Compressed Scaling of Abstract Numerosity Representations in Adult Humans and Monkeys

Merten, Katharina; Nieder, Andreas

doi:10.1162/jocn.2008.21032

Cited by 82 publications

(120 citation statements)

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“…The mean goodness-of-fit values for the linear scale, the power function with exponent of 0.5, the power function with exponent of 0.33, and the logarithmic scale were 0.75, 0.77, 0.78, and 0.78. Also similar to the behavioral data, and as predicted by a nonlinear coding model (27)(28)(29), the variance of neural distributions was more or less constant with increasing preferred numerosity when the data were plotted on a logarithmic scale (slope of linear fit = −0.022), but increased with numerosity when the data were plotted on a linear scale (slope = 0.068) (Fig. 3D).…”

Section: Resultssupporting

confidence: 79%

“…curves) was constant when the data were plotted on a power function scale with 0.33 exponent (slope of linear fit = 0.135) and the logarithmic scale (slope of linear fit = 0.007) (Fig. 1H), which is predicted by a nonlinear coding model of numerosity (27)(28)(29). Thus, performance data for numerosity judgments is better described by using a power function compressed or above all a logarithmically compressed scale, as opposed to a linear scale.…”

Section: Resultsmentioning

confidence: 88%

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Neurons selective to the number of visual items in the corvid songbird endbrain

Ditz

Nieder

2015

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

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It is unknown whether anatomical specializations in the endbrains of different vertebrates determine the neuronal code to represent numerical quantity. Therefore, we recorded single-neuron activity from the endbrain of crows trained to judge the number of items in displays. Many neurons were tuned for numerosities irrespective of the physical appearance of the items, and their activity correlated with performance outcome. Comparison of both behavioral and neuronal representations of numerosity revealed that the data are best described by a logarithmically compressed scaling of numerical information, as postulated by the WeberFechner law. The behavioral and neuronal numerosity representations in the crow reflect surprisingly well those found in the primate association cortex. This finding suggests that distantly related vertebrates with independently developed endbrains adopted similar neuronal solutions to process quantity.single-cell recordings | crow | nidopallium caudolaterale | quantity B irds show elaborate quantification skills (1-3) that are of adaptive value in naturalistic situations like nest parasitism (4), food caching (5), or communication (6). The neuronal correlates of numerosity representations have only been explored in humans (7-9) and primates (10-18), and they have been found to reside in the prefrontal and posterior parietal neocortices. In contrast to primates, birds lack a six-layered neocortex. The birds' lineage diverged from mammals 300 Mya (19), at a time when the neocortex had not yet developed from the pallium of the endbrain. Instead, birds developed different pallial parts as dominant endbrain structures (20, 21) based on convergent evolution, with the nidopallium caudolaterale (NCL) as a highlevel association area (22-26). Where and how numerosity is encoded in vertebrates lacking a neocortex is unknown. Here, we show that neurons in the telencephalic NCL of corvid songbirds respond to numerosity and show a specific code for numerical information. ResultsCrows were trained in a delayed matching-to-sample task to match the number of (one to five) dots presented on touch-sensitive computer displays ( Fig. 1 A and B). Crows watched two displays (first sample, then test) separated by a 1-s delay. They were trained to peck at the displays on the screen if the test displays contained the same number of items as the sample. We varied the exact physical appearance of the displays by randomly placing dots in arbitrary locations, and by randomly choosing dot size.The crows performed the task proficiently (73.8 ± 0.4% and 77.5 ± 0.5% correct over all recording sessions for crow A and crow J, respectively; Fig. 1C). Average performance of both crows was significantly better than chance (50%) for all sample numerosities relative to the numerically most distant nonmatches (Binomial test, P < 0.01). Better performance for sample numerosities at the low (one) and high (five) numerosity range (Fig. 1D) are most likely due to "endeffects," because one and five items had to be discriminated only fro...

