Size Perception and the Foundation of Numerical Processing

Henik, Avishai; Gliksman, Yarden; Kallai, Arava Y.; Leibovich, Tali

doi:10.1177/0963721416671323

Cited by 52 publications

(50 citation statements)

References 47 publications

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“…With time, infants explore their environment and learn by experience that usually more toys will take more space in their toy box, or put more generally, that numerosity and continuous magnitudes positively correlate. It is only after understanding this correlation that the number sense and the idea of numerosity can develop (for a similar ideas see Henik et al 2017).…”

Section: The Role Of Continuous Magnitudes In Numerical Cognitionmentioning

confidence: 98%

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

et al. 2016

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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.

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Section: The Role Of Continuous Magnitudes In Numerical Cognitionmentioning

confidence: 98%

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

et al. 2016

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“…Among these, a Theory of Magnitude (ATOM) describes the relationship between continuous magnitudes and numerosity in terms of a unique system that is capable of representing any kind of discrete and continuous magnitude, including numerosity, time (duration), and space (extension) (16). Some authors proposed a general sense of magnitude for both continuous and discrete quantities, in which size perception is developmentally and evolutionarily more primitive than numerosity, and continuous magnitude plays a key role in the development of numerical magnitude processing (17,18). There is substantial empirical evidence supporting both common and separate neural areas for numerical and continuous magnitudes (e.g., refs.…”

Section: This Article Is a Pnas Direct Submissionmentioning

confidence: 99%

The neural signature of numerosity by separating numerical and continuous magnitude extraction in visual cortex with frequency-tagged EEG

Rinsveld

Guillaumé

Kohler

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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The ability to handle approximate quantities, or number sense, has been recurrently linked to mathematical skills, although the nature of the mechanism allowing to extract numerical information (i.e., numerosity) from environmental stimuli is still debated. A set of objects is indeed not only characterized by its numerosity but also by other features, such as the summed area occupied by the elements, which often covary with numerosity. These intrinsic relations between numerosity and nonnumerical magnitudes led some authors to argue that numerosity is not independently processed but extracted through a weighting of continuous magnitudes. This view cannot be properly tested through classic behavioral and neuroimaging approaches due to these intrinsic correlations. The current study used a frequency-tagging EEG approach to separately measure responses to numerosity as well as to continuous magnitudes. We recorded occipital responses to numerosity, total area, and convex hull changes but not to density and dot size. We additionally applied a model predicting primary visual cortex responses to the set of stimuli. The model output was closely aligned with our electrophysiological data, since it predicted discrimination only for numerosity, total area, and convex hull. Our findings thus demonstrate that numerosity can be independently processed at an early stage in the visual cortex, even when completely isolated from other magnitude changes. The similar implicit discrimination for numerosity as for some continuous magnitudes, which correspond to basic visual percepts, shows that both can be extracted independently, hence substantiating the nature of numerosity as a primary feature of the visual scene. numerical cognition | numerosity extraction | fast periodic visual stimulation | quantities | nonsymbolic mathematical abilities

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“…At what processing level do these interactions arise? Although the “magnitude sense theory” postulates a shared sensory representation for numerosity and magnitude, throughout cortical recycling 20 , interference may also arise at late decisional stages, well beyond primary sensory processing. Moreover, many primary perceptual attributes interact with each other while maintaining clear separate representations.…”

Section: Introductionmentioning

confidence: 99%

Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude

Anobile

Burr

Iaia

et al. 2018

Sci Rep

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How numerical quantity is processed is a central issue for cognition. On the one hand the “number sense theory” claims that numerosity is perceived directly, and may represent an early precursor for acquisition of mathematical skills. On the other, the “theory of magnitude” notes that numerosity correlates with many continuous properties such as size and density, and may therefore not exist as an independent feature, but be part of a more general system of magnitude. In this study we examined interactions in sensitivity between numerosity and size perception. In a group of children, we measured psychophysically two sensory parameters: perceptual adaptation and discrimination thresholds for both size and numerosity. Neither discrimination thresholds nor adaptation strength for numerosity and size correlated across participants. This clear lack of correlation (confirmed by Bayesian analyses) suggests that numerosity and size interference effects are unlikely to reflect a shared sensory representation. We suggest these small interference effects may rather result from top-down phenomena occurring at late decisional levels rather than a primary “sense of magnitude”.

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Size Perception and the Foundation of Numerical Processing

Cited by 52 publications

References 47 publications

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

The neural signature of numerosity by separating numerical and continuous magnitude extraction in visual cortex with frequency-tagged EEG

Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude

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