The Moon Illusion Explained

Finally! Why the Moon Looks Big at the Horizon
and Smaller When Higher Up.

Don McCready     Professor Emeritus,

Psychology Department
University of Wisconsin-Whitewater
Whitewater, WI 53190
Email to: mccreadd at uww.edu

Introduction and Summary
[This Section and all other Sections Were Revised November 10, 2004]
[Technical Notes on the Murray, Boyaci, & Kersten (2006) experiment were added in June, 2006.]

For many centuries, scientists have been puzzled by the common illusion that the rising moon at the horizon looks considerably larger than it does later, at higher elevations toward the zenith of the sky. For at least nine centuries they have known that the angular subtense of the moon's horizontal (azimuth) diameter always measures about 0.52 degrees at an earthly observation point no matter where the moon is in the sky. In other words, there is no physical (optical) reason why the horizon moon should look larger than the zenith moon.

Because the moon's angular size remains constant, photographs of the horizon moon and zenith moon taken with the same camera settings yield images which are the same size, as represented by Figure 1.
Such pictures prove that the earth's atmosphere certainly does not "magnify" the horizon moon.

Figure 1: This sketch represents what a double-exposure photograph of the horizon moon and zenith moon looks like.
The two moon images have the same diameter on the film (and a print) because the angle the endpoints of the moon's diameter subtend at a camera lens remains the same.

Many researchers have taken such photos in order to convince themselves. They all were convinced.
You can try it yourself.

Most people are quite amazed when they first learn that fact:

They had expected, instead, that a photograph would resemble the very different sketch in Figure 2, below, with the lower circle drawn larger than the upper circle.

Figure 2.  This sketch portrays two moon-like spheres with the lower one's diameter subtending an angle at the reader's eye 1.5 times larger than the angle subtended by the upper one's diameter.

Most people will say this Figure 2 "front view" imitates their moon illusion experience.

Many research measures of the moon illusion have been published. For some people the horizon moon's angular size can look as much as twice as large as the zenith moon's, but a value from 1.3 to 1.5 times is about average. The ratio of 1.5, illustrated by Figure 2, will be used in most of the examples in this article.

The same illusion also occurs for the sun and for the constellations as they appear to move between horizon and zenith positions. The term 'moon illusion' commonly is used for all such examples, however.

A New Theory Is Needed.
For more than 100 years, various scientists interested in visual perception (a specialty within psychology) have conducted experiments on the moon illusion and published their results in reputable scientific journals.
And, for more than 50 years the illusion has been discussed in introductory psychology textbooks that typically have offered two competing explanations: The very old apparent distance theory, and a size-contrast theory . But both are unsatisfactory, so researchers have been seeking a new theory to replace them. They are critiqued in detail in Section II, but briefly described below.

The Apparent Distance Theory Description: Popular But Inadequate.
This ancient theory is still the best-known attempt to explain the moon illusion.
According to this theory we do not perceive angular sizes: By default, that means the horizon moon and zenith moon look the same angular size, so the phrase "looks larger" can refer only to the moon's linear size in meters.

The picture at the left mimics that illusion with both moon images subtending the same angular size.

The theory proposes that, with both moons appearing the same angular size. the horizon moon looks a larger linear size than the zenith moon because it looks farther away than the zenith moon.

For instance let the lower disc image in that picture represent a large hot-air balloon of diameter 10 meters, tethered 100 meters away, and suppose the upper disc represents a helium-filled party balloon 1 meter in diameter floating directly above the nearby cornstalks only 10 meters away.

A person who experiences that pictorial illusion would say that, compared with the upper balloon, the lower one looks farther away and a larger linear diameter (and volume).

Advocates of the apparent distance theory have suggested two different reasons why the horizon moon would look farther away than the zenith moon.
The most popular version of the theory appeals to the ancient idea of a "sky dome illusion" (critiqued later).
However, at least since 1962 the "sky dome" version has been rejected and replaced by a version that assigns the main cause to changes in the patterns of cues to distance in the moon's vista. The extensive researches of Rock & Kaufman (1962, Kaufman & Rock, 1962, and many others) have revealed this strong association.
For instance, the horizon moon "looks larger" when the horizon vista includes many visible cues that would signal a very great distance for that moon, while the zenith moon looks smaller when its vista includes relatively few cues that would signal a far distance.
It is important to keep this well-established data in mind, because any new theory obviously must take it into account.

