The second number-estimation elbow: Are visual numbers greater than 20 evaluated differently?

Abstract

Numerosity perception has long been understood to be divided between subitizing and estimation. In a series of three experiments (total N = 113), a new number "elbow" point in the estimation of visual number for numerosities of about 20 dots is confirmed. Below 20, mean estimates are linear with a slope of about 1 and power-function exponents for numerosity estimation approximate unity, though estimate variance increases dramatically above about 6 elements. For numerosities above 20, estimates become increasingly compressed, such that power function exponents are much lower (e.g., 0.7) and are lower still when both ranges are estimated within the same experimental procedure. The experiments described here show that the location of the inflection point appears insensitive to the range of numbers estimated and to differences in density.

Visual illusions as a tool to hijack numerical perception: Disentangling nonsymbolic number from its continuous visual properties.

“…However, it is worth noting that for numerosities higher than those we used here (e.g., >20 items), a different visual mechanism for numerical quantification exploiting area and density information may be at play (Portley & Durgin, 2019). For example, it has been recently proposed that a dedicated system for density perception may operate over larger ranges (e.g., 100 items), in which items are highly cluttered or crowded, making their segmentation hard (Anobile et al, 2014, 2016; cf.…”

“…For example, it has been recently proposed that a dedicated system for density perception may operate over larger ranges (e.g., 100 items), in which items are highly cluttered or crowded, making their segmentation hard (Anobile et al, 2014, 2016; cf. Portley et al, 2019). Specifically, these studies reported that the participants’ Weber fraction was constant over a low numerosity range, but, after a critical numerosity, it decreased proportionally to the square root of numbers (Anobile et al, 2014).…”

Parietal Contributions to Abstract Numerosity Measured With Steady State Visual Evoked Potentials

“…System" in which estimated magnitudes scale logarithmically with number of tokens has been demonstrated for quantities in a second regime between 5 and ~50 (Atkinson et al, 1976;Feigenson et al, 2004;Piazza et al, 2007;Anobile et al, 2014). A third regime has been demonstrated that invokes texture-like processing with even larger quantities (Anobile et al, 2016;Portley and Durgin, 2019).…”

“…Dot coordinates and sizes were generated using a previously published algorithm (Piazza et al, 2004) that was designed to ensure that standard and oddball updates were statistically matched in terms of non-number properties. Dots were drawn with a dark inner dot surrounded by a brighter outer ring of equal area to eliminate confounding luminance and numerosity (Carlson et al, 1984;Huk and Durgin, 1996;Portley and Durgin, 2019). The inner dot and outer ring were made to have approximately the same number of pixels, but rounding error made a perfect luminance match with the background impossible.…”

Spatial number estimation has a higher linear range than temporal number estimation; differential affordances for subdivision might help to explain why

“…In the absence of pretraining or other opportunities to calibrate spatial number estimation, Portley and Durgin (2019) observed that estimates of visual number were, on average, accurate up to about 20 items but underestimated actual number thereafter. By varying the range of numbers tested, Portley and Durgin showed that this effect was not due to some sort of central tendency but instead seemed to occur near 20 even when relatively few numbers beyond 20 were tested and most were below, or when relatively few numbers below 20 were tested and most were above 20.…”