Moon illusion

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The Moon illusion is a visual illusion (optical illusion) in which the Moon appears larger near the horizon than it does while higher up in the sky. This visual illusion also occurs with the Sun and star constellations. Indeed, this apparent magnification also occurs for very remote terrestrial objects seen at or near the apparent horizon (Higashiama, 1992, Higashiyama & Shimono, 1994.)

Proof that the effect is an illusion

The illusion has been studied for centuries with many explanations proposed. Two decades ago, twenty-six vision researchers contributed chapters to, "The Moon Illusion," edited by Hershenson (1989) which presents several theories, old and new. It includes an extensive historical review by Plug & Ross (1989) and no theory was fully accepted.

In the later very comprehensive book, "The Mystery of the Moon Illusion," Ross and Plug (2002) again concluded, "No single theory has emerged victorious" (p. 180).

This present article describes the few theories that researchers are seriously considering.

Some ancient misconceptions still persist; a popular one is that the horizon moon appears larger as a result of some kind of magnification effect caused by the Earth's atmosphere. But astronomers have known for more than 900 years that the azimuth angle the rising horizon moon's diameter subtends at an earthly position is the same from moonrise to moonset. When directly measured with a theodolite it equals 0.52 degree.

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 is 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. However, though this effect may hold during a single transit of the full moon across the sky, when comparing different full moons over a period of time it is overwhelmed by the changes in the Moon's angular diameter from 33.5 arc minutes at perigee to 29.43 arc minutes at apogee — a difference of over 10%.[1]

Therefore, photographs of the moon at all elevations on a given night are the same size if taken with the same camera settings. For instance, the sketch in Figure 1 imitates a double exposure photograph with the moon at the horizon and then at a higher elevation, commonly called the zenith moon. Vision researchers call the angle an object subtends at an observer's eye the visual angle, V degrees, so for the moon V = 0.52 degree . It also can be calculated from, V = tan S/D, where S is the linear size (metric size, physical size) of the moon's diameter, 2160 miles, and D is its physical distance from the eye, which averages about 238,000 miles. Thus, tan V = 0.009.

Actually, V deg for the vertical diameter of the just rising moon is slightly smaller than 0.52 deg because the atmosphere here acts like a weak prism. So the horizon moon (and setting sun) photograph, and appear, a bit ovoid.

An easy demonstration of that constant visual angle is to hold up a small object near the apparently enlarged horizon moon at the distance that makes them look the same angular size. For instance, a 4 mm wide object held 40 cm from the eye. When the moon is higher in the sky, hold the object at that same distance and notice that the moon still subtends that same angular 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 (Washburn, 1894).

Vision scientists also now know that the optical image of the moon on the retina remains a constant diameter (about 0.15 mm). The illusion is entirely a subjective illusion, so nearly all the representative publications in the Reference Section are by psychologists specialized in visual perception (see experimental psychology.)

An explanation of the moon illusion must take into account that people differ widely in what they experience when they compare the sizes and distances of the horizon moon and zenith moon, so a single description of the illusion will not fit all observers. The versions most often studied are described here.

Describing The Illusion

Many experimenters have measured the illusion. The horizon moon has been reported to look as much as twice as wide as the zenith moon, but average magnitudes are about 1.3 to 1.7.

The phrase "looks larger," however, is ambiguous; it must specify whether it refers to the perceived visual angle, V' degrees (perceived angular size) or to the perceived linear size, S' meters, or to both of those qualitatively different size experiences (Joynson, 1949, McCready, 1965, 1985, 1986) . Unfortunately, the commonly used simple terms "perceived size" and "apparent size" have created much confusion because they sometimes referred to V' deg and sometimes to S' meters. Two Categories: Moon illusion theories fall into two categories, VSD illusions and SD-illusions, depending upon what the report, "looks larger" refers to.

VSD-illusions include a visual angle illusion (V-illusion). A relative VSD-illusion begins with the horizon moon looking a larger angular size than the zenith moon. As a logical consequence, either the linear sizes also look unequal (an S-illusion ) or the distances look unequal (a D-illusion) or else all three illusions occur. "Looks larger" refers primarily to V' deg , and in some outcomes also refers to S' m.

