The moon illusion: I. How high is the sky?

The most common explanations of the moon illusion assume that the moon is seen at a specific distance in the sky, which is perceived as a definite surface. A decrease in the apparent distance to the sky with increasing elevation presumably leads to a corresponding decrease in apparent size. In Experiment 1 observers (N = 24) gave magnitude estimates of the distance to the night sky at different elevations. The results did not support the flattened-dome hypothesis. In Experiment 2 observers (N = 20) gave magnitude estimates of the distance to the sky at points around a 360 degrees circle just above the horizon. The results were consistent with those of Experiment 1, and in addition, estimates were highly correlated with the physical distances of buildings at the horizon. In a third, control experiment, observers (N = 20) gave magnitude estimates of the distances of buildings at the horizon. A power function fit the relation between estimated and physical distance (exponent = 1.17) as well as the relation between estimates of the sky points above the buildings (Experiment 2) and estimates of building distances (exponent = .46). Taken together, the results disconfirm all theories that attribute the moon illusion to a "sky illusion" of the sort exemplified by the flattened-dome hypothesis.     

Moon illusion in pictures: a multimechanism approach

The existence of the moon illusion in pictorial representations was demonstrated in 6 experiments. Ss either judged the size of the moon in pictures, depicted as on the horizon or high in the sky, or drew horizon and elevated moons. The horizon moon was consistently judged to be larger than the elevated moon, independent of the angle at which the pictures are viewed. The distance paradox usually observed with the moon illusion (horizon moon apparently closer than the elevated moon) also exists in pictures. The magnitude of both size and distance effects depends on the salience of depicted depth cues. The pattern of results suggests that the moon illusion is caused by several interacting mechanisms and that use of pictorial stimuli may allow the separation of various cognitive from physiological contributions to the illusion.     

A variant of the anomalous motion illusion based upon contrast and visual latency

We examined a variant of the anomalous motion illusion. In a series of experiments, we ascertained luminance contrast to be the critical factor. Low-contrast random dots showed longer latency than high-contrast ones, irrespective of whether they were dark or light (experiments 1 -3). We conjecture that this illusion may share the same mechanism with the Hess effect, which is characterised by visual delay of a low-contrast, dark stimulus in a moving situation. Since the Hess effect is known as the monocular version of the Pulfrich effect, we examined whether illusory motion in depth could be observed if a high-contrast pattern was projected to one eye and the same pattern of low-contrast was presented to the other eye, and they were binocularly fused and swayed horizontally. Observers then reported illusory motion in depth when the low-contrast pattern was dark, but they did not when it was bright (experiment 4). Possible explanations of this inconsistency are discussed.     

The horizon line, linear perspective, interposition, and background brightness as determinants of the magnitude of the pictorial moon illusion

A total of 110 undergraduate students participated in a series of three experiments that explored the magnitude of the moon illusion in pictures. Experiment 1 examined the role of the number and salience of depth cues and background brightness. Experiment 2 examined the role of the horizon line, linear perspective, interposition, and background brightness. In Experiment 3, comparative distance judgments of the moon as a function of linear perspective, interposition, and the size of the standard moon were obtained. The magnitude of the moon illusion increased as a function of the number and salience of depth cues and changes in background brightness. Experiment 2 failed to support the role of the horizon line in affecting the illusion. Experiment 3 provided additional support for the illusory distance component of the moon illusion.     

The overestimation of vertical distance and slope and its role in the moon illusion

Six experiments were conducted to test the hypothesis that overestimation of vertical distance is a pervasive phenomenon. The experiments involved judgments of: (a) vertical distance looking upward; (b) vertical distance looking downward; (c) the slope of a real hill; (d) the recalled slopes of streets; (e) the magnitudes of angles drawn on paper; (f) the distances to afterimages projected into the sky. The results showed that a very strong illusion of overestimation of both vertical distance and slope occurred in all situations except for the judgments of drawn angles by males. Furthermore, in five of the six experiments females showed a greater amount of the illusion than males. The discussion pointed out the difficulty of explaining the moon illusion by the assumptions of a flattened sky surface and Emmert’s law in light of the data.     

