The moon rises in the east and settles in the west, following a trajectory route very similar to that of figure 2a. However, during this trajectory the appearance of the moon observed larger on the horizon compared to when it is in its elevated position in the sky is known as the moon illusion for e.g. ( Kaufman et al 1962, 2000, 2006 Reed & Kuprinski 2009, Coren & Aks 1990, Weizman & Cohen 2003, Toskovich 2009, Nanavati 2009), see figure 1ab. This illusion is not only denoted to the moon, it can also be observed by other celestial constellations such as the sun and the stars (Ross and Plug, pg 1-2 2002) (Wade pg 377 2000). It has been found in some cases that the size of the horizon moon appeared almost 1-2 times the diameter of the elevated moon Kaufman and Rock (1962) Ross and Plug (1994). This experience persists even when one is familiar it is an illusion Weizman and Cohen (2003) and has been observed for many centuries, with Aristotle (384-322BC) making the first clear scientific account Ross and Plug, pg 1-2 (2002) Wade pg 377 (2000). However there have been many suggested theories from physics to physiology and now finally psychology as to why this illusion is experienced Wade pg377 (2000), but none has been accepted as the correct answer. The main conflicting issues involve contradictions as to whether it is a linear or angular illusion, thus a model which accounts for both linear and angular illusions providing a common unified explanation is required.
Elevated Moon/ Zenith moon
Figure 1a http://facstaff.uww.edu/mccreadd/ and 1b http://www.lhup.edu/~dsimanek/3d/loony.htm (Ken Amis) what the actual illusion looks like in its two comparative positions and an illustration of what the names horizon and elevated moons infer to within this text.
2. Facts regarding the moon and the illusion
This is regarded as an illusion because the increase in perception of size occurs even though the visual angle (V) subtended on the eye remains the same regardless of the trajectory position of the moon, i.e. whether the moon is on the horizon or in its elevated position-see figure 2 (For e.g. C.Reed and E. Kuprinski 2009, Kaufman et al 2000). Physically if the angular size changes then a subsequent change of the retinal image size would occur, but it remains constant and hence is regarded as a perceptual phenomenon. The value of this angle has long been accepted as a fairly constant value of 0.52 degrees regardless of elevation For e.g. (Bears, Conners and Paradiso, pg 288,3rd edition, 2006, R Casati, 2003, Ross and Plug, pg 11-14, 2002, Mccready section 1 website). Furthermore evidence can be found in photographs, where many photographers have experienced the illusion, however after photographs become developed the moon image appears small Nanavati (2009). For e.g. Ross and Plug pg60 (2002) took multiple photos of the sun during different periods of the day and found the size of the sun to be exactly the same during each interval at the different trajectories, similar to figure 2b. Since the camera can only illustrate the linear dimensions of an object this would further enforce the suggestion the illusion is in fact a perceptual phenomenon. Another demonstration involves a simple test called Hering’s manoeuvre, whereby a subject holds a coin close to their eye at arm’s length and observes the trajectory of the moon. The result of this will always be that the moon and the coin are the same size no matter what position of trajectory of the moon The Moon Illusion, a literature thesis by Bart Borghuis, (1999), Gregory (2007).
Figure 2a http://antwrp.gsfc.nasa.gov/apod/ap020130.html Credit and copyright to Shay Stephens. He picture shows the moonrise trajectory over Seattle, USA, with a snapshot taken every 2.5mins.
Figure 2 Taken from Mccready section 1 illustrating the size of the moon does not change with the trajectory and nor does the visual angle subtended.
The illusion maybe experienced in different areas of the world and the facts about the orbit of the moon around the earth can be used to explain as to why any variances in the earth-moon distance cannot play a role in the illusion. The moon travels in an orbit around the earth completing one full cycle every ~29days (1 month). The mean Earth-Moon distance is fairly constant throughout this period, however there is a degree of variance in the Earth-Moon distance caused by the elliptical shape of the orbit of travel (Nasa website). This variance causes the size of the visual angle of the horizon moon to become 2% smaller than the elevated moon and may only affect only short time viewing i.e. vieiwning the moon during separate hours in the same day Nanavati )2009), but not significant enough to cause the illusion (Mccready section 1). The distance of travel of the orbit has been monitored by NASA since the initial experimentation was carried out using retro-reflector beams/laser used in the Apollo 11 mission to the moon Faller et al (1969, 1970). The moon travels in an orbit of fairly constant mean distance of 384,000km (NASA website) from the earth and hence discounting the physical distance factor creating the illusion. The size (S) is
It has been well established the physical size, distance and visual angle do not change (or not by a significant factor), however Aristotle suggested there was a physical cause that created a real magnification on the image size Nanavati (2009). It was thought this was caused by the atmospheric refraction, which had its effects greatest on the light rays on the horizon causing an increase in the moon size The Moon Illusion, a literature thesis by Bart Borghuis (1999), Ross and Plug pg57 (2002) i.e. like a stone under water where it appears to enlarge in size. However this theory was later disregarded as there was no means of measuring the actual horizon enlargement and if any it was deemed neglible, however many writers and investigators supported the idea that it could possibly play some form of secondary role Ross and Plug pg57 (2002), Gregory (2007).
