Observers Efficiently Extract the Minimal and Maximal Element in Perceptual Magnitude Sets: Evidence for a Bipartite Format.

The mind represents abstract magnitude information, including time, space, and number, but in what format is this information stored? We show support for the bipartite format of perceptual magnitudes, in which the measured value on a dimension is scaled to the dynamic range of the input, leading to a privileged status for values at the lowest and highest end of the range. In six experiments with college undergraduates, we show that observers are faster and more accurate to find the endpoints (i.e., the minimum and maximum) than any of the inner values, even as the number of items increases beyond visual short-term memory limits. Our results show that length, size, and number are represented in a dynamic format that allows for comparison-free sorting, with endpoints represented with an immediately accessible status, consistent with the bipartite model of perceptual magnitudes. We discuss the implications for theories of visual search and ensemble perception.

Linguistic meanings as cognitive instructions.

Natural languages like English connect pronunciations with meanings. Linguistic pronunciations can be described in ways that relate them to our motor system (e.g., to the movement of our lips and tongue). But how do linguistic meanings relate to our nonlinguistic cognitive systems? As a case study, we defend an explicit proposal about the meaning of most by comparing it to the closely related more: whereas more expresses a comparison between two independent subsets, most expresses a subset-superset comparison. Six experiments with adults and children demonstrate that these subtle differences between their meanings influence how participants organize and interrogate their visual world. In otherwise identical situations, changing the word from most to more affects preferences for picture-sentence matching (experiments 1-2), scene creation (experiments 3-4), memory for visual features (experiment 5), and accuracy on speeded truth judgments (experiment 6). These effects support the idea that the meanings of more and most are mental representations that provide detailed instructions to conceptual systems.

Young children's understanding of "more" and discrimination of number and surface area.

The psychology supporting the use of quantifier words (e.g., "some," "most," "more") is of interest to both scientists studying quantity representation (e.g., number, area) and to scientists and linguists studying the syntax and semantics of these terms. Understanding quantifiers requires both a mastery of the linguistic representations and a connection with cognitive representations of quantity. Some words (e.g., "many") refer to only a single dimension, whereas others, like the comparative "more," refer to comparison by numeric ("more dots") or nonnumeric dimensions ("more goo"). In the present work, we ask 2 questions. First, when do children begin to understand the word "more" as used to compare nonnumeric substances and collections of discrete objects? Second, what is the underlying psychophysical character of the cognitive representations children utilize to verify such sentences? We find that children can understand and verify sentences including "more goo" and "more dots" at around 3.3 years-younger than some previous studies have suggested-and that children employ the Approximate Number System and an Approximate Area System in verification. These systems share a common underlying format (i.e., Gaussian representations with scalar variability). The similarity in the age of onset we find for understanding "more" in number and area contexts, along with the similar psychophysical character we demonstrate for these underlying cognitive representations, suggests that children may learn "more" as a domain-neutral comparative term.

Poverty of the stimulus revisited.

A central goal of modern generative grammar has been to discover invariant properties of human languages that reflect "the innate schematism of mind that is applied to the data of experience" and that "might reasonably be attributed to the organism itself as its contribution to the task of the acquisition of knowledge" (Chomsky, 1971). Candidates for such invariances include the structure dependence of grammatical rules, and in particular, certain constraints on question formation. Various "poverty of stimulus" (POS) arguments suggest that these invariances reflect an innate human endowment, as opposed to common experience: Such experience warrants selection of the grammars acquired only if humans assume, a priori, that selectable grammars respect substantive constraints. Recently, several researchers have tried to rebut these POS arguments. In response, we illustrate why POS arguments remain an important source of support for appeal to a priori structure-dependent constraints on the grammars that humans naturally acquire.