The "Size-Distance Paradox".
According to the apparent distance theory, all observers who say the horizon moon "looks larger" than the zenith moon are required to also say "it looks farther away." If that describes your own moon illusion, then that old explanation may fit your experience.
But you are among a very small minority.
For, as vision researchers have pointed out for at least 40 years, most people simply do not say the horizon moon looks farther away than the zenith moon (see Boring, 1962, Gregory, 1965, McCready, 1965, and many others). Instead, for most people the larger-looking horizon moon either looks about the same distance away as the zenith moon, or, more often, it looks closer than the zenith moon.
That complete contradiction between observers' reports and what the apparent distance theory requires is well-known among researchers: It also occurs in attempts to apply the apparent distance theory to many other classic "size" illusions: it is called the "size-distance paradox".
Yet it rarely is mentioned in popular articles about the moon illusion. For instance, a recent study by L. Kaufman and J. Kaufman (2000) that somehow became widely publicized in the popular press, claimed to offer support for the apparent distance theory, but it did not (could not) deal with the fatal contradiction.

The solution to properly describing most peoples' moon illusion and removing the "paradox" is to realize that the phrase "looks larger" refers, first of all, to the angular size, and secondarily may also refer to the linear size, as discussed next.

An Angular Size Illusion First.
Again, the moon illusion for most people is illustrated by the picture at the right. It is as if the angular subtense were larger for the horizon moon than for the zenith moon.
It thus is as if the optical image of the moon on the retina were larger for the horizon moon than for the zenith moon. (Optical experts have argued, convincingly, that the moon's physical retinal image has a constant diameter of about 0.15 mm.)

That claim that the constant 1/2 degree angular size of the moon looks larger for the horizon moon than for the zenith moon (McCready 1965, 1985, 1986) now is being accepted by nearly all researchers (see Ross & Plug, 2002).

The idea also has been recognized by a version of the popular "size-contrast" theory.

The Angular Size-Contrast Theory.
The best-known alternative to the failed apparent distance theory has been a "size-contrast" theory. Of course, the word "size" is ambiguous: it could refer either to angular size or to linear size.
But, Restle (1970) properly treated the basic moon illusion as an angular size illusion by proposing that it is due to the angular size contrast effect found in many other classic "size" illusions.
He pointed out that the vista near the horizon moon typically includes many visible elements that subtend angles smaller than the moon's 1/2 degree, including the short angular subtense between the rising moon and the horizon line. On the other hand, the visible elements in the zenith moon's vista usually subtend angles larger than 1/2 degree, especially a large, and relatively empty, zenith sky.
The theory merely claims that those different contrasts between the moon's 1/2 degree subtense and the smaller and larger angular subtenses in its surroundings somehow make the horizon moon's 1/2 degree subtense look larger than the zenith moon's.

Baird, Wagner and Fuld (1990) recently brought that theory up to date by phrasing it in terms of the present 'new' theory (McCready 1985, 1986).

The angular size contrast theory has difficulty, however, explaining the old, well-established observation that the large-looking horizon moon will look smaller if one bends over and views it upside down (Washburn, 1894).
Moreover, this simple theory does not go far enough to explain why the angular size contrast effect occurs. (It is critiqued in Section II).

Another Theory Needed
Until recently, those two competing theories were the only ones vision scientists took seriously. And, because both are unsatisfactory, new theories have been published. But, the two-dozen (or so) scientists most familiar with experiments on the moon illusion still have not accepted any one theory. In 2004 the jury was still out.

New Description.
What we need is an acceptable explanation for the angular size illusion the moon illusion reveals.
Moreover, this basic angular size illusion necessarily is accompanied either by a distance illusion or by a linear size illusion or else all three illusions occur together.

For instance the picture at the right imitates the moon illusion for most people. One common perceptual outcome is that the two moons look about the same distance away, so the horizon moon necessarily looks a larger linear size than the zenith moon because it looks angularly larger.
Or, as another common perceptual outcome, the two moons appear the same linear size (and volume) so the horizon moon necessarily looks closer than the zenith moon because it looks angularly larger.
Those two perceptual outcomes and some others are presently discussed in detail.

A relative new explanation for such illusions (McCready 1965, 1985, 1986) is reviewed in this present article.
However, before the new theory is elaborated, it is important to clarify the distinctions between our perceptions of angular size and linear size, because popular articles typically don't make that distinction.

The Perceived Values.
Consider the simple example illustrated by the drawing below.
Suppose we are looking at a house across the street that is 30 feet wide seen entirely through a nearby window opening that is 30 inches wide:
We can say the house looks farther away than the window. Its perceived distance is greater: we might say the house "looks about 120 feet away" and the window "looks about 5 feet away."
We also can say the house looks larger than the window, meaning that our perceived linear size for the house's width might be "about 30 feet" and the window's width "about 30 inches".

