The Moon Illusion

By Grant Ocean

Introduction

The moon appears larger when it is near the horizon than when it is high in the sky. The picture on the right can represent the phenomenon experienced by most people. Some people judge it to be as much as

twice as large, but the average estimate is 50% to 75% larger. It's not a small effect. The Sun displays the same illusion, and the same illusion is observed with any extended object in the sky, such as a constellation. All these phenomena together are called the Moon illusion. It was first mentioned in cuneiform inscriptions on clay tablets from the royal library at Nineveh in the 7th century BC and in Chinese writings at about same time and later recognized by Ptolemy, ca 150 AD. For thousands of years, the phenomenon of the moon illusion has fascinated and perplexed the greatest philosophers, mathematicians, physicists, and psychologists alike. The investigation of this phenomenon has played a crucial role in the genesis and ongoing development of the field of perception, being a major point of consideration for Aristotle, Ptolemy, Alhazen, Leonardo da Vinci, Kepler, Descartes, Roger Bacon, Christiaan Huygens, Leonard Euler, Alexander von Humboldt, Hermann von Helmholtz, Thomas Huxley II, Thomas Young, Karl Gauss, and George Berkeley. According to one source, the Internet searches on "moon illusion" have turned up more than 2,000 articles and papers. Nevertheless, the Moon illusion still remains the oldest scientific puzzle that is waiting to be solved according to some moon illusion researchers.
There are certain facts about the Moon illusion that are indisputable. The angular size of the moon is nearly constant at approximately 1/2

degree for any position in the sky. The size of the moon's image on our retinas is nearly constant for all viewing conditions. It is not a trick of atmospheric refraction, for that actually makes the moon's image slightly smaller at the horizon. It is not due to varying distance of the moon, for the moon at the horizon is actually farther from us by 1 earth radius, and this also makes it's perceived size slightly smaller there. In the picture above, the horizon moon has been enlarged to make it look more like the illusion we experience. But the picture on the left depicts the horizon moon and the zenith moon more accurately; it is the way they are in the sky. (Note: both pictures have been inspired by the similar drawings in McCready's website.) Both moons, the horizon moon and the zenith moon, are about the same distance from us and they have the same retinal image size on our retina since they are the same moon which should not change size so quickly. At this point, someone might ask why the horizon moon and the zenith moon in the picture on the left look about the same size and we do not experience the Moon illusion here. As I said in the previous article, the 2-D picture cannot represent the real 3-D world. In this 2-D picture, the visual field volume is basically the same for both moons. On the other hand, in the real 3-D world the sub-visual field volumes are different for the horizon moon and the zenith moon. As illustrated by the picture below, the same-sized moon is perceived differently when they are in the visual field of different volumes; the zenith moon is perceived as smaller when it is in the larger visual field and the horizon moon looks larger when it is in the smaller visual field. This is, by and large, my explanation for the Moon illusion. As far as why they are in different visual field volumes is concerned, we need another concept of my initiation, the converging point, to understand it.

As I promised in the previous articles, I am going to use the two concepts of mine, the visual field volume and the converging point, to explain the Moon illusion. If you have arrived at this web page directly without reading the previous three articles, (1. The Delboeuf, Ponzo and More Illusions; 2. The Ames Room Illusion; 3. Emmert's Law; and Appendix A), I recommend that you read them first. Otherwise, you will have a hard time to fully understand these concepts. As a matter of fact, after you read these articles you have already had a pretty good idea of how to explain the Moon illusion because all the "ingredients" for explaining the Moon illusion are already in there. What I am going to do in this article is to critique the conventional theories and try to explain some tough variations of the illusion which have been eluding the conventional researchers and theorists alike by using the new concepts of my own.

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The Moon Illusion Index

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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