An emergentist perspective on the origin of number sense

@article{Zorzi2018AnEP,
  title={An emergentist perspective on the origin of number sense},
  author={Marco Zorzi and Alberto Testolin},
  journal={Philosophical Transactions of the Royal Society B: Biological Sciences},
  year={2018},
  volume={373}
}
  • M. Zorzi, Alberto Testolin
  • Published 2018
  • Psychology, Medicine
  • Philosophical Transactions of the Royal Society B: Biological Sciences
The finding that human infants and many other animal species are sensitive to numerical quantity has been widely interpreted as evidence for evolved, biologically determined numerical capacities across unrelated species, thereby supporting a ‘nativist’ stance on the origin of number sense. Here, we tackle this issue within the ‘emergentist’ perspective provided by artificial neural network models, and we build on computer simulations to discuss two different approaches to think about the… Expand
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References

SHOWING 1-10 OF 111 REFERENCES
Development of Elementary Numerical Abilities: A Neuronal Model
TLDR
The computer simulations account for several phenomena in the numerical domain, including the distance effect and Fechner's law for numbers, and demonstrate that infants' numerosity detection abilities may be explained without assuming that infants can count. Expand
Is There Really an Evolved Capacity for Number?
  • R. Núñez
  • Psychology, Medicine
  • Trends in Cognitive Sciences
  • 2017
TLDR
The argument has implications for debates about the origins of other special capacities - geometry, music, art, and language. Expand
Representation of Number in Animals and Humans: A Neural Model
TLDR
This article addresses the representation of numerical information conveyed by nonsymbolic and symbolic stimuli and presents a concrete proposal on the linkage between higher order numerical cognition and more primitive numerical abilities and generates specific predictions on the neural substrate of number processing. Expand
Abstract representations of numbers in the animal and human brain
TLDR
The number domain is a prime example where strong evidence points to an evolutionary endowment of abstract domain-specific knowledge in the brain because there are parallels between number processing in animals and humans. Expand
Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review.
TLDR
It is concluded that rather than taking the ANS theory for granted, a more comprehensive explanation might be provided by a sensory-integration system that compares or estimates large approximate numerosities by integrating the different sensory cues comprising number stimuli. Expand
Ontogeny of Numerical Abilities in Fish
TLDR
The results suggest the ability of guppies to discriminate small numbers is innate and is displayed immediately at birth while discrimination of large numbers emerges later as a result of both maturation and social experience. Expand
Individual differences in non-verbal number acuity correlate with maths achievement
TLDR
There are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual Differences in the present correlate with children’s past scores on standardized maths achievement tests, extending all the way back to kindergarten. Expand
Monotonic Coding of Numerosity in Macaque Lateral Intraparietal Area
TLDR
It is shown, for the first time, that a population of neurons in the lateral intraparietal area of monkeys encodes the total number of elements within their classical receptive fields in a graded fashion, across a wide range of numerical values. Expand
Core systems of number
TLDR
This work reviews recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number, and identifies one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects. Expand
From basic network principles to neural architecture: emergence of spatial-opponent cells.
  • R. Linsker
  • Computer Science, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1986
TLDR
This paper is the first of three that address the origin and organization of feature-analyzing cells in simple systems governed by biologically plausible development rules, and introduces the theory of "modular self-adaptive networks," of which this system is an example, and explicitly demonstrates the emergence of a layer of spatial-opponent cells. Expand
...
1
2
3
4
5
...