We also can say the house looks smaller than the window, and that does not contradict the other statement because now we are referring to their angular subtenses, in degrees.
That is, we are referring to the directions in which the edges of the house and window appear to lie from our point of view, their visual directions.
For instance, the left edge of the house appears in some direction from us, which obviously differs from the perceived direction of the right edge.
By definition, an angle is the difference between two directions from a common point (the vertex).
Accordingly, the difference between the perceived directions of the outer edges of the house from our point of view is the perceived angular size for the house.
Let's say the perceived angular size for the house width is about half as large as the perceived angular size for the width of the window's opening.

It is important to understand that we experience both the linear size and the angular size comparisons (Joynson, 1949) along with seeing the distance comparison.
For a viewed object we often can state a linear size (in meters) and a distance (in meters). But we typically cannot verbally estimate an angular size (in degrees) for it. (After all, we rarely practice doing that.) Notice however that when we say one object "looks larger" than another, we most often are using the verb "looks" to describe not the perceived linear sizes, but the perceived angular sizes for them!

Obviously, whenever we say how large an object "looks" compared with another object, we should carefully specify which one of the two very different kinds of "size" experience we are comparing (Joynson, 1949).

The sketch also can be used to illustrate two important aspects of visual processing.

Visual Processing.
First there is linear size constancy. For example, the nearby window can look 1 meter tall; and the far window on the end of the house also can look 1 meter tall. If so, we say the far window looks the "same size" (linearly) as the nearby window, while at the same time it "looks smaller" (angularly) than the nearby window, and farther away.

Secondly, that example clearly illustrates the cue to distance textbooks call merely "relative size," an incredibly ambiguous term. This powerful distance cue properly should be called the relative angular size cue to distance. That is, if two objects look the same linear size (linear size constancy) and one looks angularly larger, it "automatically" looks closer.

The new theory offers complete descriptions of the many ways in which the moon's angular size, linear size and distance appear to change. The theory has four main parts, outlined below.

New Theory, Four Parts.
Part 1. An Angular Size, Linear Size and Distance Illusion:
Other vision researchers who also describe the primary "size" illusion as an angular size illusion include:   Acosta (2004)     Baird (1970)     Baird, et al. (1990)    Enright (1975, 1987a, 1987b, 1989a, 1989b)     Gogel & Eby (1994)     Hershenson (1982, 1989)   Higashiyama (1992)   Higashiyama & Shimono (1994)    Komoda & Ono (1974)     Ono (1970)     Plug & Ross (1989, 1994)     Reed (1984, 1989),   Reed & Krupinski (1992),     Restle (1970)   and Roscoe (1979, 1984, 1985, 1989).
Moreover, in their recent most comprehensive book, "The Mystery of the Moon Illusion," Ross and Plug (2002) review the long history of speculation and research on the moon illusion and accept that the basic illusion is an angular size illusion.

Also, in an earlier long review, Plug and Ross (1989) concluded that the distinction emphasized by McCready (1965, 1985, 1986) between perceived linear size and perceived angular size, as well as the idea that the horizon moon has a larger perceived angular size than the zenith moon, "....might turn out to be the most important conceptual and methodological development in the history of the moon illusion since Ibn al-Haytham [Alhazen] redefined the illusion as a psychological phenomenon" (page 22).

********* TECHNICAL NOTE Added June 7, 2006 **********
Extremely important research on visual angle illusions recently was published in Nature Neuroscience. The article is, “The representation of perceived angular size in human primary visual cortex,” by Murray, S. O., Boyaci, H., & Kersten, D. (2006).

The authors measured an angular size illusion and relate it to the moon illusion.
[Yet none of the moon illusion articles they cite describe it as an angular size illusion!]

This note summarizes what they found and how it fully supports the ‘new’ theoretical approach emphasized here..
[A more detailed analysis of their experiment is in Appendix B]

Their abstract is as follows..
   "Two objects that project the same visual angle on the retina can appear to occupy very different proportions of the visual field if they are perceived to be at different distances. What happens to the retinotopic map in primary visual cortex (V1) during the perception of these size illusions? Here we show, using functional magnetic resonance imaging (fMRI), that the retinotopic representation of an object changes in accordance with its perceived angular size. A distant object that appears to occupy a larger portion of the visual field activates a larger area in V1 than an object of equal angular size that is perceived to be closer and smaller. These results demonstrate that the retinal size of an object and the depth information in a scene are combined early in the human visual system.”

The study used a composite (photo-montage) of a hallway with two spheres on its floor at different distances and subtending the same angular size, but the angular size of the 'far' sphere looked at least 17% larger than the angular size of 'near' sphere, let's say it was about 20%.
That (copyrighted) picture can be seen at the following link (open it in a new window, and click on the image there to see a larger version).
      faculty.washington.edu/somurray/sizedemo

The crude sketch at the right resembles their picture.
But, for a detailed analysis you should use their original image.