3. Linear distance illusions
3.1 Size distance invariance hypothesis and Emmerts law
The SDIH theory proposes the cause of the horizon moon appearing bigger is due to the extended terrain viewed in between the observer and the horizon moon, thus placing it at a perceptually further distance, for e.g. Kaufman (2000, 2006, 2007), Suzuki (2007), Gregory (2007). The SDIH assumes perceived angle (V’) like the objective angle (V) is unchanged Reed and Kuprinski (2009) and implies distance is computed primarily by the visual system, while size is later inferred from this. Due to these conditions where perceived angle (V’) is kept constant, only perceived distance (D’) and size (S’) can only change, thus suggesting a linear distance/size illusion and not an angular illusion Higashiyama (2004) Lou (2007). The SDIH can be illustrated by the formula S’/D’=tan V’ (apparent size S’, apparent distance D’ and the physical visual angle V’) Higashiyama (2006) Kaufman (2006), see figure 3. The SDIH implies the perceived size (S’) is directly proportional to perceived distance (D’) and this relationship can be explained using Emmerts law. The conditions of Emmert’s law are the perceived size of an object subtending a constant visual angle is directly proportional to its apparent distance Gregory (2007) Philip Servos (2006). Emmerts law in effect is the description of the size distance invariance hypothesis (SDIH) Jones et al (2009) and is one of the more researched theories within this topic.
Afterimages are often used as a means to display Emmerts law since they have a constant visual angle always subtended at any distance and therefore a fixed retinal image size at all times disregarding any changes in angular size Lou (2007). Due to this retinal image size being a constant size, means any increase in the afterimage size cannot be due to any angular illusions. Since Emmerts law states size is proportional to apparent distance, then afterimages can be classed as one means of evidence for the SDIH.
Figure 3 SDIH diagram taken from section 2 of http://facstaff.uww.edu/mccreadd/sectionII.html
Most investigations usually conform to similar methodologies involving a form of magnitude estimation i.e. size or distance, using a reference moon to a variable moon, for e.g. (Holway and Boring 1941, Kaufman 2000, Gordon M Redding 2002, Jones& Wilson 2009, Liang Lou 2007 etc).
Kaufman (2000) used artificial moons to display the SDIH as a description of the moon illusion. Subjects viewed these artificial moons of constant angular size against a natural sky in horizon and zenith positions. They compared the size and distance of a reference moon to a variable moon. And altered the size of the variable moon using a keypad to achieve a match, see figure 5. In the results the horizon moon was perceived 3.2 times bigger and 4.2 times further away than the zenith. They found as they increased the distance between the reference and variable moon, the moon perceived size increased. Conversely when the distance was reduced the perceived size decreased therefore implying distance determines perceived size. Due to the availability of visual cues, the horizon moon is perceived at a distance D’ further than that of the zenith, causing a subsequent increase in size S’ Higashiyama (2006), (2007). Figure 4 illustrates the principles behind the SDIH and apparent distance theory, where by the black circles in the inner band exemplify the moon straight above the observers head perceived as closer and hence smaller. The horizon moon in this model is perceived further away and hence bigger.
Condition 2-Inside band (black circles) showing proposed SDIH condition
Condition 1-Outside band (white circles) showing normal condition
Horizon moon Observer Elevated moon
Figure 4 (Annotated Figure 1 from Kaufman 2000) demonstrating the two conditions. Condition 1 the outer band of circles demonstrate how the moon should be perceived right from the horizon to its elevated state with no illusion. However condition 2 using this model of the illusion is represented in the second inner band of circles, suggesting the moon straight above the observers head is perceived as closer hence smaller and horizon bigger and further.
