A shared numerical representation for action and perception

Anobile, Giovanni; Arrighi, Roberto; Togoli, Irene; Burr, David

doi:10.7554/elife.16161

Cited by 68 publications

(73 citation statements)

References 51 publications

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“…Reliability values, reported in Table 1 , ranged from 0.55 to 0.8 (average 0.65). These values are very close to levels that have yielded strong correlations 4 , 35 , giving us confidence that lack of correlation does not stem from poor reliability.…”

Section: Resultssupporting

confidence: 76%

“…Many subsequent investigations supported this theory, showing that actions shape magnitude perception and vice-versa. For example saccadic eye movements cause compression of perceived time as well as space 3 ; motor adaptation distorts numerosity perception 4 ; number magnitude influences grip aperture 5 ; self-produced hand actions modulate the interactions between auditory time and visual motion direction 6 ; voluntary actions shape time perception 7 , 8 ; locomotion impairment (paraplegia) drastically reduces visual sensitivity for perceiving biological motion 9 .…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultssupporting

confidence: 76%

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

Self Cite

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“…This result not only shows that numerosity is not derived indirectly from density, texture or other low-level features, but also casts doubts on the idea that density is a primary visual feature: rather, density seems to be derived indirectly from numerosity, reinforcing previous evidence showing that at low numerosities, density judgments are particularly unreliable and are often surrogated by number judgments . Overall our results add to a growing body of literature showing that visual numerosity is perceived directly, rather than being recalculated from area and density (Anobile, Arrighi, et al, 2016;Anobile, Castaldi, Turi, Tinelli, & Burr, 2016;Anobile et al, 2014;Anobile, Cicchini, et al, 2016;Anobile et al, 2015;Arrighi et al, 2014;Burr & Ross, 2008;Cicchini et al, 2016;DeWind et al, 2015;Hurewitz et al, 2006;Kramer, Di Bono, & Zorzi, 2011;Ross & Burr, 2010Stoianov & Zorzi, 2012).…”

Section: Items Connection Affects Ans and Texture-density 140mentioning

confidence: 62%

“…They have further extended the technique to show that action adaptation can change numerosity. After tapping for a period of time (either rapidly or slowly), the apparent numerosity of a sequence of flashes and of a dot array was strongly changed, in the opposite direction to the tapping speed (Anobile, Arrighi, Togoli, & Burr, 2016). All these adaptation effects are difficult to reconcile with the notion that numerosity is a surrogate of texture-density.…”

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confidence: 76%

Connecting visual objects reduces perceived numerosity and density for sparse but not dense patterns

et al. 2017

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How is numerosity encoded by the visual system? -directly, or derived indirectly from texture density? We recently suggested that the numerosity of sparse patterns is encoded directly by dedicated mechanisms (which have been described as the "Approximate Number System" ANS). However, at high dot densities, where items become "crowded" and difficult to segregate, "texture-density" mechanisms come into play. Here we tested the importance of item segmentation on numerosity and density perception at various stimulus densities, by measuring the effect of connecting visual objects with thin lines. The results confirmed many previous studies showing that connecting items robustly reduces the apparent numerosity of patterns of moderate density. We further showed that the apparent density of moderatedensity patterns is also reduced by connecting the dots. Crucially, we found that both these effects are strongly reduced at higher numerosities. Indeed for density judgments, the effect reverses, so connecting dots in dense patterns increases the apparent density (as expected from the physical characteristics). The results provide clear support for the three-regime framework of number perception, and suggest that for moderately sparse stimuli, numerosity -but not texture-density -is perceived directly.

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“…Interactions between seemingly unrelated perceptual attributes abound: Apparent speed depends on luminance, contrast, and color (Gegenfurtner & Hawken 1996;Thompson 1982); interval duration depends on speed (Brown, 1995;Kanai et al 2006;Kaneko & Murakami 2009); event duration depends on size (Xuan et al 2007); number depends not only on size and density, but also on eye movements (Binda et al 2012;Burr et al 2010) and the region of visual space where stimuli are displayed Hubbard et al 2005). More recently, we demonstrated interactions between action and number estimation, for both sequentially presented items and spatial arrays (Anobile et al 2016a), pointing to even more far-reaching interconnections.…”

Section: Resultsmentioning

confidence: 90%

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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A shared numerical representation for action and perception

Cited by 68 publications

References 51 publications

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

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

Connecting visual objects reduces perceived numerosity and density for sparse but not dense patterns

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

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