Size illusion, distance illusion, and terrestrial passage: comment on reed

Two assumptions of Reed's (1984) terrestrial passage theory are questioned. First, Reed assumes that the moon's failure to increase in visual subtense while elevating is accounted for strictly by perceptual distancing. This allows a formal account of the moon distance illusion, but at the expense of a compelling explanation of the moon size illusion. Second, in order to explain the distance illusion, Reed assumes that all objects, regardless of their perceived altitude, are perceived to start from a common point at the horizon. Several alternative application of Reed's terrestrial-passage foundation to the actual illusions are suggested.     

Oculomotor Effects in the Size-Distance Paradox and the Moon Illusion

Drawing on 2 concepts—the resting position of the eyes and a binocular geometry for perceived size, the moon illusion is explained as the consequence of different oculomotor adjustments caused by change in the direction of gaze contingent upon the viewing conditions of the moon. Hence, each particular moon will be viewed with a different vergence state which, in turn, yields a different amount of binocular disparity. The vergence state will determine the perceived size of an object whereas disparity will determine its perceived distance. It is further contended that the perceived size of the moon is based on a new binocular information source for size perception enabling the size of an object to be perceived even in the absence of egocentric distance information. Discussion focuses on the paradoxical aspect of the moon illusion and how the size-distance invariance hypothesis may have contributed to its effect.     

Parallel—and distance—alleys with moving points in the horizontal plane

Stimulus points were presented on the horizontal plane of eye level under both dark and illuminated homogeneous spaces. When two apparent movements towards the subject were generated and positions of points were so adjusted that the two movements appeared straight and parallel (P alley) or with a constant lateral distance (D alley), the D alley lay outside the P alley, as traditionally shown with stationary sets of points. The two alleys were constructed with various patterns and velocities of movement, and the Lüneburg formulas were used as experimental equations to describe the results. The equations have two parameters: K (curvature) and o (sensitivity in depth perception). Values of K and o obtained with stationary points in previous experiments are shown too. Predominantly, K < 0 (hyperbolic), and the same is true in the present study. No first-order effect of patterns and velocities of the movement upon K and o was found.     

Terrestrial passage theory of the moon illusion

Theories of the celestial, or moon, illusion have neglected geometric characteristics of movement along and above the surface of the earth. The illusion occurs because the characteristics of terrestrial passage are attributed to celestial passage. In terrestrial passage, the visual angle subtended by an object changes discriminably as an essentially invariant function of elevation above the horizon. In celestial passage, by contrast, change in visual angle is indiscriminable at all elevations. If a terrestrial object gains altitude, its angular subtense fails to follow the expansion projected for an orbital course: Angular diminution or constancy is equivalent to distancing. On the basis of terrestrial projections, a similar failure of celestial objects in successive elevations is also equivalent to distancing. The illusion occurs because of retinal image constancy, not--as traditionally stated--despite it.     

The relationship between vertical stimulation and horizontal attentional asymmetries

The original aim was to examine the effect of perceived distance, induced by the Ponzo illusion, on left/right asymmetries for line bisection. In Experiment 1, university students (n?=?29) made left/right bisection judgements for lines presented in the lower or upper half of the screen against backgrounds of the Ponzo stimuli, or a baseline. While the Ponzo illusion had relatively little effect on line bisection, elevation in the baseline condition had a strong effect, whereby the leftward bias was increased for upper lines. Experiment 2 (n?=?17) eliminated the effect of elevation by presenting the line in the middle and moving the Ponzo stimuli relative to the line. Despite this change, the leftward bias was still stronger in the upper condition in the baseline condition. The final experiment (n?=?17) investigated whether upper/lower visual stimulation, which was irrelevant to the task, affected asymmetries for line bisection. The results revealed that a rectangle presented in the upper half of the screen increased the leftward line bisection bias relative to a baseline and lower stimulation condition. These results corroborate neuroimaging research, showing increased right parietal activation associated with shifts of attention into the upper hemispace. This increased right parietal activation may increase the leftward attentional bias—resulting in a stronger leftward bias for line bisection.     