Figure 5 demonstrates the apparatus used in Kaufman 2000’s experiment. An IBM Think-Pad flat panel display specifically designed for this experiment was used. Virtual moons were produced as luminous disks against the natural sky. It was conducted on a hilltop on the C.W. Post campus of Long Island University in Brookville, NY. A total of four moons can be seen: one reference and one variable for both the horizon and elevated moon and subjects adjusted the variable moon using the computer accordingly.
Kaufman (2006) further investigated using noise signal detection and two alternative forced choices. Luminous discs of constant visual angles were used however viewed across a virtual terrain in this case containing distance cues. Two separate experiments were conducted on size and distance, which suggested a directly proportional relationship between the two as predicted by the SDIH. Figure 6 compares the log size (y axis) versus the log depth (x axis), inferred as distance and found the slope demonstrates a linear slope of ~1. Thus these results suggest as size increases so does distance, once again supporting the SDIH. The fact the perceived size increases as a directly proportional factor to the distance perceived, indicates that the moon illusion cannot be referred to as an angular account.
Figure 6 Kaufman 2006 shows the log perceived depth otherwise regarded as distance (x-axis) and log size (y-axis). A straight line is formed with a gradient of approximately 1, therefore suggesting size is proportional to distance as distance is to size.
Tozawa (2006) investigated the roles of motion parallax and perspective cues on size and distance perception and the results yielded were similar and supported the SDIH. Weizman and Cohen (2003) also investigated the SDIH via a matching task using 4 different groups of subjects varying in age. Results indicated 41-88% viewed the horizon moon to be of a greater size and as a consequence supporting the SDIH.
3.2 The paradox
The issue with the SDIH is it induces a paradox since many people do not experience the conditions it sets ;( the horizon moon appears both larger and further away) for e.g. (Higayshima 2006, Kaufman 2007, Kotaro Suzuki 2007, Kaufman 2006, Gregory 2007, Jones et al 2009). Instead (Mccready section 3) found up to 90% and Kaufman (2000) 9/10, view the larger horizon moon to be perceived as closer.
Size constancy is the visual systems ability to maintain the accurate perception of real size of an object regardless of the change in retinal images size Combe & Wexler (2009) Gregory (2007) i.e. when a person is walking away their physical dimensions do not appear to shrink, this relationship is maintained by size constancy regardless of the change in distance, which should create a smaller image size on the retina. One idea proposed as an answer is observers use the perceived distance to scale perceived size, as in SDIH. When enquired about distance, this scaled size and previous experience of sizes of objects from size constancy are used to determine distance. Hence due to this experience the observer makes a logical choice, thus in effect proposing there is a bias towards experiencing bigger objects to appear closer Kaufman (2000) (2007). However what is suggested in effect is there are two different routes taken to decipher size from distance and distance from size and without any direct evidence these ideas cannot be accepted as yet.
3.3 The apparent distance theory
The apparent distance theory states the perceived distance is not only determined by the retinal image size, but factors such as visual cues within the surrounding terrain play a controlling role in judgment, for e.g. (Gregory 2008), Suzuki (2007), Kaufman (2000).
There are many different types of visual cues from which the visual system can infer distance from and the amount of effect each cue has also varies. The terrain in one direction and its absence in the other play a vital role in the illusion Kaufman and Rock (1962). The role of cues plays an integral part in the SDIH, since the perceived distance determines the judged size and in effect can be described as SDIH since the findings directly support it. Pictorial representations of the illusion have been used as a methodology for investigation of depth cues, for e.g. (Coren and Aks 1990, Redding 2002, Jones et al 2009).The benefit of this being that any structural factors such as accommodation that may contribute towards the processing of size and distance are eliminated as cues and only visual cues i.e. terrain are left to investigate Redding (2002) Coren & Aks (1990). The apparent distance theory would predict the horizon moon appears bigger due to distance cues placing it at a further distance and the zenith moon as closer, hence smaller, just as in SDIH.