Their picture looks like a photograph taken when one sphere was five times farther away from the camera lens than the other. Both spheres subtended the same angle at the camera lens, so the linear (metric) diameter of the far sphere had to be about five times the diameter of the near one.
In a likely pictorial (3D) illusion the perceived distance of the “far’ sphere is about five times greater than for the ‘near sphere.
And, for an example, suppose the ‘near’ sphere has a perceived linear diameter, of, say, 6 inches, so the far one looks about 30 inches in diameter.

If the spheres correctly look the same angular size, then that huge (5-times) linear size illusion for them illustrates the dominant approach to such illusions (the apparent distance theory, Emmert's law and "misapplied size-constancy scaling", see later).
But that mundane, 5-times larger, linear size illusion is not the illusion that was measured.

Instead, the interesting illusion was the angular size illusion, which also occurs for the two disks on the screen which are the images of the spheres.
Those disks correctly appear at the same distance, and form equal sized images on the retina, but the perceived angular size of the disk that is the image of the ‘far sphere’ measured at least 17% larger than the perceived angular size of the disk that is the image of the ‘near sphere’.
The observers were asked to make the two disks look the same angular size, and also look the same linear size, which tasks yield the same final setting when the disks have the same perceived distance (to the screen).
Hence, the perceived linear sizes of the disks likewise differed by at least 17%.

The major new discovery was that the sizes of the activity patterns in cortical area V1 that corresponded with the equal retinal images of the two disks, were not equal, and their measured size difference correlated almost perfectly with the perceived angular size difference (say, 17%) for the two disks (and also for the apparent "spheres").

The authors point out that those results do not support the dominant approaches to "size" illusions.

For instance, a University of Washington website offers a review of the study at,
          http://www.uwnews.org/article.asp?articleID=23005
It quotes Dr. Murray as follows,
   "It almost seems like a first grader could have predicted the result. But virtually no vision or neuroscientist would have. The very dominant view is that the image of an object in the primary visual cortex is just a precise reflection of the image on the retina. I'm sure if one were to poll scientists, 99 percent of them would say the 'large' moon and the 'small' moon occupy the same amount of space in the primary visual cortex , assuming they haven't read our paper!"

That comment overlooks the fact that, like first graders, but using 10th grade geometry, quite a few of us vision scientists (previously listed) have pointed out, at least since 1965, that the angular size illusion for the moon (and in other classic illusions) is   as if   the constant retinal image size changed when distance cue patterns changed.

Because that is very basic illusion, and given what has long been known about the neural projections of the retinal surface into area V1 (Brodmann area 17), it has seemed quite likely that the 'size' change would already appear that early in the brain.

After all, angular size perception is nothing more than perception of the different directions of two seen points from oneself, which perception is important for rapid orienting responses that are vital to survival.
[Indeed, in many animals' visual systems, the superior colliculi are very much concerned with direction perception, so one could make a wild guess and speculate that these even more primative brain loci are involved in the creation of angular size illusions.]

The Murray, et al. study directly relates to studies of the moon illusion in pictures (Enright, 1987a, 1987b, 1989a) which were not mentioned (see later here, in Section I).
Also not mentioned was that the results fully support the ‘newer’ approaches that explicitly describe angular size illusions controlled by changes in distance cues, as advocated here.

A difficulty is that, in the article's discussion section the interpretations actually use the 'dominant approach' (the apparent distance theory) and confuse perceived angular size and perceived linear size (called ‘perceived behavioral size’).
For instance, it is suggested that distance cues evoke a supposed “scaling” of some entity called the viewed object's ‘retinal projection” to yield a “perceived behavioral size” for the object, "whereby retinal size is progressively removed from the representation" (p.422).

That very old idea overlooks that the (flexible) perceptual correlate of the extent between two stimulated retinal points is not a perceived linear size, but the perceived angular size. And, as the authors clearly showed, the perceived angular size is more precisely a perceptual correlate of the extent of the activity in area V1.
In other words, the discussion section offers the 'dominant' interpretation which does not even describe the angular size illusion that was measured, let alone explain it.

As was easily predictable, other articles already are mis-interpreting the Murray, et al. experiment in the 'dominant' way. For instance, the results have been said to illustrate Emmert’s Law and ‘misapplied size-constancy scaling’ which do not (cannot) apply to an angular size illusion.

The Murray, et, al. findings are mentioned again in several places here, as support for the present approach.
Also, the experiment is analyzed in Appendix B, including a section that shows how the oculomotor micropsia/macropsia formulation can fit the data.