A test of size-scaling and relative-size hypotheses for the moon illusion

In two experiments participants reproduced the size of the moon in pictorial scenes under two conditions: when the scene element was normally oriented, producing a depth gradient like a floor, or when the scene element was inverted, producing a depth gradient like a ceiling. Target moons were located near to or far from the scene element. Consistent with size constancy scaling, the illusion reversed when the "floor" of a pictorial scene was inverted to represent a "ceiling." Relative size contrast predicted a reduction or increase in the illusion with no change in direction. The relation between pictorial and natural moon illusions is discussed.     

Vertical-horizontal illusion: One eye is better than two

The vertical-horizontal illusion is the tendency for observers to overestimate the length of a vertical line relative to a horizontal line that has the same length. One explanation of this illusion is that the visual field is elongated in the horizontal direction, and that the vertical-horizontal illusion is a kind of framing effect (Künnapas, 1957a, 1957b, 1957c). Since the monocular visual field is less asymmetric than the combined visual field, this theory predicts that the illusion should be reduced with monocular presentation. This prediction was tested in five experiments, in which the vertical-horizontal illusion was examined in a variety of situations—including observers seated upright versus reclined 90°, monocular presentation with the dominant versus the nondominant eye, viewing in the dark versus in the light, and viewing with asymmetrical frames of reference. The illusion was reliably reduced with monocular presentation under conditions that affected the asymmetry of the phenomenal visual field.     

Yang's iris illusion: External contour causes length‐assimilation illusions1

The Delboeuf illusion and the Ebbinghaus illusion (also known as the Titchener illusion) demonstrate that an external contour can lead to size‐assimilation and size‐contrast perception. This paper explores a novel illusion, revealing that neighboring external contours can also lead to a distortion in length perception. The illusion was originally discovered from a face stimulus (Experiment 1) in which a face was depicted alongside its mirror image so as to make the four irises absolutely equidistant. The distance between the middle two irises was underestimated in Asian faces, but overestimated in Caucasian faces. The illusion was also maintained when the facial stimuli were replaced by line drawings of eyes (Experiment 2). However, the illusion vanished when the irises were presented alone. Further scrutiny of the differences in facial characteristics between Asian and Caucasian faces reveals that the illusion might be elicited by the relative position of the eye shapes. This hypothesis was confirmed in Experiment 3, in which the distances between the eye shapes and the irises were manipulated.     

Tendencies to eye movement,and misperception of curvature,direction, and length

From previous studies of eye movements, three types of eye-movement tendency can be inferred: (1) tendency to rectilinear eye movements, (2) tendency to horizontal or vertical eye movements, and (3) tendency to center-of-gravity fixations. The possible influence of these eye-movement tendencies on perception was investigated in two experiments. In Experiment 1, errors in perceived location of intersection in arc figures were studied varying arc-point distance and are length. Tendencies 1 and 2 accounted very well for the resultant S-shaped functions. In Experiment 2, the Müller-Lyer illusion with three different oblique angles and a line-segment illusion were measured as a function of the distance between the vertex and the center of gravity of the arrowhead. Tendency 3 accounted well for the inverted-U forms of the obtained functions but not for the increase of error with increasing angle.     

A simple but powerful theory of the moon illusion

Modification of Restle's theory (1970) explains the moon illusion and related phenomena on the basis of three principles: (1) The apparent sizes of objects are their perceived visual angles. (2) The apparent size of the moon is determined by the ratio of the angular extent of the moon relative to the extents subtended by objects composing the surrounding context, such as the sky and things on the ground. (3) The visual extents subtended by common objects of a constant physical size decrease systematically with increasing distance from the observer. Further development of this theory requires specification of both the components of the surrounding context and their relative importance in determining the apparent size and distance of the moon.     

Infants' perception of illusions in sound localization: reaching to sounds in the dark.