Publications that describe many classic "size" illusions as VSD-illusions, and explicitly or implicitly treat the moon illusion as a VSD-illusion, are in Reference List A.

SD-illusions, on the other hand, do not include a visual angle illusion. The horizon moon looks the same angular size as the zenith moon, but it looks farther away (a D-illusion) so it must look a larger linear size (an S-illusion). "Looks larger" refers only to S' m. The publications in Reference List B describe and explain classic "size" illusions, including the moon illusion, only as SD-illusions. They overlook the idea that a person can experience a V-illusion.

However, according to publications in List A, the moon illusion for nearly all people (perhaps 90%) is a VSD-illusion, and only a few people (perhaps 5%) suffer the SD-illusion.

The illustrations below may allow readers to identify their own moon illusion.

VSD -Illusions in Brief.

To explicitly state that "looks larger" refers primarily to the moon's visual angle, is a relatively recent development (McCready, 1965, 1985, 1986, Plug & Ross, 1989, p.22, Enright 1989b, Hershenson, 1982, 1989b, Reed, 1989, Roscoe, 1989.) This "new" claim was reasserted by Ross & Plug (2002) who cited those articles and others in List A below, including one website (McCready, 2001).

The sketch in Figure 2 imitates how the V-illusion looks if the perceived visual angle, V' deg, is 1.5 times larger for the horizon moon than for the zenith moon, an average value.

Articles in list A also point out that this V-illusion logically must be accompanied either by an S-illusion or by a D-illusion or else all three illusions occur together.

For instance the "size and distance" report most often given by observers in experiments and in surveys has been that the horizon moon "looks larger and closer " than the zenith moon (Boring, 1962, Hershenson, 1982, McCready, 1965, 1986, Restle, 1970). That outcome is easy to imagine while looking at Figure 2.

The incomplete report, "looks larger and closer" often means that the visual angle looks larger, and the linear sizes look the same (no S-illusion) so the horizon moon looks closer (the D-illusion) because it looks a larger angular size. Here the reason the horizon moon and zenith moon look the same linear size (a perceptual result known as linear size constancy) is because, in agreement with common knowledge, they appear to be the same moon, a cognitive condition known as identity constancy. Those equal appearing linear sizes thus establish the basis for that powerful distance cue (depth cue) properly called the relative visual angle cue to distance. A second popular incomplete report is that the horizon moon "looks larger and about the same distance away" as the zenith moon (also easy to imagine while looking at Figure 2). Here, in agreement with common knowledge, both moons appear the same distance away, so, because the horizon moon looks angularly larger than the zenith moon, it necessarily looks a large linear size. They don't appear to be the same moon. The report "looks larger"now refers both to V' deg and to S' meters .

In a third popular outcome, the abbreviated report, "looks larger and closer" covers all three illusions occurring at the same time: The horizon moon looks a larger angular size, a larger linear size, and closer.

The Explanatory Problem.

The major task has been to explain the basic V-illusion that nearly all people experience. A great step toward that end has been the common experimental finding that the factor most responsible for changing V' deg for a target of constant V deg is a change in the efficacy of indicators of the target's distance, mostly the pattern of cues to distance. As a rule, when distance cues for a target of constant V deg change in a manner that would indicate a large increase (decrease) in its perceived distance, the perceived visual angle for it slightly increases (decreases), whether or not its perceived distance changes in the manner specified by those cue changes that induced the V-illusion. A V-illusion tied to changes in distance cue patterns is also the most puzzling component of other classic illusions, including the Ponzo illusion, the Mueller-Lyer Illusion, the Ebbinghaus illusion (Titchner's Circles) and the Hering illusion. The largest such V-illusion evidently is convergence micropsia a form of oculomotor micropsia/macropsia (McCready, 1963, 1965, 1994a, Ono, 1970, Komoda, & Ono, 1974). These V-illusions are the ones for which "no theory has emerged victorious." However, two theories have received the most attention in List A articles, a "relative size" theory and an oculomotor micropsia/macropsia theory, discussed later. On the other hand, there is no mystery surrounding the minority SD-illusion. The accepted explanation for it is the well-known, apparent distance theory, discussed next.