********** End of Technical Note of June 07, 2006 **********

Part 2. Distance Cue Control:
As already noted, any explanation of the moon illusion must take into account that virtually all research has shown that the changes in the moon's perceived angular size correlate most strongly with changes in those visible patterns in the moon's vista that are known to be strong cues to distance.
These distance cues are the visual patterns that make objects look three-dimensional and appear at different distances from us. They are well understood by photographers and artists who use them in a flat (2D) picture to create a 3D pictorial illusion.
Concerning the moon illusion, the distant-looking moon will look angularly larger when changes in the available distance cue patterns in its vista 'signal' that it is even farther away from us: That often happens for the horizon moon. (But it typically doesn't look farther away because other cues dominate the perception.)
And, when changes in distance cues indicate a shorter distance to the moon, or else if the distance cues are greatly reduced, the moon will look angularly smaller than it did. That often happens for the zenith moon. (But it typically doesn't look closer because other cues dominate the perception.)

    Consequently, the fundamental scientific task is to explain why changes in distance cue patterns can make the constant angular size of an object appear to change.

The present theory is one of the few that offers a plausible explanation for that association. It begins by appealing to another, more basic illusion known as oculomotor micropsia/macropsia.

Part 3. Oculomotor Micropsia/Macropsia:
Among the many classic "size" illusions, the largest, by far, seems to be oculomotor micropsia/macropsia. It was first described by the physicist, Charles Wheatstone (1852) in an article reporting observations he made using the research stereoscope he had invented earlier. For more than a century the illusion was described merely as follows:
While one is looking at a fixed object that subtends a constant angular size, if one then accommodates and converges one's eyes to a distance much closer than the object's distance, the object's "apparent size" ("perceived size") decreases. Of course, those ambiguous terms could refer to the perceived angular size, or to the perceived linear size.
Since 1965, several researchers have specified that it is primarily a visual angle illusion (McCready, 1965, 1983, 1985; Ono, 1970; Komoda & Ono, 1974). And, it necessarily is accompanied, secondarily, either by a linear size illusion, or by a distance illusion, or else all three illusions occur.

Moreover, it certainly is controlled by distance cues (McCready, 1965, 1983, 1985).
Although much less familiar than other illusions, oculomotor micropsia/macropsia is not only large, but also ubiquitous. Indeed, I have proposed that it is the basic angular size illusion behind many of the best-known "size" illusions (see later).
Its manifestations can be briefly described as follows:

A.  It is controlled by adjustments of the eyes.
    (1). As a rule, when the eyes focus and converge to a closer distance than a viewed object its angular size appears to become smaller (micropsia) than it was before the readjustment.
     (2). And, when the eyes adjust to a farther distance, the angular size of a viewed object appears to become larger (macropsia) than it was before.

Most readers can conduct the following demonstration of oculomotor micropsia.

A Simple Demonstration.
The next time you look at the horizon moon, deliberately create oculomotor micropsia by strongly converging ("crossing") your eyes, say by looking at the bridge of your nose, but pay attention to the moon. That over-convergence of the eyes will create double vision of the moon and some blurring, but notice that the moon's angular size momentarily looks smaller than it did. At the same time, the moon will look either farther away than it did, or its linear size will look smaller, or else both of those secondary illusions will occur. That angular size illusion resembles what occurs during viewing of the zenith moon (except that the eyes don't have to be strongly "crossed.")
However, in this demonstration the apparent decrease in angular size undoubtedly is greater than the decrease found during natural viewing of the zenith moon. [Indeed, this demonstration of micropsia even works for the zenith moon, which already looks angularly smaller than the horizon moon.]

When you then return both eyes to being aimed straight ahead (their "far," divergence position) the moon will look single again and momentarily will look angularly larger than it just did (relative macropsia). Hence it also will look either closer than it just did, or its linear size will look larger, or else both of those secondary illusions will occur.

B.  Eye adjustments are controlled by distance cues, etc.
     (1). Oculomotor adjustments to "far" typically are triggered by cues to a very far distance. In turn, that induces macropsia. (And, despite the eyes' adjustment to a farther point, the now "larger-looking" object typically does not appear to move farther away, because some other cues dominate the final perception.)
Enright (1975, 1989) and Roscoe (1989) have shown that this macropsia condition usually occurs during viewing of the horizon moon.

    (2). On the other hand, cues to a near distance trigger oculomotor changes to "near" which, in turn, induce micropsia. (And, despite the eyes' adjustment to a nearer point, the now "smaller-looking" object typically does not appear to move closer because some other cues to distance dominate the final percept.)

