The Role of Visual Information in Numerosity Estimation

Mainstream theory suggests that the approximate number system supports our non-symbolic number abilities (e.g. estimating or comparing different sets of items). It is argued that this system can extract number independently of the visual cues present in the stimulus (diameter, aggregate surface, etc.). However, in a recent report we argue that this might not be the case. We showed that participants combined information from different visual cues to derive their answers. While numerosity comparison requires a rough comparison of two sets of items (smaller versus larger), numerosity estimation requires a more precise mechanism. It could therefore be that numerosity estimation, in contrast to numerosity comparison, might rely on the approximate number system. To test this hypothesis, we conducted a numerosity estimation experiment. We controlled for the visual cues according to current standards: each single visual property was not informative about numerosity. Nevertheless, the results reveal that participants were influenced by the visual properties of the dot arrays. They gave a larger estimate when the dot arrays consisted of dots with, on average, a smaller diameter, aggregate surface or density but a larger convex hull. The reliance on visual cues to estimate numerosity suggests that the existence of an approximate number system that can extract numerosity independently of the visual cues is unlikely. Instead, we propose that humans estimate numerosity by weighing the different visual cues present in the stimuli

Beyond spheres of influence: the myth of the state and Russia’s seductive power in Kyrgyzstan

This article questions the analytical value of “spheres of influence” for understanding power and the state in the post-Soviet region and beyond, based on a critical deconstruction of the ontological and epistemological assumptions inherent in the concept. It proposes an alternative reading of power and the state, drawing on the concept of “seductive power” at a distance and Timothy Mitchell’s “state effect.” Rather than the concept of a sphere of influence, a highly politicized concept that conveys an ontology that flattens and divides space, essentializes the state, and relies on an intentionalist account of power, we need an analytical framework that can help us make sense of the multiple, varied spatialities and historical legacies that produce the state and power. I demonstrate this through an extended discussion of Russian power in Kyrgyzstan, a country often described as a Russian client state. Mobilizing recent re-conceptualizations of state and power in anthropology and political geography, I present an analysis of Russia’s seductive power in Kyrgyzstan and the way it contributes to producing Kyrgyz state-ness. I also show how Russia’s Great Power myth is itself evolving and conclude that the differentiated, relational production of space and power in either Kyrgyz or Russian myths of the state is not captured by a the concept of a return to spheres of influence

Do two and three year old children use an incremental first-NP-as-agent bias to process active transitive and passive sentences? : A permutation analysis

We used eye-tracking to investigate if and when children show an incremental bias to assume that the first noun phrase in a sentence is the agent (first-NP-as-agent bias) while processing the meaning of English active and passive transitive sentences. We also investi-gated whether children can override this bias to successfully distinguish active from passive sentences, after processing the remainder of the sentence frame. For this second question we used eye-tracking (Study 1) and forced-choice pointing (Study 2). For both studies, we used a paradigm in which participants simultaneously saw two novel actions with reversed agent-patient relations while listening to active and passive sentences. We compared English-speaking 25-month-olds and 41-month-olds in between-subjects sentence struc-ture conditions (Active Transitive Condition vs. Passive Condition). A permutation analysis found that both age groups showed a bias to incrementally map the first noun in a sentence onto an agent role. Regarding the second question, 25-month-olds showed some evidence of distinguishing the two structures in the eye-tracking study. However, the 25-month-olds did not distinguish active from passive sentences in the forced choice pointing task. In contrast, the 41-month-old children did reanalyse their initial first-NP-as-agent bias to the extent that they clearly distinguished between active and passive sentences both in the eye-tracking data and in the pointing task. The results are discussed in relation to the development of syntactic (re)parsing

Sometimes area counts more than number

Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size interfered with judgments of which array had more circles. Experiment 2 used displays in which circle size varied within and between arrays. Between-array differences in the amount of “circle stuff” (area occupied by circles) interfered with judgments of number. Experiment 3 examined whether variation in number also interferes with judgments of area. Interference between discrete and continuous stimulus dimensions occurred in both directions, although it was stronger from the continuous to the discrete than vice versa. These results bear on interpretations of studies with infants and preschoolers wherein subjects respond on the basis of continuous quantity rather than discrete quantity. In light of our results with adults, these findings do not license the conclusion that young children cannot represent discrete quantity. Absent data on attentional hierarchies and speed of processing, it is premature to conclude that infant and child quantity processes are fundamentally different from that of adults