the Web:

http://facstaff.uww.edu/mccreadd/index.html
http://www.lhup.edu/~dsimanek/3d/moonillu.htm
http://en.wikipedia.org/wiki/Moon_illusion
http://retina.anatomy.upenn.edu/~bart/scriptie.html
http://www.pnas.org/content/97/1/500.full
http://nspb.net/index.php/nspb/article/view/6/3

Appendix A


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