In this review, we are pitting two theories against each other: the more accepted theory, the number sense theory, suggesting that a sense of number is innate and non-symbolic numerosity is being processed independently of continuous magnitudes (e.g., size, area, and density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities and (2) a sense of number might not be innate. In the first part of this review, we discuss the number sense theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore, the results of behavioral and imaging studies with infants, adults, and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the sense of magnitude theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test and consider whether such an assumption is even testable in the light of the correlation of numerosity and continuous magnitudes.

Non-symbolic stimuli (i.e., dot arrays) are commonly used to study numerical cognition. However, in addition to numerosity, non-symbolic stimuli entail continuous magnitudes (e.g., total surface area, convex-hull, etc.) that correlate with numerosity. Several methods for controlling for continuous magnitudes have been suggested, all with the same underlying rationale: disassociating numerosity from continuous magnitudes. However, the different continuous magnitudes do not fully correlate; therefore, it is impossible to disassociate them completely from numerosity. Moreover, relying on a specific continuous magnitude in order to create this disassociation may end up in increasing or decreasing numerosity saliency, pushing subjects to rely on it more or less, respectively. Here, we put forward a taxonomy depicting the relations between the different continuous magnitudes. We use this taxonomy to introduce a new method with a complimentary Matlab toolbox that allows disassociating numerosity from continuous magnitudes and equating the ratio of the continuous magnitudes to the ratio of the numerosity in order to balance the saliency of numerosity and continuous magnitudes. A dot array comparison experiment in the subitizing range showed the utility of this method. Equating different continuous magnitudes yielded different results. Importantly, equating the convex hull ratio to the numerical ratio resulted in similar interference of numerical and continuous magnitudes.

Humans and animals are capable of estimating and discriminating nonsymbolic numerosities via mental representation of magnitudes-the approximate number system (ANS). There are two models of the ANS system, which are similar in their prediction in numerosity discrimination tasks. The log-Gaussian model, which assumes numerosities are represented on a compressed logarithmic scale, and the scalar variability model, which assumes numerosities are represented on a linear scale. In the first experiment of this paper, we contrasted these models using averaging of numerosities. We examined whether participants generate a compressed mean (i.e., geometric mean) or a linear mean when averaging two numerosities. Our results demonstrated that half of the participants are linear and half are compressed; however, in general, the compression is milder than a logarithmic compression. In Experiments 2 and 3, we examined averaging of numerosities in sequences larger than two. We found that averaging precision increases with sequence length. These results are in line with previous findings, suggesting a mechanism in which the estimate is generated by population averaging of the responses each stimulus generates on the numerosity representation.

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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