Jones and Wilson (2009) findings supported the apparent distance theory and demonstrate the level of effect of cues on the perceived distance. They used pictorial representations of of different salience as cues to depth, figure 7 displays the pictures used in increasing salience of each picture from A-D. Subjects viewed a reference moon placed on the horizon and zenith on the different scenes (figure 7 A-D) and compared this to a set of variable moon sizes on a computer, judging the match in size. A positive score (above 0) in the results from figure 8 indicated a perceived increase in size. Results show as the salience increases so does the perception of size for both moon trajectories, therefore these findings emphasize regardless of salience of cues, the mere presence of some form of cues effectively increase perceived size. However in all scenes the horizon moon is perceived bigger and significantly more so in the two scenes of high salience (figure 7 C and D). This infers proximity is a key factor and thus illustrates why the horizon moon is judged bigger, since it is in closer proximity to the terrain and the greater salience exaggerates this effect.
Figure 7 taken from Stephanie 2009 figure 1 illustrating the different pictorial representations used as devices for the different depths of cues. A) Drawing of lowest depth cue salience B) Drawing of intermediate depth cue salience C)Drawing of high depth cue salience- Town scene D) Drawing of high depth cue salience- City scene.
Figure 8 From Stephanie et al 2009 experiment number 1. The results were based on the size of error scores between the subjective responses of perceived size of the variable moon compared to the control moon size. Significant differences in size between the horizon moon and elevated moon indicated the degree of strength each cue played on that particular moon. The positive error score indicated an increase in perceived size and negative score a decrease.
Redding (2002) also supported that cues in the terrain are essential for size scaling to create the impression of a bigger horizon moon, as well as the proximity to the terrain. A pictorial representation of an upright and inverted gradient, with two moons positioned like figure. The upright gradient produces fine details very close together giving the impression of a receding distance like in the horizon. However the upright gradient was more spaced out mimicking the large expanses of space surrounding the zenith moon. The apparent distance theory would predict a reverse in the illusion if the visual scene was inverted i.e. the horizon moon would now look smaller than the zenith. The results show the mean illusion, where a positive score indicates the normal moon illusion occurred and negative the reverse. These results demonstrate the prediction was correct since the horizon moon size increased in the upright direction and reversed in the inverted.
Within virtual environments it has been found the size constancy mechanism is very strong when the object being viewed is surrounded by an environment, where comparisons can be made to decipher distance from, for e.g. (Kenyon et al 2007, Tanaka & Fujita 2007, murgia and sharkey 2009).
It has been suggested the elevated moon is perceived smaller due to the lack of surrounding visual cues for e.g. (Higashiyama 2006, Kaufman 2000, Jones et al2009). The proposed idea is the zenith moon due to no visual cues is placed at default distance related to the resting focus of approximately 1-2m regarded as empty space myopia, thus leading to its small perceived size (Da Silva 1989, Gogel & Mertz, 1989, Redding 2002, Gregory 2007, Suzuki 2007).
3.4 Sky dome illusions
The apparent shape of the sky was previously replicated in a drawing by King and Gruber (1962), where they made subjects project afterimages onto the sky in different directions (horizon 45. Zenith). Results had shown 81% of subjects viewed the moon bigger in the horizon sky than at 45. and 87% viewed horizon bigger than the zenith. Weizman and Cohen (2003) found the sky is perceived as an oblate profile i.e. like an inverted bowl with a flat top (see figure) and cues within this frame are used to judge the distance.
It has been proposed this flattened dome top causes the zenith moon to appear closer and thus smaller. This theory implies a mental map of the shape of the sky as an oblate- bowl shape, with the flat portion directly above the observers head. This flatter area causes the perception of a shorter distance to the sky just above the observers head and thus causes the zenith moon to be perceived as smaller. This is very similar to the SDIH approach which states the same fundamental reasons, but the SDIH suggests it’s the absence of visual cues that place the zenith moon at a closer distance and hence smaller, not a mental map model of the sky.
However Toskovich (2009) examined to test if the flattened sky caused the moon size to reduce and suggested otherwise. Subjects viewed the moon in the horizon, 45° and zenith positions using head movements and were positioned at 1m, 3m and 5m from the moon. They were instructed to determine distance and size estimates from these positions. Results had shown from 1m subjects perceived distance is the same in all directions thus indicating at close distances the visual system is able to interpret very accurately. However from 3m and 5m found the distances perceived to the zenith as larger than towards the horizon and no differences in size estimations at any direction. This is opposite to the flattened sky dome approach and proposes the sky is rather perceived as elongated towards the zenith and not flat. These findings suggest the illusion is affected by head position and location.