    (3). During viewing of a distant object, some closer objects near the line of sight can make the eyes adjust to a short distance and induce micropsia for the distant object (and all objects). This occurs especially when one is looking through a window screen or a wet windshield (see Roscoe, 1989).

    (4). Moreover, vision researchers are well aware of two natural phenomena that can induce micropsia.
Night myopia refers to the common result that eye adjustments to a near distance usually occur in the dark.
And, empty-field myopia refers to the common result that eye adjustments to a near distance also occur when there is a relative lack of distance cues in the field of view.
Enright (1975, 1989) and Roscoe (1989) have noted that those two natural 'myopia' conditions often occur during viewing of the zenith moon, and induce micropsia.

C.  Overt Muscle Activity Is Not Required.
    (1) Oculomotor micropsia can occur even when the internal eye muscles responsible for accommodation (focusing) are paralyzed by eye drops (Heineman, Tulving, and Nachmias, 1959). Thus older people with presbyopia have the illusion when they merely try to focus closer.
That finding has made researchers understand that the muscles most responsible for the illusion are the external muscles that make the eyes converge and diverge.
    (2) An important further finding has been that, to induce micropsia/macropsia, overt changes in the convergence muscles often are not necessary: There seems to be a conditioned relationship, by which changes in distance cues have gained the power to induce micropsia and macropsia directly (automatically) without causing the eye muscles to change.

These matters are discussed in detail in Section III.

In other words, the present theory is that the moon illusion is an example of the basic illusion of oculomotor micropsia/macropsia, induced by changes in the distance cue patterns in the moon's vista, even when the eye muscles don't change.

Part 4. A Theory of Oculomotor Micropsia/Macropsia:
    To describe the basic moon illusion as an angular size illusion is itself an important 'new' idea. To propose that it is an example of a more basic angular size illusion, such as oculomotor micropsia/macropsia, only redescribes it, and does not yet fully explain it. To have a complete theory it is necessary to also explain why oculomotor micropsia/macropsia occurs.
One explanation has been shown to fit (mathematically) the published research measures of oculomotor micropsia/macropsia very much better than do any other theories (McCready, 1965, 1983, 1985, 1994; Komoda & Ono, 1974; Ono, 1970). It is reviewed in Section IV.
Briefly stated, oculomotor micropsia seems to be a normal perceptual-motor adaptation which "corrects" angular size (direction difference) perceptions in order to make them more accurate visual predictors of orienting bodily movements (such as rapid head rotations) aimed at targets that lie in different directions at different distances and that demand immediate full attention.
Enright (1989) has offered a similar perceptual-motor adaptation explanation.

***************
A Note. (Revised June 7, 2006)
In January, 2000, many articles in the popular media announced that a "new" theory of the moon illusion had been published by L. Kaufman and J. Kaufman (2000).
However, it is simply the old apparent distance theory, advocated by L. Kaufman and I. Rock in 1962.
It explicitly rejects use of the perceived angular size concept, so it cannot possibly explain the majority moon illusion.
The article also claims that the data contradict the present oculomotor micropsia theory (McCready, 1965, 1985, 1986).
But the oculomotor micropsia theory is not properly described as an angular size illusion.
When you read the original article, if you insert the otherwise 'forbidden,' perceived angular size concept "between the lines," you can see that the data do not contradict the oculomotor micropsia theory.

The recent research by Murray, et al. (2006) (discussed above) clearly found a physical basis for angular size illusions like the moon illusion, and that completely contradicts the apparent distance theory.
How oculomotor micropsia can also apply to the Murray, et al, data will be discussed in Appendix B.

*****************

Now consider some more detailed descriptions of the moon illusion.

Versions of the Moon Illusion.
Absolute Moon Illusions
The moon's linear diameter is 2160 miles, but it obviously looks much smaller than that. Its perceived linear size (in meters) varies widely among people and even changes for one person as the viewing conditions change.

The moon's distance from us averages about 238,000 miles, but it obviously looks much closer than that. Its perceived distance (in meters) varies widely among people and even changes for one person as the viewing conditions change (such as while driving among hills or in a city).

The moon's angular subtense measures an essentially constant 0.52 degree. Its absolute perceived angular size has not yet been determined for any location, but that doesn't matter here, because scientists are most interested in the relative illusion. Namely, the constant angular size appears to change.

Relative Moon Illusions
The three most common versions of the moon illusion are outlined below using the picture at the right if you use your imagination.
The lower disc looks a larger angular size than the upper disc to imitate the moon illusion that most people suffer. We also must consider how far away the moon looks, and how large its linear size looks.

