Overflow, first-sight, and vanishing point distances in visual imagery

The relationship between the size of a familiar object and the distances at which it is imaged is examined in three experiments. The distance at which an imaged object overflows the visual field is linearly related to object size, a result consistent with the size-distance invariance hypothesis (Kosslyn, 1980). The distance at which an object is initially imaged, first-sight distance, is related to the object size by a power function with an exponent less than 1. In addition, time required to scan from the first-sight to the overflow distance increases as a function of the difference between the two distance estimates. The distance at which an imaged object becomes too small to be identified, vanishing point distance, is related to object size by a power function with an exponent less than 1. This result does not support predictions made from the size-distance invariance hypothesis or Kosslyn's model of visual imagery. Implications for a theory of visual imagery and memory are discussed.

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 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 moon illusion: II. A reference theory

The present theory provides explanations for the moon illusion and related issues involving size and distance perception in natural, outdoor settings. Although some assumptions of previous theories are rejected, other pivotal aspects are retained in this formulation. In particular, the present theory states that both the sky and ground are important referents in judging the spatial extent of the moon. Neither factor alone can account for all the available data, but quantitative models incorporating both factors do quite well when applied to the parametric findings of Holway and Boring, as well as to the results obtained by Kaufman and Rock. The reference theory and its associated class of specific models suggest new theoretical directions and experimental tests to narrow yet further the selection of appropriate explanations for one of visual perception's oldest unsolved puzzles.

The moon illusion: II. A reference theory

The present theory provides explanations for the moon illusion and related issues involving size and distance perception in natural, outdoor settings. Although some assumptions of previous theories are rejected, other pivotal aspects are retained in this formulation. In particular, the present theory states that both the sky and ground are important referents in judging the spatial extent of the moon. Neither factor alone can account for all the available data, but quantitative models incorporating both factors do quite well when applied to the parametric findings of Holway and Boring, as well as to the results obtained by Kaufman and Rock. The reference theory and its associated class of specific models suggest new theoretical directions and experimental tests to narrow yet further the selection of appropriate explanations for one of visual perception's oldest unsolved puzzles.

Variability and sequential effects in cross-modality matching of area and loudness

Individual subjects' performance was examined for cross-modality matching (CMM) of loudness to visual area, as well as for magnitude estimation (ME) of the component continua. Average exponents of power functions relating response magnitude to stimulus intensity were .73 for area, .20 for loudness, and 2.44 for CMM. Predictions of the CMM exponent based on ME were higher than the empirical values, whereas more accurate predictions were made from magnitude production exponents obtained in a previous study. Sequential dependencies were assessed by comparing the response on trial n to the response on trial n--1. The coefficient of variation of the response ratio Rn/Rn-1 was systematically related to the stimulus ratio Sn/Sn-1 for both area and loudness. The coefficient was lowest for ratios near 1 and increased for larger or smaller values. For CMM, the coefficient of variation appeared to be independent of stimulus ratios. The correlation between log Rn and log Rn-1 was also related to Sn/Sn-1 for both ME and CMM. The correlation was highest when Sn/Sn-1 was 1 and dropped to 0 with increasing stimulus separation, but CMM yielded a shallower function than ME.

Variability and sequential effects in cross-modality matching of area and loudness

Individual subjects' performance was examined for cross-modality matching (CMM) of loudness to visual area, as well as for magnitude estimation (ME) of the component continua. Average exponents of power functions relating response magnitude to stimulus intensity were .73 for area, .20 for loudness, and 2.44 for CMM. Predictions of the CMM exponent based on ME were higher than the empirical values, whereas more accurate predictions were made from magnitude production exponents obtained in a previous study. Sequential dependencies were assessed by comparing the response on trial n to the response on trial n--1. The coefficient of variation of the response ratio Rn/Rn-1 was systematically related to the stimulus ratio Sn/Sn-1 for both area and loudness. The coefficient was lowest for ratios near 1 and increased for larger or smaller values. For CMM, the coefficient of variation appeared to be independent of stimulus ratios. The correlation between log Rn and log Rn-1 was also related to Sn/Sn-1 for both ME and CMM. The correlation was highest when Sn/Sn-1 was 1 and dropped to 0 with increasing stimulus separation, but CMM yielded a shallower function than ME.

