Comparing Performance in Discrete and Continuous Comparison Tasks

Abstract

The approximate number system (ANS) theory suggests that all magnitudes, discrete (i.e., number of items) or continuous (i.e., size, density, etc.), are processed by a shared system and comply with Weber's law. The current study reexamined this notion by comparing performance in discrete (comparing numerosities of dot arrays) and continuous (comparisons of area of squares) tasks. We found that: (a) threshold of discrimination was higher for continuous than for discrete comparisons; (b) while performance in the discrete task complied with Weber's law, performance in the continuous task violated it; and (c) performance in the discrete task was influenced by continuous properties (e.g., dot density, dot cumulative area) of the dot array that were not predictive of numerosities or task relevant. Therefore, we propose that the magnitude processing system (MPS) is actually divided into separate (yet interactive) systems for discrete and continuous magnitude processing. Further subdivisions are discussed. We argue that cooperation between these systems results in a holistic comparison of magnitudes, one that takes into account continuous properties in addition to numerosities. Considering the MPS as two systems opens the door to new and important questions that shed light on both normal and impaired development of the numerical system.

One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks

“…Piazza et al suggested the results obtained under these controlled conditions should be attributed to the processing of numerosity and not to continuous magnitudes. However, this method was criticized on several grounds (Gebuis & Reynvoet, 2011;Leibovich & Henik, 2013, 2014Leibovich, Henik, & Salti, 2015). Mainly, disassociating a single continuous magnitude ignores the possibility that participants might rely on several continuous magnitudes or even switch between them (see Leibovich & Henik, 2014).…”

“…However, this method was criticized on several grounds (Gebuis & Reynvoet, 2011;Leibovich & Henik, 2013, 2014Leibovich, Henik, & Salti, 2015). Mainly, disassociating a single continuous magnitude ignores the possibility that participants might rely on several continuous magnitudes or even switch between them (see Leibovich & Henik, 2014). Reynvoet (2011, 2012b) created a code that manipulates congruency between numerosity and one or several continuous magnitudes.…”

“…Leibovich and Henik (2014) presented participants with pairs of dot arrays containing 5-25 dots each and asked them to choose the group containing more dots. They found that the ratio between the continuous magnitudes accounted for half of the explained variance in response times.…”

Asymmetric Processing of Numerical and Nonnumerical Magnitudes in the Brain: An fMRI Study

“…These visual properties are continuous, noncountable dimensions such as density, total surface area, and so forth (hereafter, we will refer to all continuous properties as "nonnumerical magnitudes"). Therefore, it is also possible that, when you are deciding which line to join in the supermarket, you are using nonnumerical magnitudes or a combination of numerical and nonnumerical magnitudes (Leibovich & Henik, 2013;Henik, Leibovich, Naparstek, Diesendruck, & Rubinsten, 2012;Mix et al, 2002).…”

“…Indeed, there is evidence that both numerical (Cantlon, Libertus, et al, 2009;Nieder & Dehaene, 2009) and nonnumerical (e.g., Leibovich & Henik, 2013Gebuis & Reynvoet, 2011;Mix et al, 2002;Clearfield & Mix, 1999) magnitudes are being processed automatically when comparing numerical magnitudes. That is, for example, when deciding which of two dot arrays is numerically larger, the task-irrelevant nonnumerical magnitudes (e.g., array, density) influence RTs and accuracy although they are not relevant to the task.…”