1.   Same Distance Outcome: Here the portrayed horizon moon looks angularly larger than the zenith moon, and, in agreement with one's factual knowledge, they look about the same distance away. Hence the horizon moon must look a larger linear size than the zenith moon (by the same proportion that its angular size looks larger) and that contradicts one's knowledge that the moon remains the same linear size (and volume).
For an analogy, suppose the picture shows a large balloon and a smaller balloon floating directly above it.

In order to understand how this visual processing works, consider a very simple example using just the two circles in that flat picture. Various distance cues make that pattern appear to be on the same flat page (screen), so the circles correctly look the same distance from you.
Consequently, the lower circle's linear diameter (in mm) on the page correctly looks about 1.5 times larger than the upper circle's because its angular size (in degrees) correctly looks about 1.5 times larger.

2.   Same Linear Size Outcome: Here the horizon moon again looks angularly larger than the zenith moon, but now, in agreement with one's factual knowledge, both moons look the same linear size. So, the horizon moon looks closer than the zenith moon.
For an analogy, imagine the picture shows two balloons that are the same linear size (and volume). If so, then the lower one looks closer than the upper one because it looks a larger angular size.
In other words, that linear size constancy outcome sets up the powerful, relative angular size distance cue discussed earlier.

3.   Intermediate Outcome: Here all three illusions occur. Compared with the zenith moon, the horizon moon looks angularly larger and closer and a larger linear size. Now the phrase, "looks larger" refers both to the linear size and to the angular size.
But, most people seem to be satisfied with saying merely that it "looks larger and closer" without bothering to mention that both the angular size and the linear size look larger. They can be more specific if they realize that there are the two different "size" experiences.
This outcome may be the most popular one.

Those three outcomes are described in much more detail in Section I using side-view diagrams.

Now compare, again, the new theory with the apparent distance theory.

A Quick Comparison Of The Two Theories:
The illustration compares the present new description with the apparent distance theory.
The stack of circles on the left illustrates the new description: The angular size of the moon appears to decrease as the moon rises toward the zenith.

The stack of equal-sized discs on the right illustrates the old description by the apparent distance theory. As the moon rises, its angular size appears to remain constant, and the basic illusion is that it appears to come closer as it approaches the zenith, so the horizon moon will look farther away than the zenith moon, hence look a larger linear size.

If that "old" sequence of circles imitates your own moon illusion, then you are among the few whose experience can be described by the apparent distance theory.

Because the conventional theory does not describe most peoples' moon illusion, it is fair to ask why so many readers and authors have not noticed that it fails to describe their own moon illusion.

I am convinced that a major source of the problem is that virtually all articles that present the apparent distance theory do not use appropriate front views. Instead, they offer only a side-view diagram that can easily trick readers into thinking the side-view is describing their own moon illusion, but it doesn't.

The Misinterpretation Problem.
A terribly misleading side-view is the very popular sky dome diagram, which fails to describe or explain most peoples' moon illusion.

The Sky Dome 'Explanation'.  
Diagram A illustrates the sky dome idea so often used in presentations of the apparent distance theory.
For this side-view we are looking north at a person at point O who is facing east (to the right) to see the horizon moon indicated by circle H. The moon rises into various zenith positions shown by the large Z circles all at the same radial distance from point O.
According to an ancient idea the sky looks like the ceiling of a flattened dome, with the zenith sky looking closer than the horizon sky. The moon supposedly appears to sit upon that illusory sky surface and glide along it as it rises. So, the moon appears to take up the positions shown by the smaller, z circles drawn along the imaginary dome, so, for the person at point O. the z moon appears to come closer.
Because that distance illusion has the 'H moon' looking farther away than a 'z moon' the horizon moon necessarily must look a larger linear size than a zenith moon in order to keep their angular sizes looking equal.

Notice that all the angles are drawn equal, which specifies that, for the person at point O, all the perceived zenith moons look the same angular size as the perceived horizon moon.
For us to experience what that person is seeing, we must look, instead, at the front view at the left: Here we are looking east to see a string of rising 'moons' that all look the same angular size.
Well, if that front view happens to imitate your own moon illusion, then you are among the few for whom the apparent distance theory and sky dome idea might apply.
Obviously, the sky dome diagram fails to describe most peoples' moon illusion. So why is it so popular?

The big problem here is that for us readers the H circle in the diagram obviously looks angularly larger than each z circle. And, that happens to imitate a front view of most peoples' moon illusion. But that is not at all what the diagram is meant to show. Instead, the diagram is meant to show, as a side-view, that the observer at point O sees all those moons as having the same angular size. That is, what the person at point O is seeing is not shown to us by using unequal circles.
Yet, because those unequal-looking circles imitate most reader's moon illusion, that perception "rings true," so a reader could mistakenly think Diagram A is describing his or her own moon illusion, but it doesn't.

