Holistic processing of numerical arrays.

Abstract

At the early stages of concept acquisition, physical properties are inseparable of the concepts they form. With development, the concept seems to depart from the physical entities from which it emerged and seems to exist beyond its physical attributes. Numerosity is an abstract concept; however, physical properties such as diameter, area, and density have been shown to affect its perception in nonsymbolic comparison tasks. It remains unclear how these properties interact with numerosity and which property is most influential. We equated the ratio of 3 physical properties (average diameter, total surface area, and convex hull area) to the numerical ratio in order to examine which property is most discriminable and, therefore, most likely to be used. Our results demonstrate that convex hull is the most discriminable property. We suggest that holistic processing through global properties, such as convex hull, bridges between the physical world and abstract concepts. (PsycINFO Database Record

The averaging of numerosities: A psychometric investigation of the mental line

“…Research over the past two decades has converged on the idea that humans (including infants) and animals have at their disposal a set of analog numerosity (or magnitude) representations, which allows them to estimate and discriminate the numerosity of large sets of items (e.g., dots in a visual display or rapid sequences of sound clicks) without counting (Barth, Kanwisher, & Spelke, 2003 ; Dehaene, Dehaene-Lambertz, & Cohen, 1998 ; Feigenson, Dehaene, & Spelke, 2004 ; Gallistel & Gelman, 2000 ; Katzin, Salti, & Henik, 2018 ; Leibovich & Henik, 2014 ; Nieder, Freedman, & Miller, 2002 ; Nieder & Miller, 2003 ; Piazza, Pinel, Le Bihan, & Dehaene, 2007 ; Whalen, Gallistel, & Gelman, 1999 ). These numerosity representations, also labeled as the approximate number system (ANS), are akin to a “number line,” which is thought to be mediated by broadly tuned numerosity detectors in the parietal cortex (Nieder et al, 2002 ; Nieder & Miller, 2003 ).…”

Shaping the way from the unknown to the known: The role of convex hull shape in numerical comparisons

“…Importantly, different physical properties are correlated with numerosity and are intercorrelated with one another (Salti, Katzin, Katzin, Leibovich, & Henik, 2017). Two arrays with different numerosities cannot have the same physical properties (Katzin, Salti, & Henik, 2019;Leibovich & Henik, 2013). Therefore, it is impossible to dissociate the physical properties and numerosity of non-symbolic arrays (Gebuis & Reynvoet, 2011;Leibovich et al, 2017;Salti et al, 2017).…”

“…Extrinsic properties include density and the convex hull (CH) and consider the locations and sizes of the elements. The CH is the smallest polygon containing all objects in an array with all of its angles less than or equal to 180 degrees (Katzin et al, 2019;Weisstein, 2002). A common way to describe the CH is the shape that emerges if a rubber band is wrapped around the array (Bentley, Kung, Schkolnick, & Thompson, 1978;Day, 1988;Liao, Lu, Ma, Xue, & Yu, 2012).…”

“…In contrast, in an incongruent trial, one physical property was equal to the inverse of the numerical ratio, while the rest of the properties were also incongruent, but not necessarily equal to the inverse of the numerical ratio. Studies that used this method (Katzin et al, 2019;Salti et al, 2017) and other studies (Gebuis & Reynvoet, 2012;Gilmore, Cragg, Hogan, & Inglis, 2016) showed that the CH-Area is the physical property that influences numerical comparisons. Importantly, these studies did not control for or attend the effects of CH-Shape during numerical comparisons.…”

“…Our first objective was to examine whether CH-Shape has a role in numerical comparisons in addition to its role in enumeration (Katzin et al, 2020). For that purpose, we re-analyzed the data from Katzin et al (2019) and included data on the CH-Shape. We hypothesized that the CH-Shape would have an effect on performance above and beyond the effect of the rest of the stimuli physical properties, including the CH-Area (that was specifically examined in Katzin et al's [2019] experiments).…”