SD-ILLUSION. Figure 3

For some people the horizon moon looks the same angular size as the zenith moon but looks a larger linear size and farther away than the zenith moon.

The apparent distance theory proposes that some indicators of perceived distance for the horizon moon make it look farther away than the zenith moon, so it must look a larger linear size in order subtend the same visual angle as the zenith moon. That theory is emphasized in the publications in List B, which present different reasons why the horizon moon will look farther away.

However, at least since 1962 it has been pointed out that very few observers say, "it looks larger and farther away" (Boring, 1962). The apparent distance theory can explain that minority SD-illusion, but cannot explain why, as noted earlier, the most popular reports are, "it looks larger and closer" and "it looks larger and the same distance away."

It is important to understand the logic (geometry) being used to describe how an observer's three perceptual experiences, V' deg, S' meters, and D' meters relate to each other. The following description of an SD -illusion for the moon uses Figure 3 to clarify that logic. Its application to VSD-illusions is described later.

An SD-illusion.

Figure 3 describes a relative SD-illusion by using a side view as well as a front view that can create a pictorial illusion. The front view in Figure 3 may appear to be a picture of a terrain with rows of clipped corn stalks receding toward a distant horizon, and two distant trees. This pictorial "3D" illusion is created by the monocular cues to distance, especially linear perspective, texture gradients, and the relative angular size cue.

For an SD-illusion example unrelated to the moon, one can imagine that the lower disc portrays a huge spherical balloon, 40 ft in diameter, nestled directly above two, 25-foot tall trees that are 100 yards away, and 40 feet apart. And, the upper disc portrays a 4 foot diameter balloon floating over the nearby terrain, only 10 yards away. So, compared with the upper sphere, the lower sphere looks the same angular size, looks 10 times farther away and 10 times the linear size, to illustrate an SD-illusion of magnitude 10.

When those disks represent the moon, we are looking eastward, and the "horizon moon" and "zenith moon" look the same angular size. They both look extremely far away . For an average SD-illusion of magnitude 1.5, the horizon moon looks 1.5 times farther away than zenith moon, and 1.5 times the linear size. It may be hard to imagine that outcome by looking at that front view, so consider the side view. The side-view illustrates an SD-illusion of magnitude 1.5 being experienced by an observer at point O. We now are looking northward toward that person who is facing east (way off to our far right).

The lowest semi-circle represents that person's experience of the full horizon moon. It must be drawn as a semi-circle because the observer obviously doesn't see the moon's far side.

The upper semi-circles represent possible perceived zenith moons at the same perceived elevation angle. In the front view the upper disk thus represents both of those "zenith moons."

All three "moons" have the same perceived visual angle, V', arbitrarily specified as 1.0 angular unit.

Understanding The Perceived Visual Angle.

The proposal that people have the visual angle experience, V' deg, (McCready 1963, 1965, Rock & McDermott, 1964, Baird, 1970)) is accepted in the publications in list A but not accepted in the publications in List B. To consider how it is defined, keep in mind that an angle is the difference between two directions from a given point (the apex). So the perceived visual angle, V' deg is simply the difference between two perceived directions from oneself. [The place from which one feels one is viewing the world is the visual egocenter.]

For instance, in the side view, the arrow from O through the horizon moon's lowest edge indicates a perceived direction, d_o, which the person at O might call, "due east" and also "an elevation of zero degrees." For the upper edge, the perceived direction, d_u, is both "due east" and "an elevation greater than d_o."

The difference between those two subjective visual directions is the perceived visual angle for the moon's diameter. That is, V' = (d_u - d_o) deg. In the front view the center of the horizon moon " looks due east" (an azimuth of 90°), while the left limb " looks slightly northeast" and the right limb "looks slightly southeast".

Here one's perceived visual angle experience, V' deg, specifies the amount by which one should rotate one's eye to look from that left edge to the right edge. (See eye tracking, eye movement). V' deg also predicts the angle through which one should rotate one's head in order to aim one's nose from one edge to the other, so that the eyes and ears are squarely positioned toward the other edge in order to pay more attention to it (See orienting response). V' also predicts the angle through which one would point one's finger or arm from one edge to the other. Accordingly, in order to measure V', researchers have used, for example, eye rotations (Yarbus, 1967) and pointing gestures (Komodo & Ono, 1974). For the moon, such rotations are too small to be measured reliably, and no values of V' deg have been published for it. In other words, whether V' is equal to, larger or smaller than 0.52 deg for the moon in any of its positions remains unknown.

