Nonverbal Estimation during Numerosity Judgements by Adult Humans

Abstract

On an automated task, humans selected the larger of two sets of items, each created through the one-by-one addition of items. Participants repeated the alphabet out loud during trials so that they could not count the items. This manipulation disrupted counting without producing major effects on other cognitive capacities such as memory or attention, and performance of this experimental group was poorer than that of participants who counted the items. In Experiment 2, the size of individual items was varied, and performance remained stable when the larger numerical set contained a smaller total amount than the smaller numerical set (i.e., participants used numerical rather than nonnumerical quantity cues in making judgements). In Experiment 3, reports of the number of items in a single set showed scalar variability as accuracy decreased, and variability in responses increased with increases in true set size. These data indicate a mechanism for the approximate representation of numerosity in adult humans that might be shared with nonhuman animals.

Quantity representation in children and rhesus monkeys: Linear versus logarithmic scales

“…Some of these circles were colored fully in white whereas others were unfilled. We used this manipulation because it resulted in trials of the same quantity including a wide range of illumination levels to help dissociate illumination and quantity (see Beran et al, 2006). At the bottom of the screen, a white letter "L" was on the left side of the screen, and a white letter "M" was on the right side of the screen.…”

“…The quantity discriminations made by many species are restricted in their accuracy on the basis of the ratio between those sets (e.g., Barth, Kanwisher, & Spelke, 2003;Beran, 2007;Beran, Taglialatela, Flemming, James, & Washburn, 2006;Brannon, Cantlon, & Terrace, 2006;Brannon & Terrace, 2000;Call, 2000;Huntley-Fenner, 2001). Comparisons with larger ratios (as determined by dividing the smaller quantity by the larger quantity) lead to lower performance levels, even when the distance between sets is constant (e.g., 8 versus 10 is more difficult than 2 versus 4).…”

“…All monkeys were trained prior to this experiment to respond to computer generated stimuli using joysticks, and these animals had participated in some previous experiments in which they choose the larger of two sets of analog stimuli (e.g., Beran, 2007). However, only two of the monkeys had ever participated in a bisection task similar to the one used here (Beran et al, 2006). …”

Comparing children’s Homo sapiens and chimpanzees’ Pan troglodytes quantity judgments of sequentially presented sets of items

“…Across all set sizes, success was determined by the ratio between sets, not on the basis of the magnitude of the sets. Subsequent use of the one-by-one sequential presentation method with rhesus monkeys (Beran, 2007), capuchin monkeys (Beran et al, 2008;Evans et al, 2009), gorillas, bonobos, and orangutans (Hanus and Call, 2007), and even adult humans who were prevented from counting the arrays (Beran et al, 2006) indicated this same relation between performance and ratio between sets. This suggests that a similar mechanism may be operating across species to facilitate performance on this task.…”

Visual Nesting of Stimuli Affects Rhesus Monkeys' (Macaca mulatta) Quantity Judgments in a Bisection Task

“…The authors anticipated that this arrangement would create difficulty for the participants because the nesting would make it more difficult to individuate the circles and properly enumerate or estimate their number. If these nested stimuli led to "missed" counts of some of the circles because of their arrangement, those counts could not be added to the tally for the whole set.Normally, without such misses, and under conditions of briefly presented stimuli (Kaufman, Lord, Reese, & Volkmann, 1949) or situations in which formal counting was prevented (Beran, Taglialatela, Flemming, James, & Washburn, 2006;Cordes, Gelman, Gallistel, & Whalen, 2001), humans were fairly good at estimating such quantities, although their performance followed the predictions of Weber's Law as estimates become less precise and more variable as a function of the true array size getting larger (Gallistel & Gelman, 2000). However, when Chesney and Gelman (2012) presented the nested sets, participants' response times were longer and their estimations were lower for those sets compared to sets without nested configurations.…”