Don't let the sky dome illustration trick you into thinking it describes and explains your own moon illusion or the majority moon illusion.
Nowhere else have I seen a sky dome diagram accompanied by an appropriate front view like the one above.

Some other very misleading diagrams are critiqued in Section II.

Side-views for the new descriptions are presented in Section I.

Why Is The New Theory "New"?
In the long history of speculation about the moon illusion, the present description and the explanation for it are very recent developments. That happens because, first of all, this theory applies the relatively new general theory of the perception of linear size, distance, and the visual angle (McCready, 1965, 1985). This new general theory wholly replaces the most commonly used old rule known as the "size-distance invariance hypothesis" (discussed in Section II).

Theorists who accept this 'new' general theory include, Baird, Wagner, & Fuld, (1990), Enright (1989), Komodo & Ono, (1974), Gogel & Eby, (1994), Higashiyama, (1992), Higashiyama & Shimono (1994), Ono, (1970), and Reed, (1989. That is, although this present article focuses upon the moon illusion, the arguments go far beyond that illusion: They need to be taken into consideration in all discussions of visual perception of spatial relationships.

The present theory also is 'new' because its formulation has depended upon information about oculomotor micropsia published only since 1965: Likewise, it has depended upon having moon illusion research data published since about 1975 (Enright, 1975 to 1989; Iavecchia, et al, 1983; Roscoe, 1979 to 1989).

In 2002, Ross and Plug published their excellent book, "The Mystery of the Moon Illusion." It currently is the most complete source of information about the illusion. On page 195 they state: "The moon illusion is one of the few perceptual phenomena that tap a broad spectrum of sciences: astronomy, optics, physics, physiology, psychology, and philosophy. Its explanation illustrates the history of scientific explanation, and in particular the history of perceptual psychology."

Ross and Plug review the incredibly long history of speculation about the illusion, and examine in detail the published experimental research data that any theory must explain. They strongly support the idea that the moon illusion begins as an angular size illusion.

They evaluate current theories including the present "new" theory (McCready, 1965, 1985, 1986) even citing this present web article (as it was in 2001).

They also conclude, of course, that, "No single theory has emerged victorious." (p. 188).

Four Other "New" Explanations for the Moon Illusion.
Four other relatively new explanations also treat the majority moon illusion as an angular size illusion.
1. Hershenson (1982, 1989) offered a theory which appeals to a perceptual process he calls the "loom-zoom system."
2. Reed (1984, 1989) appealed to a perceptual experience he calls "terrestrial passage."
I won't try to review those two theories. They are reviewed in Ross & Plug (2002).

3. Baird, Wagner, & Fuld (1990) have offered a 'simple explanation' of the moon illusion. They have revived the "size"-contrast explanation advocated by Restle (1970), and clearly stated it in terms of the present "new" general theory. That theory is critiqued in Section II.

4. Enright (1989) has proposed that the moon illusion certainly illustrates oculomotor micropsia/macropsia: His many experiments have left little doubt about that.
The explanation he proposes for oculomotor micropsia (Enright, 1989) is similar to the perceptual adaptation explanation I have offered, but differs in some details (see Section IV).

5. Roscoe (1984, 1985, 1989) and his colleagues (Acosta, 2003, Iavecchia, et al 1983) have conducted many experiments which clearly show that the moon illusion illustrates oculomotor micropsia.
Roscoe's many publications (see Roscoe, 1979, 1989) have emphasized the largely overlooked role that oculomotor micropsia can play in some airplane crashes when, to land the airplane during bad weather, the pilot depends upon a "heads up" viewing device that shows an image of the airport's landing strip. Briefly stated, this nearby screen induces oculomotor micropsia, so the pilot "sees" the airport runway as too far away, and may land ("crash") beyond the runway (and some have).
A similar condition with the eyes unwittingly adjusting to a near distance exists for a person driving with a wet windshield, especially at night, or driving in a fog. The resulting oculomotor micropsia can make objects in the road ahead look too far away, so the driver will overestimate the safe braking distance, and may discover, too late, that an object was much closer than it appeared.
In other words, trying to understand the causes of the 'moon illusion' is more than just an idle pursuit.


Index page.
Introduction and Summary.
Section I. New Description of the Moon Illusion
Section II. Conventional Versus New Descriptions
Section III. Explaining the Moon Illusion
Section IV. Explaining Oculomotor Micropsia
Bibliography and McCready VITA
Appendix A. The (New) Theory

Appendix B. Analysis of the Murray, Boyaci & Kersten (2006) Experiment