The Perceived Metric Values.

The perceived linear size, S', for the "horizon moon" in the side view is arbitrarily specified as 30 units. For instance, the person at point O might say the horizon moon's diameter appears about 30 yards, or 30 meters, or 30 stories tall. Of course, it looks much smaller than 2160 miles; there always is an absolute S-illusion . Ross & Plug (2002) offer many examples of the huge range of linear sizes that people have reported. The distance of each semi-circle from point O scales the perceived distance , D' m, of that apparent moon. The moon obviously looks closer than 238,000 miles so there always is an absolute D-illusion. For instance, Hershenson (1989) noted that many people say the horizon moon appears just beyond the most distant terrestrial objects.

Of course, the term "moon illusion" refers, instead, to the relative illusions that have been measured.

Relative SD-illusion Outcomes.

It should be mentioned that some people, a very few, say they have no relative moon illusion. This rare experience is represented in Figure 3 by the "zenith moon" of perceived linear size , S' = 30, drawn at the same radial distance from point O as the "horizon moon." A relative SD-illusion of magnitude 1.5 is represented by the "zenith moon" with S' = 20. The person at O says, that, compared with the zenith moon, the horizon moon looks the same angular size, but 1.5 times farther away and 1.5 times the linear size. They don't appear to be the same moon.

Perceptual Logic

The relationship of the three perceptual magnitude illustrated in Figure 3 is stated by the equation, S'/D' = tanV' . This equation (McCready, 1965, 1985, 1986), states the logic (geometry) used in the articles in List A, especially by Enright (1975, 1987b, 1989a, 1989b), Hershenson (1982, 1989), Komodo & Ono (1974), Ono (1970), Plug & Ross (1989), Reed (1984, 1989), and Roscoe (1984, 1989). Ross & Plug (2002, page 31) named it the "perceptual size-distance invariance hypothesis."

A very much different logic is used in the publications in List B, in textbooks and in the popular media. It is called the "size distance invariance hypothesis" (SDIH). It is stated by the equation, S'/D = tanV, which omits the perceived visual angle concept, V' deg. Accordingly, the side view diagrams used in List B articles resemble Figure 3 except that the equal angles are defined not as V' deg, but as the physical visual angle, V deg. These popular side views overlook the fact that people have the perceived visual angle experience. That is, they overlook the fact that one sees the different directions of two viewed points from oneself.

Explaining SD-illusions; The Apparent Distance Theory .

The two "zenith moons" in the side view illustrate the apparent distance theory. Namely, if the perceived visual angle, V' deg, remains constant for a viewed object, then S' m must become greater if D' m becomes greater. This rule is known as Emmert's law. Accordingly, for an SD-illusion, the reason S' m becomes greater is because D' becomes greater. The two best-known surviving explanations for why the horizon moon will look farther away than the zenith moon are the idea of a sky illusion, and a change in the pattern of cues to distance.

Two proposed sky illusions.

The oldest sky illusion, which Plug & Ross (1989, 2002) attribute to the 11th century astronomer, Ibn al-Haytham (known to us Alhazen) is that the sky appears to be a flat surface, like an illusory ceiling, along which the rising moon appears to glide, becoming closer to us, and because it remains the same angular size, its linear size appears to get smaller.

The other very old idea is that the sky surface looks not flat but like the inside of a flattened dome, along which the moon appears to move. A classic "sky dome" diagram has been the side view most often used in popular discussion of the moon illusion.

Explanations based upon these hypothetical sky illusions became controversial. Indeed, recent experiments by Baird & Wagner (1982) confirmed earlier criticisms that the supposed flat sky or sky dome illusions are not common experiences. A better explanation appeals to the role of cues to distance.

The Demonstrated Role of Distance Cues.

