Moon illusion

The Moon illusion is a visual illusion (or optical illusion) in which the Moon appears larger near the horizon than it does while higher up in the sky. This optical illusion also occurs with the Sun and star constellations.

Common misconceptions

It is a commonly held belief that the Moon appears larger near the horizon as a result of some kind of magnification effect caused by the Earth's atmosphere. This is not true, although the atmosphere does change the color of the Moon. Actually, the measured optical angle of the Moon's vertical diameter is smaller for the horizon moon than for the zenith moon, so when the rising moon is on the horizon it appears (both visually and in photographs) to be a bit squashed down (ovoid). This occurs because the atmosphere here acts like a weak prism (not a lens). This same real optical 'flattening' also occurs for the rising and setting sun. In addition, the angle the Moon subtends is about 1.5% smaller when it is near the horizon than when it is high in the sky, because it is farther away from the observer by almost one Earth radius.

The angle the moon subtends at an observer's eye is its angular size or visual angle, V degrees. It can be measured directly with a theodolite to show that it remains constant overnight.

It also can be calculated from the rule, V = tan S/D, where S is the linear size of the moon's diameter (2160 miles) and D is its distance from the eye (which averages about 238,000 miles). Thus, tan V = 0.009. So V = 0.52 degree, or 0.009 radian.

Proof of illusion

Besides actually measuring the moon's subtended 1/2 degree angle with a theodolite to prove that it remains constant overnight, another proof is that photographs of the moon at the horizon and higher up are exactly the same size (if taken with the same camera settings).

Another way of demonstrating that the effect is an illusion is to hold a small coin at arm's length with one eye closed, positioning it next to the seemingly large moon. When the Moon is higher in the sky positioning the same coin near the moon will reveal no change in size. Yet another way to see that the effect is an illusion is to view the Moon with one's head upside-down, say by bending over and looking through the legs, the moon on the horizon will appear smaller.

Possible explanations

Clouds near the horizon are typically farther away from the viewer, while those high in the sky are closer, giving the impression of a flat, or gently curved, sky surface

After reviewing the many different explanations in their 2002 book The Mystery of the Moon Illusion, Ross and Plug conclude "No single theory has emerged victorious" (p 180). What follows is a brief summary of some of the better-known contenders. It is, of course, possible that the correct explanation is some combination of these and others described in the external links.

Apparent distance hypothesis

One explanation is the ancient apparent distance theory, which was first clearly described by Cleomedes around AD 200. The theory proposes that we tend to perceive the sky as more or less a surface, but unlike a hemispherical surface, it does not seem to be equally distant from us at all points. When we see clouds, birds and airplanes in the sky, those near the horizon are typically farther away from us than those overhead. If we see an airplane overhead, its image gets smaller and smaller as it nears the horizon. This results in the perception of the sky as a fairly flat surface. In other words, we perceive the sky near the horizon to be farther away than the sky overhead. This assumption is usually illustrated by the well-known drawing of the "flattened sky dome."

If we perceive the Moon to be like other objects we see in the sky, we would expect it to behave in the same way and get farther away as it approaches the horizon, which should result in a smaller visual angle and Retinal image. But since its retinal image is the same size whether it is near the horizon or not, the low moon appears a larger physical size (linear size). This effect is known as Emmert's Law. That is, if two objects have the same angular size (visual angle) at the eye but appear to lie at different distances from the viewer, the object which seems further away will appear a larger linear size.

However, very few people (perhaps about 5%) see the horizon moon as being both larger and farther away. Indeed vision researchers have found that most people (perhaps 90%) say the horizon moon looks both larger and closer than the zenith moon. And most of the rest say it looks larger and about the same distance away as the zenith moon. (Also a few people do not have a "moon illusion.") The apparent distance theory requires that, if the horizon moon "looks larger" it must also look farther away. This common disagreement between that theory and the research data for the moon illusion (and other similar illusions) is known as the "size-distance paradox." Accordingly, vision scientists have published other theories to describe and explain the type of illusion that most people experience.

Relative size hypothesis

The "relative size hypothesis" has been the most popular substitute for the unsatisfactory apparent distance theory.

In loose terminology it states that the 'perceived size' of an object depends not only on its retinal size, but also on the 'size' of objects in its immediate visual environment.

But the term 'perceived size' can have two quite different meanings. It can mean perceived angular size, V' degrees, and it can mean perceived linear size, S' meters.

So, a 'relative size' hypothesis can refer either to relative angular size (in degrees) or to relative linear size (in meters).

It now seems clear that, for most people the Moon Illusion begins as an angular size illusion. So, what is most relevant is the relative angular size theory.

Oculomotor Micropsia hypothesis

Entry to be posted here soon.

Cognitive processes hypothesis

This general hypothesis applies to (is part of) all the above 'moon illusion' hypotheses. It applies, as well, to normal everyday seeing. It claims that visual illusions are due to the fact that the neural circuitry in our visual system evolves, by neural learning, to a system that makes very efficient interpretations of usual 3D scenes based in the emergence of simplified models in our brain that speed up the interpretation process but give rise to many optical illusions in unusual situations. In this sense, the cognitive processes hypothesis can be considered a framework for an understanding of optical illusions as the signature of the empirical statistical way vision has evolved to solve the inverse problem [1].

Research indicates that 3D vision capabilities emerge and are learned jointly with the planning of movements. After a long process of learning, an internal representation of the world emerges that is essentially well adjusted to the perceived data coming from closer objects. The representation of distant objects near the horizon is less "adequate." In fact, it is not only the Moon that seems larger when we perceive it near the horizon. In a photo of a distant scene, all distant objects are perceived as smaller than when we observe them directly using our vision.

The retinal image is the main source driving vision but what we see is a "virtual" 3D representation of the scene in front of us. We don't see a physical image of the world. We see objects; and the physical world is not itself separated into objects. We see it according to the way our brain organizes it. The names, colors, usual shapes and other information about the things we see pop up instantaneously from our neural circuitry and influence the representation of the scene. We "see" the most relevant information about the elements of the best 3D image that our neural networks can produce. The perceived properties of the objects, such as brightness, angular size, and color, are unconsciously "determined" and are not real physical properties. The illusions arise when the "judgments" implied in the unconscious analysis of the scene are in conflict with reasoned considerations about it.

References

ISBN links support NWE through referral fees

• Ross HE and Plug C (2002) The mystery of the moon illusion: Exploring size perception. Oxford University Press. ISBN 0-19-850862-X.

External links

• A vision scientist reviews and critiques moon illusion theories.
• A physicist reviews past and current theories
• Summer Moon Illusion - NASA
• Why does the moon look so big now?
• Inflatable Moon (explanation of an early illusion)
• Explanation visual gestalt effects, which may also apply to the moon illusion
• Why does the Moon appear bigger near the horizon? (from The Straight Dope)
• Moon illusion illustrated
• Moon illusion discussed at Bad Astronomy website
• Four Answers to the Why Question about the Moon Illusion
• APOD Moon Illusion page

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