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

How accurate is size and distance perception for very far terrestrial objects? Function and causality

This study investigated absolute estimation of size and distance for natural and artificial objects at viewing distances of 1.1-15.3 km (Experiments 1 and 2) and 0.4-5.0 m (Experiment 3). The main results were that, regardless of distance range, size and distance estimates (S' and D') were related to objective size and distance (S and D), respectively, by a power function with an exponent of unity, but great individual differences in exponent were obtained for the far objects. The ratio S'/D' was reasonably represented by S'/D' = K theta n and S'/D' = tan(a theta +b), rather than S'/D' = tan theta, where theta is the visual angle. Partial correlations were obtained to examine whether (1) apparent size is determined by taking apparent distance into account or (2) both apparent size and apparent distance are determined directly by external stimuli. The combined data for the far objects and the data for the close objects showed that there were high correlations between S and S' and between D and D' and a low correlation between D' and S'. The data of Experiment 2 showed that both D' and S' were highly correlated with S, D, and theta, and there was a high positive correlation between D' and S'. It was suggested that the direct-perception model is valid under some situations, but the taking-into-account model is not supported in any set of 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.

The registered distance of the celestial sphere: some historical cross-cultural data

Estimates of the diameters of the sun and moon expressed in centimetres have been reported by several authors in the past. These estimates imply that the sizes of the sun and moon are perceived as if these bodies are only some tens of metres distant. In this study five units of length that were used by ancient astronomers to estimate arcs on the celestial sphere were investigated. The purpose was to determine whether the lengths and angles represented by these units imply a specific registered distance of the star sphere. The sizes of the Babylonian cubit, Arab fitr and shibr, Greek eclipse digit, and Chinese chang support the conclusion that the registered distance of the stars was about 10 to 40 metres in these four cultures over the last two millennia.

Scales for measuring subjective distance in children and adults in a large open field

Five age levels (6, 8, 10, 12 years, and adults, N = 127) estimated distance in a large open field by the fractionation method. Scales for subjective distance were derived for each group. It was found that (a) the adults differed from all the other groups, (b) the 12-year-olds differed from the six-year-olds, (c) all the exponents were smaller than 1, (d) perceived distance in a large open field was characterized by underconstancy, and (e) underconstancy was greater for the younger subjects.