In extensive experiments, Kaufman & Rock (1962a, 1962b, 1962c, Rock & Kaufman, 1962a, 1962b) measured the moon illusion under many different viewing conditions. They found that the most effective way to change the "perceived size" of the moon is to change the pattern of distance cues in its vista (See Depth perception, linear perspective, Texture gradient.) They pointed out that it was not necessary to appeal to a flattened sky dome illusion.

For example, they found that the horizon moon will look smaller when cues to a great distance are subtracted from its vista, and the zenith moon will look larger if cues to a great distance are artificially added near it. Many other experiments described in the articles in both List B and List A have revealed this great contribution of changes in distance cues to the moon illusion (and to other classic "size" illusions).

The apparent distance theory recently has been strongly advocated by Kaufman (Kaufman & Rock, 1989, Kaufman & Kaufman, 2000. Kaufman, et al, 200x). The apparent distance theory and the SDIH also provide the logic used in all the descriptions of perceptual outcomes called "size-constancy scaling," "misapplied size-constancy scaling" and "retinal size scaling" (Gregory, 1963, 1965a, 1965b, 1970, 1998, Trehub, 1991).

A Side View Problem.

The most popular "side views " of the moon illusion, such as the famous "sky dome" picture, easily can mislead readers. The problem is that hasty readers may think those side-views illustrate their own VSD-illusion, rather than just an SD-illusion. This mistake can occur because those side views use full circles, and the circle for the "horizon moon" correctly looks angularly larger than the smaller "zenith moon"circle, and that imitates the visual angle illusion that most readers experience; the diagram seems to "ring true." But an uncritical reader may overlook that the circles drawn at different distances from point O must have different angular sizes in order to subtend the same angle at point O and thereby illustrate that the observer at O sees the moon as having the same angular size at all locations. These diagrams certainly are not designed to illustrate the V-illusion that most readers suffer. This possible misreading of side views may explain why those diagrams still survive, in spite of the fact that they fail to explain the most common moon illusions.

Vision researchers who offer those side-views to describe the moon illusion only as an SD-illusion, would not be misled by those diagrams, so they evidently do not experience the V-illusion that most people experience. Accordingly, they might find it difficult to accept the descriptions in the publications in List A. A side view that describes moon illusions as VSD-illusions appears below. Such side-views have been published in very few places (Hershenson, 1982, 1989, McCready, 1986, 1999-2007; Reed, 1989, Ross & Plug, 2002).

THE MAJORITY VSD-ILLUSIONS Figure 4.

In the front view of Figure 4, the lower disk's optical image on the retina is 1.5 times wider than upper disk's retinal image. So both the visual angle, V deg, and the perceived visual angle, V', for the pictured "horizon moon" are 1.5 times those for the portrayed "zenith moon." The pictorial illusion thus imitates a VSD-illusion of magnitude 1.5 for the moon. Keep in mind that the majority moon illusions are as if the retinal image were larger for the horizon moon than for the zenith moon.

The VSD-illusion Side view. The logic illustrated in the side view is stated, again, by the equation, S'/D' = Tan V'.

The "horizon moon" is arbitrarily assigned a perceived visual angle value of 1.5 units. For the "zenith moons," V' is 1.0, and all four have the same perceived elevation angle. So, in the front view the upper disk represents all four perceived zenith moons. For every outcome the person at O says "the horizon moon looks 1.5 times angularly larger than the zenith moon."

The horizon moon's perceived linear size, S', arbitrarily is 30 linear units. The "zenith moons" perceived linear sizes are 15, 20, 25, and 30 units . The distance of each semi-circle from point O represents (to scale) the perceived distance , D' m, of that apparent moon.

Four possible outcomes of the illustrated VSD-illusion

1. The Same Distance Outcome is represented by "zenith moon," 20. The horizon moon and zenith moon appear the same radial distance away so the horizon moon's linear size necessarily looks larger than the zenith moon's by the same proportion that its angular size looks larger. They don't appear to be the same moon. A report "looks larger" refers both to V' deg and to S' meters . Here the "same distance" percept may be due to the observer's knowledge about the moon, or due to an "equidistance tendency" (Gogel, 1965, McCready, 1965). 2. The Same Linear Size Outcome is represented by "zenith moon" 30. The horizon moon and zenith moon look the same linear size, so in order to have the perceived visual angle of 1.0 unit, the zenith moon looks 1.5 times farther from point O than the horizon moon. This "equal linear size" percept illustrates linear size constancy. It might result simply from the knowledge that the two moons are the same moon (identity constancy). The popular report that the horizon moon "looks larger and closer" fits this linear size constancy outcome, and the observer doesn't mention that they appear to be the same moon. This linear size constancy outcome also illustrates the powerful distance cue of relative perceived visual angle. That is, the horizon moon looks closer because V' deg has "zoomed" while S' m remains constant (so the moon "loomed up.").

