How do people apprehend large numerosities?

How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled?

“…As is presented in Table 1, the results of experiments in which experienced observers participated have shown little or no effect of element size and array area Burgess & Barlow, 1983). On the contrary, studies that have introduced naive or less experienced observers have shown the effects of element size and array area (Ginsburg & Nicholls, 1988;Shuman & Spelke, 2006;Sophian & Chu, 2008). Apart from human studies, it has been reported that extensive training was required, at least in the initial phase of an experiment, in studies that required animals to respond to numerosity under controls for perceptual variables (e.g., Nieder et al, 2002;Tomonaga, 2008).…”

“…Learned knowledge, such as "a larger area is supposed to have a large number of elements" or "smaller elements are usually more numerous than larger ones," may influence numerosity judgments. Sophian and Chu (2008) pointed out that the knowledge that a smaller size is often associated with a larger numerosity in daily experience led observers to judge an array composed of smaller elements as more numerous.…”

“…Approximate numerical representation may be abstract, but the process of extracting numerical information requires perceptual information, such as density of elements, cumulative area, spacing, and so forth. Many studies have pointed out that some properties of spatial arrangements of element sets affect a numerosity judgment (e.g., Ginsburg, 1991;Sophian & …”

“…Likewise, Burgess and Barlow (1983) demonstrated that display size and density had little ef-f f fect on precision in numerosity comparison by a 16-fold change of linear dimensions. As for the effect of element size, Ginsburg and Nicholls (1988), Shuman and Spelke (2006), and Sophian and Chu (2008) demonstrated an inverse relationship between item size and the estimation of numerosity, such as when larger items appeared less numerous than small items. By examining Weber fractions in the numerosity discrimination task, Ross (2003) demonstrated that when the size of elements in comparison was altered, the Weber fractions increased, suggesting that the difference in the size of elements elicited the deterioration of precision in numerosity comparison.…”

“…Different processes at the response stage could produce different outcomes for those tasks in numerosity judgments. For example, the recent study by Sophian and Chu (2008) demonstrated that the accuracy of verbal estimates of the numerosities of arrays made upon completion Ginsburg, 1991;Ginsburg & Nicholls, 1988;Krueger, 1972;Shuman & Spelke, 2006;Sophian & Chu, 2008), as well as in young children (Clearfield & Mix, 1999;Cordes & Brannon, 2008Mix, Huttenlocher, & Levine, 2002;Rousselle, Palmers, & Noel, 2004).…”