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.     

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.     

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.     

An auditory illusion predicted by a theory of brain function.

A theory of brain function has resulted in the hypothesis that dichotic auditory stimuli of differing intensities would be subjectvely heard to occur at different times if presented together. The louder of the two tones would always be heard first. The results of an experiment designed to test the hypothesis have established that the predicted illusory judgment will invariably be made. The further prediction that the magnitude of the effect would closely parallel certain reaction time data was substantiated. It seems reasonable to conclude that the same paradigm must underlie both sets of data. The theory and obtained results provide a possible neurophysiological basis for the perception of rhythm. A review of the literature has shown that results analogous to those reported here have previously been reported for the visual and tactile modalities, as would be predicted from the general considerations of the theory which gave rise to the specific hypotheses tested in this experiment.     

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.     

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.     

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.     

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 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.     

A depth processing theory of the Poggendorff illusion

The Poggendorff illusion is attributed to the processing of the oblique lines of the Poggendorff figure as receding horizontal lines with their inner ends equidistant because of attachment to a frontal plane (defined by the parallel lines of the figure). Collinearity in three-dimensional space is inconsistent with such equidistance; one line must lie on a higher horizontal plane than the other. This necessarily noncollinear resolution of the lines in depth processing (which is inferred irrespective of the O’s consciousness of depth) is assumed to influence apparent projective relationships within the figure, thus accounting for the illusion. Predictions from the theory, involving manipulations of the plane defined by the parallels, were confirmed experimentally. In addition, the theory is shown to account very well for the effects of amputations and rotations of the figure, which other theories of the illusion cannot handle.     

The solitaire illusion: An illusion of numerosity

A new illusion in which the apparent number of elements of two kinds is determined by their spatial arrangement is described. The illusion is such that one large cluster appears to contain more elements than several small clusters, clustering being determined by Gestalt principles. The illusion was found both in adults and in children of 8 years.     

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.     

An illusion of ingestion

Three experiments were conducted to find out why subjects ingest substantially more liquid than required when asked to match a visually displayed volume. All three experiments replicated the basic illusion phenomenon, and Experiments 1 and 2 indicated that it was attributable to the subjects’ underestimating the volume of liquid in their mouths. Experiment 3 revealed that the illusion was not present with solid substances, but it was evident with liquids when a quite different measurement procedure was employed.