An apparent initial retreat. In this linear size constancy outcome, the just rising moon logically will at first appear to move farther away, retreating to the east before it appears to move further up. Hershenson (1982) noted that this particular distance illusion sometimes occurs in reverse for the setting sun, which appears to approach just before it finally sets. 3. An intermediate outcome is represented by "zenith moon" 25. Indeed all semi-circles that can be drawn between the ones labeled 20 and 30 will illustrate intermediate outcomes. All three relative illusions occur: The observer's complete report is that, compared with the zenith moon, "the horizon moon looks angularly larger, linearly larger and closer." The common abbreviated report "looks larger and closer" thus fits all intermediate outcomes and the linear size-constancy outcome. Vertical Ascent. To the observer at O, "zenith moon" 25 appears almost directly above the 'horizon moon'. A characteristic of most intermediate outcomes is that the rising moon appears to rise almost straight up for a while before it appears to begin its trip overhead toward the zenith.

Most readers should find their own moon illusion described as a VSD-illusion. Much more detailed diagrams like Figure 4 have been published in Plug & Ross (2002, Figure 10.8), and in McCready (1986, 1999-2007).

Cue Conflicts

Notice that in all three outcomes above, the distance cues that signal a greater distance for the horizon moon do not make it look farther away. Those cues are responsible for increasing V' deg, but this increase in V' then acts as the powerful, monocular cue to a shorter distance which dominates the final percept in the linear size constancy and intermediate outcomes. On the other hand is the same distance outcome which can result from the "equidistance tendency" that overrules the "greater distance" cues as well as the "looks closer" cue of the larger perceived angular size. Of course, some observers report that the horizon moon "looks larger and farther away" than the zenith moon. This abbreviated report obviously can describe the minority SD-illusion (Figure 3) which does not include a V-illusion. But it also may describe a fourth possible VSD-illusion outcome, as follows. 4. A "greater distance" outcome is represented in Figure 4 by "zenith moon" 15. Here the horizon moon looks 1.5 times angularly larger than the zenith moon and, in some agreement with the distance cues that induce that V-illusion, the horizon moon looks 1.33 times farther away than the zenith moon, where it looks twice the linear size of the zenith moon. For such outcomes the complete report would be "it looks farther away, looks angularly larger, and looks a larger linear size."

Physiological Correlates of V-illusions.

Physical (neurological) evidence for a visual angle illusion was obtained for the first time in some recent experiments by Murray, Boyaci & Kersten (2006 ). They related their findings to the moon illusion.

The abstract of their article is, "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 {see retinotopy ] 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."

Their observers viewed a flat, photo-montage with two disks of the same angular size (V = 6.5 deg) in a pattern that creates a pictorial illusion in which the disks may portray two spheres on the floor of a hallway. The crude sketch at the right imitates the picture they used.

In their more realistic picture, the "far sphere" looks about five times farther away, thus five times the linear diameter of the "near" one. But this SD-illusion of magnitude 5.0 is not interesting. The interesting illusion was, instead, the VSD-illusion in which the "far" sphere also looked about 15% to 20% angularly larger than the "near" sphere, so it looked, say, about 5.17 times the linear size. This VSD-illusion thus imitates a greater-distance outcome for the moon illusion, but upside down. More importantly, the illusion makes the upper disk on the screen look, on average, both 17% angularly larger, and 17 % linearly larger than the lower disk,. This "same distance" outcome of the VSD-illusion was the illusion they measured directly. It is analagous to the "same distance" outcome for the moon illusion.

