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Kirschhock ME, Nieder A. Numerical Representation for Action in Crows Obeys the Weber-Fechner Law. Psychol Sci 2023; 34:1322-1335. [PMID: 37883792 DOI: 10.1177/09567976231201624] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2023] Open
Abstract
The psychophysical laws governing the judgment of perceived numbers of objects or events, called the number sense, have been studied in detail. However, the behavioral principles of equally important numerical representations for action are largely unexplored in both humans and animals. We trained two male carrion crows (Corvus corone) to judge numerical values of instruction stimuli from one to five and to flexibly perform a matching number of pecks. Our quantitative analysis of the crows' number production performance shows the same behavioral regularities that have previously been demonstrated for the judgment of sensory numerosity, such as the numerical distance effect, the numerical magnitude effect, and the logarithmical compression of the number line. The presence of these psychophysical phenomena in crows producing number of pecks suggests a unified sensorimotor number representation system underlying the judgment of the number of external stimuli and internally generated actions.
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Affiliation(s)
| | - Andreas Nieder
- Animal Physiology Unit, Institute of Neurobiology, University of Tübingen
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2
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Streri A, de Hevia MD. How do human newborns come to understand the multimodal environment? Psychon Bull Rev 2023; 30:1171-1186. [PMID: 36862372 DOI: 10.3758/s13423-023-02260-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 02/18/2023] [Indexed: 03/03/2023]
Abstract
For a long time, newborns were considered as human beings devoid of perceptual abilities who had to learn with effort everything about their physical and social environment. Extensive empirical evidence gathered in the last decades has systematically invalidated this notion. Despite the relatively immature state of their sensory modalities, newborns have perceptions that are acquired, and are triggered by, their contact with the environment. More recently, the study of the fetal origins of the sensory modes has revealed that in utero all the senses prepare to operate, except for the vision mode, which is only functional starting from the first minutes after birth. This discrepancy between the maturation of the different senses leads to the question of how human newborns come to understand our multimodal and complex environment. More precisely, how the visual mode interacts with the tactile and auditory modes from birth. After having defined the tools that newborns use to interact with other sensory modalities, we review studies across different fields of research such as the intermodal transfer between touch and vision, auditory-visual speech perception, and the existence of links between the dimensions of space, time, and number. Overall, evidence from these studies supports the idea that human newborns are spontaneously driven, and cognitively equipped, to link information collected by the different sensory modes in order to create a representation of a stable world.
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Affiliation(s)
- Arlette Streri
- Université Paris Cité, CNRS, Integrative Neuroscience and Cognition Center, F-75006, Paris, France
| | - Maria Dolores de Hevia
- Université Paris Cité, CNRS, Integrative Neuroscience and Cognition Center, F-75006, Paris, France.
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3
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Bosshard TC, Salazar LTH, Laska M. Numerical cognition in black-handed spider monkeys (Ateles geoffroyi). Behav Processes 2022; 201:104734. [PMID: 35970272 DOI: 10.1016/j.beproc.2022.104734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Revised: 06/14/2022] [Accepted: 08/10/2022] [Indexed: 11/16/2022]
Abstract
We assessed two aspects of numerical cognition in a group of nine captive spider monkeys (Ateles geoffroyi). Petri dishes with varying amounts of food were used to assess relative quantity discrimination, and boxes fitted with dotted cards were used to assess discrete number discrimination with equally-sized dots and various-sized dots, respectively. We found that all animals succeeded in all three tasks and, as a group, reached the learning criterion of 70% correct responses within 110 trials in the quantity discrimination task, 160 trials in the numerosity task with equally-sized dots, and 30 trials in the numerosity task with various-sized dots. In all three tasks, the animals displayed a significant correlation between performance in terms of success rate and task difficulty in terms of numerical similarity of the stimuli and thus a ratio effect. The spider monkeys performed clearly better compared to strepsirrhine, catarrhine, and other platyrrhine primates tested previously on both types of numerical cognition tasks and at the same level as chimpanzees, bonobos, and orangutans. Our results support the notion that ecological traits such as a high degree of frugivory and/or social traits such as a high degree of fission-fusion dynamics may underlie between-species differences in cognitive abilities.
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Affiliation(s)
- Tiffany Claire Bosshard
- IFM Biology, Linköping University, SE-581 83 Linköping, Sweden; Cognitive Ethology Laboratory, German Primate Center, D-37077 Göttingen, Germany
| | | | - Matthias Laska
- IFM Biology, Linköping University, SE-581 83 Linköping, Sweden.
