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 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.     

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.     

Moon illusion simulated in complete darkness: planetarium experiment reexamined

In 1962, Kaufman and Rock reported that the moon illusion did not occur in the darkness of a planetarium or in a completely dark room. The present study reexamined their findings. Two pairs of light points, separated by 3.5 degrees, were presented on the dome screen of a planetarium. Subjects compared the distance between the two light points presented in the horizontal direction with the distance between the two light points at the zenith. Three illumination conditions were used: The inside of the planetarium was completely dark, was lighted, or was projected with the silhouette of a city under a starry sky. The effect of eye elevation on the illusion was also examined. Contrary to Kaufman and Rock's results, a size discrepancy comparable to the moon illusion was obtained in the horizon-and-stars condition and even in the complete-darkness condition. Little or no illusion was obtained in the lighted-room condition. The results also showed that eye elevation affected the magnitude of the illusion.     

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.     

Stereoscopic depth and the occlusion illusion

In the occlusion illusion, the visible portion of a partly occluded object appears larger than a physically identical nonoccluded region. Stereoscopic displays allowed for a direct test of the apparent-distance hypothesis. In Experiments 1A and 1B, we measured both the perceived size and the perceived depth of partly occluded targets when the binocular disparity of both targets and occluders was varied. Stereoscopic occlusion greatly increased perceived target size but not perceived target distance. A reduced illusion was still present when the target was stereoscopically in front of the abutting rectangle, however. Experiments 2A and 2B showed similar results, even when the occluding figures were illusory rectangles that formed no explicit T-junctions. Experiment 3 showed that an unexpected negative size illusion on control trials was primarily due to adaptation to the occlusion illusion on other trials. The present findings eliminate apparent-distance explanations of the occlusion illusion but are consistent with other hypotheses, such as partial modal completion and selective dimensional expansion.     

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.     

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.     

The moon tilt illusion.

Besides the familiar moon illusion [e.g. Hershenson, 1989 The Moon Illusion (Hillsdale, NJ: Lawrence Erlbaum Associates)], wherein the moon appears bigger when it is close to the horizon, there is a less known illusion which causes the moon's illuminated side to appear turned away from the direction of the sun. An experiment documenting the effect is described, and a possible explanation is put forward.     

Anisotropic perception of visual angle: implications for the horizontal-vertical illusion, overconstancy of size, and the moon illusion.

Three experiments investigated anisotropic perception of visual angle outdoors. In Experiment 1, scales for vertical and horizontal visual angles ranging from 20 degrees to 80 degrees were constructed with the method of angle production (in which the subject reproduced a visual angle with a protractor) and the method of distance production (in which the subject produced a visual angle by adjusting viewing distance). In Experiment 2, scales for vertical and horizontal visual angles of 5 degrees-30 degrees were constructed with the method of angle production and were compared with scales for orientation in the frontal plane. In Experiment 3, vertical and horizontal visual angles of 3 degrees-80 degrees were judged with the method of verbal estimation. The main results of the experiments were as follows: (1) The obtained angles for visual angle are described by a quadratic equation, theta' = a + b theta + c theta 2 (where theta is the visual angle; theta', the obtained angle; a, b, and c, constants). (2) The linear coefficient b is larger than unity and is steeper for vertical direction than for horizontal direction. (3) The quadratic coefficient c is generally smaller than zero and is negatively larger for vertical direction than for horizontal direction. And (4) the obtained angle for visual angle is larger than that for orientation. From these results, it was possible to predict the horizontal-vertical illusion, over-constancy of size, and the moon illusion.     

An illusion of movement complementary to the horizontal-vertical illusion

Blindfolded subjects moved a stylus held in the hand over a standard distance of 4.5 ins. in a given direction. They then attempted to move the same distance in a direction at right angles to the first. Eight combinations of movements were investigated. The results reveal an illusion such that the extent of movements to left or right across the body is underestimated, while the extent of movements towards or away from the body in the mid-line is overestimated. The illusion applies to speed as well as extent of movement. Movement up or down in a vertical plane is equivalent to movement towards or away from the body in a horizontal plane.

The interaction of this illusion with the well-known horizontal-vertical illusion of visual perception explains a failure to find any net illusory effect where lines visually displayed in different orientations were matched for length by unseen movements in similar orientations.

Whether the visual and movement illusions simply co-exist or whether they are functionally related is not yet clear.     

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.     

Six-month-old infants perceive the hollow-face illusion

In this study we investigated infants' perception of the hollow-face illusion. 6-month-old infants were shown a concave mask under monocular and binocular viewing conditions and the direction of their reaches toward the mask was recorded. Adults typically perceive a concave mask as convex under monocular conditions but as concave under binocular conditions, depending on viewing distance. Based on previous findings that infants reach preferentially toward the parts of a display that are closest to them, we expected that, if infants perceive the hollow-face illusion as adults do, they would reach to the center of the mask when viewing it monocularly and to the edges when viewing it binocularly. The results were consistent with these predictions. Our findings indicated that the infants perceived the mask as convex when viewing it with one eye and concave when viewing it with two eyes. The results show that 6-month-old infants respond to the hollow-face illusion. Our finding suggests that, early in life, the visual system uses the constraint, or assumption, that faces are convex when interpreting visual input.     

