A general explanation for the observer's ability to judge the mean size of simple geometrical figures, such as circles, was advanced. Results indicated that, contrary to what would be predicted by statistical averaging, the precision of mean size perception decreases with the number of judged elements. Since mean size discrimination was insensitive to how total size differences were distributed among individual elements, this suggests that the observer has a limited cognitive access to the size of individual elements pooled together in a compulsory manner before size information reaches awareness. Confirming the associative law of addition means, observers are indeed sensitive to the mean, not the sizes of individual elements. All existing data can be explained by an almost general theory, namely, the Noise and Selection (N&S) Theory, formulated in exact quantitative terms, implementing two familiar psychophysical principles: the size of an element cannot be measured with absolute accuracy and only a limited number of elements can be taken into account in the computation of the average size. It was concluded that the computation of ensemble characteristics is not necessarily a tool for surpassing the capacity limitations of perceptual processing.

The perception of ensemble characteristics is often regarded as an antidote to an established bottleneck in focused attention and working memory, both of which appear to be limited in capacity to a few objects only. In order to test the associative law of summation, observers were asked to estimate the mean size of four circles relative to a reference circle. When there was no time to scrutinize each individual circle, observers discriminated the mean size difference identically, irrespective of whether the same summary size increment or decrement was added to or subtracted from the size of only one, two, or all four circles. Since observers judged the size of individual circles, the position of which was indicated after they were displayed, considerably less accurately than the mean size of the four circles, it is very unlikely that explicit knowledge of the size of the individual elements is the basis of mean size judgments. The sizes of individual elements were pooled together in an obligatory manner before size information had reached awareness. The processing of size information seems to be largely constrained to only one measure at a time, with a preference for mean size rather than the individual measures from which it is assembled.

In this age of data visualization, it is important to understand our perception of the symbols that are used. For example, does the perceived size of a disc correspond most closely to its area, diameter, circumference, or some other measure? When multiple items are present, this becomes a question of ensemble perception. Here, we compare observers' performance across three different tasks: judgments of (i) the mean diameter, (ii) the total diameter, or (iii) the total area of (N = 1, 2, 3, or 7) test circles compared with a single reference circle. We draw a parallel between Anne Treisman's feature integration theory and Daniel Kahneman's cognitive systems, comparing the preattentive stage to System 1, and the focused attention stage to System 2. In accordance with Kahneman's prediction, average size (diameter) of the geometric figures can be judged with considerable accuracy, but the total diameter of the same figures cannot. Like the total length, the cumulative area covered by circles was also judged considerably less accurately than the mean diameter. Differences in efficiency between these three tasks illustrate powerful constraints upon visual processing: The visual system is well adapted for the perception of the mean size while there are no analogous mechanisms for the accurate perception of the total length or cumulative area. Thus, in visualizing data, using bubble charts proportional to area may be misleading as our visual system seems better adapted to perceive disc size by the radius rather than the area.

No abstract

Most of the research done with spatial demonstratives (words such as this, here and that, there) have focused on the production, not the interpretation, of these words. In addition, emphasis has been largely on demonstrative pronouns, leaving demonstrative adverbs with relatively little research attention. The present study explores the interpretation of both demonstrative pronouns and demonstrative adverbs in Estonian—a Finno-Ugric language with two dialectal-specific demonstrative pronoun systems. In the South-Estonian (SE) dialectal region, two demonstrative pronouns, see—“this” and too—“that”, are used. In the North-Estonian (NE) region, only one, see—“this/that”, is used. The aim of this study is twofold. First, we test if the distance and the visual salience of a referent have an effect on the interpretation of demonstratives. Second, we explore if there is a difference in the interpretation of demonstratives between native speakers from SE and NE. We used an interpretation experiment with 30 participants per group (total n = 60) and compared the SE and NE group responses. The results clearly show that the distance of the referent has an effect on how demonstratives are interpreted across the two groups, while the effect of visual salience is inconclusive. There is also a difference in the interpretation of demonstratives between the two dialectal groups. When using the Estonian with an influence of the SE dialect, the NE speakers rely on demonstrative adverbs in interpreting the referential utterance that includes demonstrative pronoun and adverb combinations, whereas the SE speakers also take into account the semantics of demonstrative pronouns. We show that, in addition to an already known difference in the production, there is also a difference in the interpretation of demonstratives between the two groups. In addition, our findings support the recognition that languages that have distance neutral demonstrative pronouns enforce the spatial meaning of a referring utterance by adding demonstrative adverbs. Not only is the interpretation of demonstrative pronouns affected, but the interpretation of demonstrative adverbs as well. The latter shows the importance of studying adverbs also, not just pronouns, and contributes to further knowledge of how demonstratives function.