4. Visual angle illusions
To begin with Descartes, 1664 Wade 2000 pg (354-355) suggested associations with familiar objects, accommodation and convergence are all cues to distance. The apparent-distance theory is built upon the assumption the actual perceived visual angle is interpreted as the same as the physical linear visual angle Reed and Kuprinski (2009). However, alternative theories suggest the perceived visual angle may be affected by oculomotor processes unconsciously Mccready (2006) Keef and Kuprinski (2009) and size/distance then subsequently inferred from this.
4.1 The retinal representation of the moon illusion
If the illusion causes the perceived visual angle to change by becoming enlarged, then subsequently the perceived retinal image size should also increase. Murray et al (2006) found illusions such as the moon illusion affect retinal representation of the image size in the primary visual cortex (V1). Using functional magnetic resonance imaging (fMRI) and a 3d scene of a hallway with walls, an image had been produced containing information to apparent depth, see figure 9a for an illustration. Two 6.5 degree sized spheres were arranged like in figure 9a and the results showed the back sphere appeared to be 17% larger in angular size than the front sphere (even when of the same physical angular size). The results in figure 9a also illustrate the peak MRI signal responses were found higher at higher eccentricities for the perceptually larger back sphere than the front and the back sphere occupied a larger area in the V1 cortex. Thus implying the perceived bigger size of the back sphere created a bigger images size on the retina.
Furthermore these results were compared to the responses generated by two physically different sized spheres without any illusion (6.5° versus 8.125° and 4.875° versus 6.875° sized spheres, as shown in figure 9bc). The findings demonstrate the responses generated from two physically different sized spheres yielded a response very similar to 9a. Therefore indicating the illusion created an actual change in the retinal image size and a greater eccentricity was occupied by the back sphere as a result. Thus the depth illusion causes a change in the perceived angular size on the retina and hence providing evidence towards scaling processes affecting the representation on the retina (Murray et al 2006). Since only a change in the physical visual angle or perceived visual angle may cause this change in retinal image size.
Figure 9 taken from Murray et al 2006 displaying the hallway and the walls creating the illusion. the trial response graph shows the perceptual difference in angular size between the two objects. The top graph illustrates the fMRI activity for the perceived larger back object extending in eccentricity beyond that of the perceived smaller front object. The bottom row shows a similar response is triggered when two objects of physically different angular sizes are shown (with no hallway illusion placed). Therefore indicating the cause in the back object to be perceived more distant is due to an increase in angular size.
4.2 Accommodative micropsia
The visual terrain contribution to the moon illusion may be mediated by the state of the oculomotor system and not via the size-distance invariance mechanism, or size constancy scaling Suzuki (2007). The perceived distance may affect the accommodation response or the converse of this may also be true i.e. the level of accommodation may affect the perceived distance of a stimulus (Edgar 2007, Suzuki 2007, Lou 2007). The micropsia phenomenon causes objects to appear smaller than usual and macropsia bigger, whereby they can be induced by changes in accommodation/ Vergence leading to underestimation/ overestimation of its apparent size Howard & Rogers (2002).
When viewing the zenith moon there is no depth cues and the moon is isolated in an empty space. This causes the eyes to converge onto the single object of the zenith moon, thus increasing in convergence as it does. This increase in convergence induces increase in accommodation causing the decrease in angular size and is known as micropsia, for e.g. Howard & Rogers (2002) Mccready (2004) section 4, Lou (2007), Suzuki (2007). However when viewing the horizon moon in its natural settings, objects acting as depth cues in the terrain may cause the AC/V system to adjust from near to far distance thus increased divergence invoking an increase in angular size known as macropsia (Lou 2007, Mccready 2004 section 4, Tanaka & Fujita 2007, Suzuki 2007).
Lou (2007) used afterimages of dark circles viewed against a mobile white background on which this reference circle was projected on, see figure 10. These afterimages were projected from the various distances and subjects adjusted the variable stimulus on a computer screen when perceived a match with the reference. Results indicated subjects perceived afterimages to decrease in size at focal distances less than 1m i.e. distances at a closer range. Figure 11 displays the 30cm, 90cm and 200cm distances from where the afterimage was projected and regardless of these distances the same response of decrease in matched size. The focal distances affected the matched size and not the distance the afterimages were projected from, Lou (2007) suggested these findings are representation of accommodation micropsia.