Results Unpredicted? The authors noted that virtually all current theories about the brain activities involved in "size" perception would not have predicted those results, [Most of those theories conform to the conventional SDIH logic and describe only SD-illusions.] However, some publications in List A stated long ago that a relative V- illusion for two targets that subtend the same visual angle, is as if the retinal image of one were larger than the equal retinal image of the other. So, it is as if the activity pattern in area V1 were larger for the one target than for the other. That is what Murray et al, discovered. It now is fair to say that the extent of the neural activity pattern in cirtical area V1, is a physiological precursor of the subjective magnitude, V' deg.

Inappropriate Explanation. The Murray et al, results would not be obtained for an SD-illusion. But, in order to extrapolate their findings to the moon illusion, the authors cited publications that describe it only as an SD-illusion. Moreover, the explanations offered in the discussion section use only the SDIH logic, referring to Emmert’s law, the apparent distance theory, “misapplied size-constancy scaling,” and a so-called, “scaling of retinal size.” Again, those approaches do not use V' deg, so they cannot describe or explain the angular size illusion that the authors measured. A detailed meta-analysis, and quite different explanation of the Murray et al results appear as Appendix B in McCready (2007).

Explaining The Majority Moon Illusions.

As already noted, the observers in many experimenters compared the real moon with a surrogate moon, or compared two surrogate moons indoors as well as outdoors, and the "moon illusion" was found to be most strongly controlled by changes in monocular distance cues to the targets' distances.

Indeed, a small "moon illusion" even has been measured in flat pictures. (Coren & Aks, 1990, Enright, 1987a, 1987b). For instance in Fig 1 and Fig. 3, both V' deg and S' mm, may be slightly larger for the lower disk than for the upper disk.

Why changes in distance cues make V' change away from V deg has been the primary task addressed in articles in List A.

Reviewed below are the two explanations that have received the most attention, the "Relative Size" Theory and the Oculomotor Micropsia/Macropsia Theory. They are fully reviewed in Ross & Plug (2002) and in McCready (2007).

Two other theories reviewed by Ross & Plug (2002) have received less attention and are not discusssd here; the Loom-zoom Theory (Hershenson, 1982, 1989) and the Terrestrial Passage Theory (Reed, 1984, 1989, 1996).

The Relative Angular Size Theory

Historically, the best-known alternative to the "apparent distance theory" has been a "relative size theory" that is widely used to address the "size contrast effect" found in many well-known illusions. Of course, the terms "relative size" and "size contrast" are ambiguous. They can refer either to angular size or linear size.

For the moon illusion, Restle's (1970) "relative size" theory implicitly treated it not as a relative linear size illusion, but as a relative angular size illusion with the horizon moon looking angularly larger than the zenith moon. Recently, Baird, Wagner & Fuld (1990) explicitly proposed a relative visual angle theory of the moon illusion.

There are many kinds of visual angle contrast illusions. A simple example is the classic Ebbinghaus illusion shown at the right and arranged so that the lower central circle surrounded by small circles can represent the horizon moon which appears angularly larger than the upper central circle, that represents the zenith moon.

Restle (1970) and Baird, et al. (1990) began by suggesting that selected visual extents near the horizon moon typically subtend visual angles smaller than the moon's, ½ degree, while selected visual extents often in the region of the zenith moon, such as a large empty sky, subtend visual angles larger than ½ degree. Accordingly, two statements can be made: the horizon moon's ½ deg looks larger than the angles of it context extents, and the zenith moon's ½ deg looks smaller than the angles of its context extents.

Those two statements describe the proposed situation, but do not explain why those contrasts make V' larger for the horizon moon than for the zenith moon. After all, those statements remain true if both moons happen to correctly look the same angular size., or even if the horizon moon looks angularly smaller than the zenith moon. The visual angle contrast effect remained unexplained.

Various explanations of visual angle contrast effects have been published outside of the moon illusion literature and will not be reviewed here. No theory has been fully accepted. The connection between an angular size contrast effect and the demonstrated role of changes in distance cues is that, the small angular subtenses of extents in the horizon moon's vista (such as a fine texture gradient) can provide a relative angular size cue to a great distance, and the much larger angular extents in the zenith moon's vista can "cue" that it is closer. That connection is illustrated by the Ebbinghaus illusion as a pictorial illusion. For instance, the small context circles in the lower pattern can portray objects of the same linear size and twice as far away as the objects portrayed by the large context circles in the upper pattern. The mystery still is, why would the distance cues make the visual angle of the lower central circle look slightly larger than the equal visual angle of the upper central circle? That problem is addressed by the other "new" theory, below.

