Academic journal article Attention, Perception and Psychophysics

How Might the Discrepancy in the Effects of Perceptual Variables on Numerosity Judgment Be Reconciled?

Academic journal article Attention, Perception and Psychophysics

How Might the Discrepancy in the Effects of Perceptual Variables on Numerosity Judgment Be Reconciled?

Article excerpt

It has been claimed that a genuinely abstract numerical representation would be capable of representing the numerosity of any set of discrete elements independently of the attributes of the individual elements. In practice, however, perceptual variables, such as element size, density, and others, affect numerosity judgment. In this study, we examined how perceptual variables affect the performance of numerosity judgments under the control of factors such as amount of practice and set size. In Experiment 1, we introduced the numerosity comparison task to less experienced observers in order to examine the effect of element size and array area. In Experiment 2, we examined whether and how practice would influence precision and accuracy in numerosity comparison and demonstrated that the effects of perceptual variables mostly disappeared. In Experiment 3, we examined whether the effect of practice could transfer to the performance in different stimulus conditions. Taking the results together, we demonstrate that differences in practice might be the source of inconsistent results for perceptual variables.

The ability to judge the relative numerosity of items in the visual field is quite adaptive. For various species, many situations require them to judge which items are greater in number without counting serially. For instance, when the decision is made to fight or run, it is necessary to judge which side, friends or foes, is more numerous. Alternatively, when collecting food, it is crucial to judge which location has more pieces of fruit or a greater abundance of prey.

Substantial empirical evidence has supported the idea that humans possess innate neural mechanisms that generate approximate, not precise, numerical representations. Results from studies of numerical competence in infants, young children, and nonhuman animals have shown that the approximate numerical representation system is evolutionally old and is equipped early in human development (e.g., Brannon, 2006; Cantlon, Platt, & Brannon, 2009; Dehaene, 1997; Feigenson, Dehaene, & Spelke, 2004; Whalen, Gallistel, & Gelman, 1999). Futhermore, converging empirical findings from several areas of cognitive neurosience have argued for biologically determined mechanisms for approximate numerical representation (e.g., Cantlon, Brannon, Carter, & Pelphrey, 2006; Cappelletti, Barth, Fregni, Spelke, & Pascual-Leone, 2007; Dehaene, Dehaene-Lambertz, & Cohen, 1998; Eger, Sterzer, Russ, Giraud, & Kleinschmidt, 2003; Nieder & Dehaene, 2009; Nieder, Freedman, & Miller, 2002; Nieder & Miller, 2003; Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004). For example, neurophysiological research has provided evidence for the existence in monkeys' prefrontal cortex of neurons that are tuned for small numbers (Nieder & Miller, 2003) and large numbers such as 30 (Nieder & Merten, 2007). The characteristics of the neurons suggested that the performance of discrimination obeys the Weber law, which implies that numerical tuning is approximate and is broader for larger numerosities. Many studies of numerosity discrimination have shown that discriminability depends on the ratio of the numerosities to be compared (e.g., Allik, Tuulmets, & Vos, 1991; Brannon, 2006; Krueger, 1972, 1984; Nieder & Dehaene, 2009). Piazza et al. found that the intraparietal site coding for number in humans is compatible with that observed in macaque monkeys. It should be noted that in this study, the approximate numerical representation referred mainly to the representation of nonverbal or nonsymbolic numerical value.

In line with these arguments, it has been claimed that a genuinely abstract numerical representation would be capable of representing the numerosity of any set of discrete elements, whether they were events or items, presented sequentially or simultaneously, independently both of the spatial arrangement of the stimuli and of the attributes of the individual elements such as size, color, and shape. …

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