Anisotropic perception of visual angle: Implications for the horizontal-vertical illusion,overconstancy of size,and the moon illusion

Three experiments investigated anisotropic perception of visual angle outdoors. In Experiment 1, scales for vertical and horizontal visual angles ranging from 20° to 80° were constructed with the method of angle production (in which the subject reproduced a visual angle with a protractor) and the method of distance production (in which the subject produced a visual angle by adjusting viewing distance). In Experiment 2, scales for vertical and horizontal visual angles of 5°–30° were constructed with the method of angle production and were compared with scales for orientation in the frontal plane. In Experiment 3, vertical and horizontal visual angles of 3°-80° were judged with the method of verbal estimation. The main results of the experiments were as follows: (1) The obtained angles for visual angle are described by a quadratic equation, θ′=a+bθ+cθ² (where θ is the visual angle; θ′, the obtained angle;a, b, andc, constants). (2) The linear coefficientb is larger than unity and is steeper for vertical direction than for horizontal direction. (3) The quadratic coefficientc is generally smaller than zero and is negatively larger for vertical direction than for horizontal direction. And (4) the obtained angle for visual angle is larger than that for orientation. From these results, it was possible to predict the horizontal-vertical illusion, over-constancy of size, and the moon illusion.     

An airplane illusion: apparent velocity determined by apparent distance

When a small drone plane appears to be a normal-sized airplane, it appears to be very far away and moving too fast. This is the airplane illusion. In the illusory situation, familiar size determines the apparent size and distance of the plane. It sets the depth for the frontal-plane component of the perceived motion and the relative depth difference for the motion-in-depth component. Because these perceived distances are very large, the perceived velocities are very large in the respective directions. Cognition can override familiarity and produce a veridical perception of the drone.     

Evolved navigation theory and the descent illusion

Researchers often assume that height perception results from all of the same mechanisms as does other distance perception. Evolved navigation theory (ENT) proposes that natural selection has differentiated some psychological processes, including height perception, in response to the navigational outcome of falling. We tested predictions from three theories in two experiments. Only ENT predicted greater height perceived from the top than from the bottom of a vertical surface (because descent results in falls more often than does ascent). Participants across experiments perceived an average of 32% greater vertical distance when viewing from the top than when viewing from the bottom. We discuss selected implications and suggest ENT for uniting isolated findings, including the vertical-horizontal illusion.     

An illusion of eccentricity

The illusion investigated here is that two concentric arcs, drawn in different (though possibly overlapping) circular sectors and having the same angular extent, appear to be eccentric. Three possible explanations of the illusion are tested. The first hypothesis is that concentricity judgments are made by elongating the arcs to see if they intersect, the illusion being due to the tendency, when elongating a curve, to follow the end-tangent. The second hypothesis is that concentricity judgments are based on a test of coincidence of centers, the illusion being due to the overestimation of the radius of short arcs. The third hypothesis is that both of these factors contribute in equal measure. These hypotheses make different predictions about the effect (on the magnitude of the illusion) of the following variables: (1) the angular distance between the arcs; (2) the radial distance between the arcs; (3) the degree of curvature of the arcs; and (4) the angular extent of the arcs. The observed values of the illusion angle (obtained by the method of limits) in relation to these variables did not uniformly support any of the hypotheses. A more complex model that is consistent with the observed results is therefore proposed.     

Spatial limits on the nonvisual self-touch illusion and the visual rubber hand illusion: Subjective experience of the illusion and proprioceptive drift

The nonvisual self-touch rubber hand paradigm elicits the compelling illusion that one is touching one’s own hand even though the two hands are not in contact. In four experiments, we investigated spatial limits of distance (15 cm, 30 cm, 45 cm, 60 cm) and alignment (0°, 90° anti-clockwise) on the nonvisual self-touch illusion and the well-known visual rubber hand illusion. Common procedures (synchronous and asynchronous stimulation administered for 60 s with the prosthetic hand at body midline) and common assessment methods were used. Subjective experience of the illusion was assessed by agreement ratings for statements on a questionnaire and time of illusion onset. The nonvisual self-touch illusion was diminished though never abolished by distance and alignment manipulations, whereas the visual rubber hand illusion was more robust against these manipulations. We assessed proprioceptive drift, and implications of a double dissociation between subjective experience of the illusion and proprioceptive drift are discussed.     

Radical Epistemic Self-Sufficiency on Reed’s Long Road to Skepticism

Baron Reed has developed a new argument for skepticism: (1) contemporary epistemologists are all committed to two theses, fallibilism and attributabilism; unfortunately, (2) these two theses about knowledge are incompatible; therefore, (3) knowledge as conceived by contemporary epistemologists is impossible. In this brief paper I suggest that Reed's argument appears to rest on an understanding of attributabilism that is so strong (call it maximal attributabilism) that it's doubtful that many contemporary epistemologists actually embrace it. Nor does Reed offer any direct argument for the truth of maximal attributabilism. Therefore, we need not be persuaded by Reed's new argument for skepticism.     

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.