Sixteen infants each at 4, 6, and 8 months of age were tested for reaching to sounding toys in the dark under two auditory illusion conditions: the Haas-effect, which creates the illusion of a single lateralized sound based on an interaural intensity difference (the toy was visible and invisible under some test conditions); and the midline illusion, which creates the illusion of a single sound at midline due to an absence of any interaural time or intensity differences (invisible toy condition only). No-sound control trials indicated the level of spontaneous reaching in the dark. Results indicate that by 4 months infants perceive both the Haas-effect and midline illusions. The ability to reach both for invisible and visible sounding objects in the dark was well developed by 4 months of age, although developmental changes in aspects of reaching behavior were observed and, at all ages, object contact was most frequent when visual localization cues accompanied sound localization cues. The incidence of spontaneous reaching in the dark was low and did not vary with age. Theoretical and methodological implications of this research are discussed.     

Brightness contrast effects in a pupillometric experiment

The effect of depth displacement of test bars from the induction wedge of the Ponzo illusion was investigated in two experiments. Either two wedges of opposite orientation were presented simultaneously, one at a near and the other at a far distance, or only one wedge was presented at either the near or the far distance. The test bars were stereoscopically either in the plane of the wedge or displaced from the wedge in distance. When the two wedges were presented simultaneously, the direction of the Ponzo illusion was determined by the wedge at the same perceived distance as the test bars. When only one wedge was present, stereoscopic displacement of the bars in front of, but not behind, the wedge decreased the magnitude of the illusion. The results are interpreted in terms of the adjacency principle.

     

The Moses, mega-Moses, and Armstrong illusions: integrating language comprehension and semantic memory

This study develops a new theory of the Moses illusion, observed in responses to general knowledge questions such as, "How many animals of each kind did Moses take on the Ark?" People often respond "two" rather than "zero" despite knowing that Noah, not Moses, launched the Ark. Our theory predicted two additional types of conceptual error demonstrated here: the Armstrong and mega-Moses illusions. The Armstrong illusion involved questions resembling, "What was the famous line uttered by Louis Armstrong when he first set foot on the moon?" People usually comprehend such questions as valid, despite knowing that Louis Armstrong was a jazz musician who never visited the moon. This Armstrong illusion was not due to misperceiving the critical words (Louis Armstrong), and occurred as frequently as the Moses illusion (with critical words embedded in identical sentential contexts), but less frequently than the mega-Moses illusion caused when Moses and Armstrong factors were combined.     

Decrement of the Müller-Lyer illusion with saccadic and tracking eye movements

Subjects viewed the Müller-Lyer illusion, making either saccadic or smooth tracking eye movements between the apexes of the arrow heads. The decrement in the magnitude of the illusion was significantly greater for Ss in the saccadic viewing condition. Saccadic and smooth tracking eye movements are separately controlled,and information about eye position is more readily available from the efferent signals issued to control a saccadic eye movement. The experimental findings were consistent with the hypothesis that Ss in the saccadic condition learned a new afferent efferent association. The results support a theory that visual perception is determined by efferent readiness activated by visual afferent stimulation.     

Large errors in the perception of vertically are generated by luminance borders (integrated across space) not by subjective borders

The rod-and-frame illusion shows large errors in the judgment of visual vertical in the dark if the frame is large and there are no other visible cues (Witkin and Asch, 1948 Journal of Experimental Psychology 38 762-782). Three experiments were performed to investigate other characteristics of the frame critical for generating these large errors. In the first experiment, the illusion produced by an 11 degrees tilted frame made by luminance borders (standard condition) was considerably larger than that produced by a subjective-contour frame. In the second experiment, with a 33 degrees frame tilt, the illusion was in the direction of frame tilt with a luminance-border frame but in the opposite direction in the subjective-contour condition. In the third experiment, to contrast the role of local and global orientation, the sides of the frame were made of short separate luminous segments. The segments could be oriented in the same direction as the frame sides, in the opposite direction, or could be vertical. The orientation of the global frame dominated the illusion while local orientation produced much smaller effects. Overall, to generate a large rod-and-frame illusion in the dark, the tilted frame must have luminance, not subjective, contours. Luminance borders do not need to be continuous: a frame made of sparse segments is also effective. The mechanism responsible for the large orientation illusion is driven by integrators of orientation across large areas, not by figural operators extracting shape orientation in the absence of oriented contours.