The Oculomotor Micropsia/Macropsia Theory

The theory proposes that the moon illusion is an example of oculomotor micropsia/macropsia (McCready, 1985, 1986, 1999-2007, Enright, 1989b, Roscoe, 1989, Acosta, 2004). Many studies of oculomotor micropsia have shown that an increase in convergence of the eyes makes V' deg decrease for a viewed target of constant V deg (for reviews see Komoda & Ono, 1974; McCready, 1965, Ono, 1970).

This illusion, also known as convergence micropsia, was first described by Charles Wheatstone (1852) who used the stereoscope he had invented. He noted in passing that the target did not appear to come closer, as demanded by the prevailing verision of the "apparent distance theory." That is, the overt muscular convergence of the eyes does not necessarily dictate a shorter perceived distance to the target. Indeed, further studies have revealed that the crucial factor controlling micropsia is, instead, the neural activity (motor efference) the eye muscle (oculomotor) system is prepared to send out to the eye muscles to adjust them to a closer distance, even if no overt adjustment occurs. This covert "efference readiness" (Festinger, Burnham, Ono, & Bamber, 1967) is not unlike an efference copy

For the moon illusion, it is proposed that the changes in distance cue patterns that would indicate a shorter perceived distance for the zenith moon signal an efference readiness that, if sent out, would converge the eyes to a closer distance than they would for the horizon moon, and that induces micropsia.

The converse illusion is oculomotor macropsia. When distance cue patterns "signal" an increased distance to the horizon moon, they would evoke an efference readiness that could diverge the eyes, and V' would increase. Moon illusion experiments by Enright (1987a, 1987b, 1989a, 1989b), by Roscoe (1979, 1984, 1985, 1989), and by Acosta (2004) clearly have shown that, when observers view the horizon moon (or moon surrogate), their eyes tend to adjust to a very great distance, actually slightly diverge, and their eyes converge to a shorter distance when the zenith moon (or a surrogate) is viewed. The resulting measures of micropsia/macropsia were as large as 30%, not quite as large as commonly found for natural viewing of the moon.

To propose that the moon illusion is an example of the more general illusion of oculomotor micropsia/macropsia is a step forward, but does not explain it. It becomes necessary to explain why oculomotor micropsia/macropsia occurs during normal everyday viewing whenever the eyes change the distance to which they are aimed.

Explaining oculomotor micropsia/macropsia

No explanation for oculomotor micropsia/macropsia has yet been widely accepted. It undoubtedly is the largest visual angle illusion. In general, published measures from many experiments on V-illusions reveal that the changes in V' deg away from V deg are relatively small and limited to target extents that don't subtend large angles in the field of view. For instance, even in oculomotor micropsia /macropsia, V' rarely becomes less than half of V deg or more than twice V deg for targets of small visual angles. Two recent theories propose that this ubiquitous V-illusion is a normal perceptual adaptation which improves the accuracy of an orienting response of the head and body (Enright, 1989, McCready. 1965, 1985, 1994b, 1999-2007). Specifically, V' deg visually guages the angle through which the head must rotate in an emergency shift of attention from one viewed point to another in a different direction, V deg away.

For nearby objects the angle of the required head turn must be less tnan V deg, because the head's rotation axes are several inches posterior to the eyes. The proposal is that V' deg thus becomes less than V deg (micropsia) in order to specify a more accurate turn of the head.

This idea yields a rationally derived simple equation for the amount by which V' deg would need to change away from V deg as a function of the distance to which the efference readiness would converge the eyes (McCready, 1965, 1985, 1994, 1999-2007). The simple equation has been shown to fit quite well the published results from experiments on several kinds of visual angle illusion, including the results of the 2006 experiment by Murray et al, (see McCready, 2007, Appendix B) .

But, for the moon illusion, the simple equation doesn't predict a relative illusion as large as 1.30.

As they say, further research is needed.

REFERENCES

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