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Section: Resultssupporting

confidence: 79%

Section: Resultsmentioning

confidence: 88%

Neurons selective to the number of visual items in the corvid songbird endbrain

Ditz

Nieder

2015

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

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156

187

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“…If the magnitude of the ratio is small, for example, 15 dots versus 16 dots (15:16 ratio), responses tend to be slower than in the easy ratio condition, and the accuracy is typically lower (Barth, et al., 2003; Cordes, Gelman, Gallistel, & Whalen, 2001; Pica, Lemer, Izard, & Dehaene, 2004), indicating harder comparison. Converging evidence from developmental and comparative studies as well as studies with people whose languages do not have number words shows ratio‐dependent performance on nonsymbolic number comparison tasks suggesting a key feature of the ANS: independence from language (Cantlon, Brannon, Carter, & Pelphrey, 2006; Izard, Sann, Spelke, & Streri, 2009; Libertus and Brannon, 2009; Lipton & Spelke, 2003; Nieder, 2009; Pica et al., 2004; Xu & Spelke, 2000). …”

Section: Introductionmentioning

confidence: 99%

The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

et al. 2018

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IntroductionAdults can represent numerical information in nonsymbolic and symbolic formats and flexibly switch between the two. While some studies suggest a strong link between the two number representation systems (e.g., Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004 Neuron, 44(3), 547), other studies show evidence against the strong‐link hypothesis (e.g., Lyons, Ansari, & Beilock, 2012 Journal of Experimental Psychology: General, 141(4), 635). This inconsistency could arise from the relation between task demands and the closeness of the link between the two number systems.MethodsWe used a passive viewing task and event‐related potentials (ERP) to examine the temporal dynamics of the implicit integration between the nonsymbolic and symbolic systems. We focused on two ERP components over posterior scalp sites that were found to be sensitive to numerical distances and ratio differences in both numerical formats: a negative component that peaks around 170 ms poststimulus (N1) and a positive component that peaks around 200 ms poststimulus (P2p). We examined adults' (n = 55) ERPs when they were passively viewing simultaneously presented dot quantities and Arabic numerals (i.e., nonsymbolic and symbolic numerical information) in the double‐digit range. For each stimulus, the nonsymbolic and symbolic content either matched or mismatched in number. We also asked each participant to estimate dot quantities in a separate behavioral task and observed that they tended to underestimate the actual dot quantities, suggesting a need to adjust the match between nonsymbolic and symbolic information to reflect the perceived quantity of the nonsymbolic information.ResultsUsing this adjustment, participants showed greater N1 and P2p amplitudes when perceived dot quantities matched Arabic numerals than when there was a mismatch. However, no differences were found between the unadjusted match and mismatch conditions.ConclusionOur findings suggest that adults rapidly integrate nonsymbolic and symbolic formats of double‐digit numbers, but evidence of such integration is best observed when the perceived (rather than veridical) dot quantity is considered.

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“…probability density functions) that indicate subjects' behavioural representations of cardinal number. So far, numerical scaling has only been tested in two primate species: rhesus monkeys and humans [46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Numerosity representations in crows obey the Weber–Fechner law

Ditz¹,

Nieder²

2016

Proc. R. Soc. B.

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The ability to estimate number is widespread throughout the animal kingdom. Based on the relative close phylogenetic relationship (and thus equivalent brain structures), non-verbal numerical representations in human and nonhuman primates show almost identical behavioural signatures that obey the Weber-Fechner law. However, whether numerosity discriminations of vertebrates with a very different endbrain organization show the same behavioural signatures remains unknown. Therefore, we tested the numerical discrimination performance of two carrion crows (Corvus corone) to a broad range of numerosities from 1 to 30 in a delayed match-to-sample task similar to the one used previously with primates. The crows' discrimination was based on an analogue number system and showed the Weber-fraction signature (i.e. the 'just noticeable difference' between numerosity pairs increased in proportion to the numerical magnitudes). The detailed analysis of the performance indicates that numerosity representations in crows are scaled on a logarithmically compressed 'number line'. Because the same psychophysical characteristics are found in primates, these findings suggest fundamentally similar number representations between primates and birds. This study helps to resolve a classical debate in psychophysics: the mental number line seems to be logarithmic rather than linear, and not just in primates, but across vertebrates.

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Compressed Scaling of Abstract Numerosity Representations in Adult Humans and Monkeys

Cited by 82 publications

References 47 publications

Neurons selective to the number of visual items in the corvid songbird endbrain

Neurons selective to the number of visual items in the corvid songbird endbrain

The integration between nonsymbolic and symbolic numbers: Evidence from an EEG study

Numerosity representations in crows obey the Weber–Fechner law

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