Although oculomotor cues are used as cues to distance just as visual pictorial cues are used also, they are less effective up to distances >2m Kaufman (2000). Oculomotor cues and pictorial cues play a role in judging distance, however at longer distances pictorial cues play a greater role as determinants of distance Kaufman (2000), Coren and Aks (1990). become slightly near-sighted in relative darkness (night myopia) proof is just to show accomodtaion/convergence effort changes when viewing horizon and elevated moons
Figure 11 taken from figure 2b (Lou 2007). This figure demonstrates the 30cm, 90cm and 200cm distances from which the afterimages were viewed from and the perceived angular match to the control afterimage of size 4.25degrees. The straight angular line indicates the actual size of the afterimage (4.25 degrees). The perceived match of the angular size (y-axis) versus calculated focal distance (x-axis).
All about enright and roscoedifferent eye adjustement for horizon/zenith moon measured
In conclusion against oculomotor micropsia/macropsia, oculomotor cues are less effective in regards to objects being viewed at longer distances. Here the visual/ perceptual system becomes more dependent on other cues such as pictorial factors Arditi (1986) from Kaufman (2000). Kaufman et al’s claim is that because the moon is far away, pictorial cues dominate oculomotor cues for distance perception.
Kaufman (2006) in the end argues that distance is interpreted first and then angular size. Arguing against the micropsia theory. Also , absence of these surrounding environments the size constancy changes to visual angle performance Kenyon (2007) As you look up to the sky convergence increases therefore increased accommodation occurs causing perception of closer moon distance, therefore according to SDIH a smaller perceived size. REFER TO KAUFMAN 2000
But, these micropsia and macropsia illusions cause angular size differences of less than 10%, nowhere near large enough to account for the moon illusion seen by most persons.
Also, if accommodation were involved in the moon illusion, you’d think that elderly people who have lost nearly all accommodation should not perceive the illusion. Yet they do. Persons with eye lens implants have no accommodation, and they do perceive the moon illusion. Covering one eye removes convergence from consideration, but that doesn’t make the moon illusion go away.
4.3 Angle of regard
When looking at the horizon moon the head is positioned at eye level, where as when viewing the elevated moon the head position is further elevated by almost 45degs. It has been suggested the tilt or elevation of the head or eyes may affect the judgment of distance and thus implying the moon illusion as anisotropy (directionally dependent) for e.g. Holway and Boring (1940), Higashiyama & Adachi (2006), Suzuki (2007), Toskovich (2009).
Suzuki (2007) investigated the ratio of size of afterimages projected onto the horizon and zenith sky. Subjects were instructed to project the afterimages onto the horizon sky at eyelevel and then project the image again however after elevating the eye position by 60 degrees (using neck movements) onto the same area of the sky. This was also repeated for the zenith sky and the results yielded indicate the illusion is 1.09 times greater when the eyes are in an elevated position compared to eye level. These findings indicate the level of elevation of the eyes has an effect on the illusion magnitude and is consistent with previous findings.
Proprioceptve descriptions suggest non visual components may contribute to judging distance using head direction, body posture, vestibular and kinetic information Toskovich (2009). Furthermore Toskovich suggested head tilt upwards could cause the perceived space to elongate.
Figure 11 taken from (Roscoe and Acosta 2008)~figure 4. The number 0 would indicate a perfect size match and a positive value indicates an increase in size and negative vice versa. The x-axis displays the accommodative effort exerted by the visual system and the y-axis the interpretation of the moon size.
End with (Perceived size and perceived distance of targets viewed from between the legs: Evidence for proprioceptive theory 2006) and how this supports direct perception model rather than the apparent distance model. (Therefore supports everything except this model)
In another experiment 2 Toskovich (2009) measured size at the 3 distances and found size did not change in the three viewing directions and thus suggested the moon illusion may not be caused by a linear account, instead a more contributed input of vestibular information.
(Higashiyama & Adachi 2006) supported this theory and found the illusion disappeared when viewing through the legs. Thus suggesting the moon illusion is caused by the elevation of head tilt.
who views the moon above the horizon from low-earth orbit lacks terrain cues to
distance. We now know that in this situation the illusion vanishes (Lu et al., 2006) from (Kayfman et al 2007).
The terrestrial passage theory offers an alternative idea regarding the visual angle theories mentioned. It states the subjects learn to form an expected change in visual angle when viewing objects at different projections from past familiar experiences (Reed and Kuprinski, 2009). In a sample of 48 subjects this hypothesis was tested and the c