Studies of the cognitive representation of spatial relations: II. A familiar environment

This experiment tested the ability of people to recall the locations of buildings in a familiar campus setting. Ten graduate students represented the relative locations of buildings by pairwise distance judgments (on a 100-point scale) and by direct mapping of locations on a Tektronix cathode ray terminal. As evaluated by Stevens's power law, both methods led to accurate judgments of relative distance (the average exponent was close to 1). In addition, the pairwise judgments were analyzed by multidimensional scaling (MDS) and the buildings were located in a two-dimensional map. When asked to choose between the MDS representation and the map created directly on the Tektronix, all 10 subjects chose the latter as the more accurate. Moreover, 6 out of 10 subjects thought the direct map was more accurate than the actual map of the building locations. These results suggest that either pairwise judgment or direct mapping yield accurative representations of spatial relations in a familial environment, but that subjects favor the direct map.

Studies of the cognitive representation of spatial relations: III. A hypothetical environment

This experiment investigated people's preferences for the location of facilities in an ideal town. Ten graduate students represented the relative locations of facilities (such as home, school, factory) by two methods: (a) pairwise ideal distances on a 100-point scale and (b) direct planning of locations on a Tektronix cathode ray screen. The pairwise distances were analyzed by multidimensional scaling (MDS) and the facilities were thus situated in a two-dimensional space. Subjects then expressed a preference between the direct plan and the one created by MDS. In addition, the rank order priorities of the facilities were determined for each subject. The entire procedure was repeated after 4 mo. A common central plan was evident in all cases (and rank order priorities were stable), but there was within-subject variability in the plans for different methods and test occasions. Despite such variability, subjects generally preferred their direct plan over the one created by MDS (based on pair estimates). A second group of subjects showed equal preference (on the average) for both types of town representations created by the first group. Both the pair and direct technique seem appropriate for studying cognitive representations of a hypothetical environment.

Studies of the cognitive representation of spatial relations: I. Overview

The present article reviews the major results and conclusions of two experiments on the mapping and planning of actual (campus buildings) and hypothetical (ideal town facilities) items in a two-dimensional space. Direct mapping (planning) techniques are preferred over the method of pair comparisons, especially in the case of the actual environment.

Social workers' orientations toward community mental health concepts

Relations between ideological priorities in social work and community mental health were examined by a Likert-type questionnaire containing statements representing Caplan's Conceptual Models in Community Mental Health. Seventy social workers were sampled, with equal subsamples representing the five largest fields of practice in social work. This sample appeared to be highly representative of the national social work population by fields of personal service. By analyses of variance and correlation, significant differences were found between levels of approval for respective models by the total sample, but no significant differences were found by fields of practice, or any other professional or demographic attribute. This indicates a consensual integrity in the social work profession's community mental health orientation, and strong mutuality between social work and community mental health value orientations.

Test of a cognitive theory of psychophysics: size discrimination

The cognitive theory of psychophysics proposed in an earlier paper by Baird claims that the ratio of exponents obtained in the method of magnitude estimation for 2 stimulus attributes is equal to the ratio of information transmitted in the method of absolute judgment for those attributes. This theoretical prediction was tested experimentally for visual length and area. Results partially supported the prediction, inasmuch as the ordinal relations among exponents (length higher than area) was the same as the ordinal relation among information measures. However, in one instance, the exact quantitative relationship was significantly different from the predicted value.

Circular polarization of vacuum ultraviolet light by piezobirefringence

An instrument has been constructed that can produce any degree of elliptical polarization from linear to circular in the vacuum uv range 1050 A to 1450 A using a piezobirefringent retarder of LiF. The apparatus is conveniently described by the Mueller matrices. One of the piezobirefringence constants, P(11) - P(12), ranged from 4.0-10.0 x 10(-13) cm(2)/dyn for various samples of LiF, and the index of refraction at 1216 A was 1.79 +/- 0.14.

Stimulus and response factors in size instruction effects

In two experiments observers adjusted the size of a near comparison stimulus to match the size of a distant standard. Different instructions, psychophysical methods, and stimulus figures were used. The general results agreed with previous instruction effects but also suggested that such estimates depend upon the isolated and concordant influence of several stimulus and response factors.