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4
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Efficient coding of numbers explains decision bias and noise. Nat Hum Behav 2022; 6:1142-1152. [DOI: 10.1038/s41562-022-01352-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 04/12/2022] [Indexed: 01/29/2023]
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5
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Zhang LQ, Stocker AA. Prior Expectations in Visual Speed Perception Predict Encoding Characteristics of Neurons in Area MT. J Neurosci 2022; 42:2951-2962. [PMID: 35169018 PMCID: PMC8985856 DOI: 10.1523/jneurosci.1920-21.2022] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Revised: 01/18/2022] [Accepted: 01/19/2022] [Indexed: 11/21/2022] Open
Abstract
Bayesian inference provides an elegant theoretical framework for understanding the characteristic biases and discrimination thresholds in visual speed perception. However, the framework is difficult to validate because of its flexibility and the fact that suitable constraints on the structure of the sensory uncertainty have been missing. Here, we demonstrate that a Bayesian observer model constrained by efficient coding not only well explains human visual speed perception but also provides an accurate quantitative account of the tuning characteristics of neurons known for representing visual speed. Specifically, we found that the population coding accuracy for visual speed in area MT ("neural prior") is precisely predicted by the power-law, slow-speed prior extracted from fitting the Bayesian observer model to psychophysical data ("behavioral prior") to the point that the two priors are indistinguishable in a cross-validation model comparison. Our results demonstrate a quantitative validation of the Bayesian observer model constrained by efficient coding at both the behavioral and neural levels.SIGNIFICANCE STATEMENT Statistical regularities of the environment play an important role in shaping both neural representations and perceptual behavior. Most previous work addressed these two aspects independently. Here we present a quantitative validation of a theoretical framework that makes joint predictions for neural coding and behavior, based on the assumption that neural representations of sensory information are efficient but also optimally used in generating a percept. Specifically, we demonstrate that the neural tuning characteristics for visual speed in brain area MT are precisely predicted by the statistical prior expectations extracted from psychophysical data. As such, our results provide a normative link between perceptual behavior and the neural representation of sensory information in the brain.
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6
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Bryer MAH, Koopman SE, Cantlon JF, Piantadosi ST, MacLean EL, Baker JM, Beran MJ, Jones SM, Jordan KE, Mahamane S, Nieder A, Perdue BM, Range F, Stevens JR, Tomonaga M, Ujfalussy DJ, Vonk J. The evolution of quantitative sensitivity. Philos Trans R Soc Lond B Biol Sci 2022; 377:20200529. [PMID: 34957840 PMCID: PMC8710878 DOI: 10.1098/rstb.2020.0529] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability. This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.
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Affiliation(s)
- Margaret A H Bryer
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA.,Department of Psychology, University of California-Berkeley, Berkeley, CA 94720, USA
| | - Sarah E Koopman
- School of Psychology and Neuroscience, University of St. Andrews, St Andrews KY16 9AJ, UK
| | - Jessica F Cantlon
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Steven T Piantadosi
- Department of Psychology, University of California-Berkeley, Berkeley, CA 94720, USA
| | - Evan L MacLean
- School of Anthropology, University of Arizona, Tucson, AZ 85719, USA.,College of Veterinary Medicine, University of Arizona, Tucson, AZ 85719, USA
| | - Joseph M Baker
- Center for Interdisciplinary Brain Sciences Research, Division of Brain Sciences, Department of Psychiatry and Behavioral Sciences, School of Medicine, Stanford University, Stanford, CA 94305, USA
| | - Michael J Beran
- Department of Psychology and Language Research Center, Georgia State University, Atlanta, GA 30302, USA
| | - Sarah M Jones
- Psychology Program, Berea College, Berea, KY 40403, USA
| | - Kerry E Jordan
- Department of Psychology, Utah State University, Logan, UT 84322, USA
| | - Salif Mahamane
- Behavioral and Social Sciences Department, Western Colorado University, Gunnison, CO 81231, USA
| | - Andreas Nieder
- Animal Physiology Unit, Institute of Neurobiology, University of Tübingen, Tübingen 72076, Germany
| | - Bonnie M Perdue
- Department of Psychology, Agnes Scott College, Decatur, GA 30030, USA
| | - Friederike Range
- Domestication Lab, Konrad Lorenz Institute of Ethology, Department of Interdisciplinary Life Sciences, University of Veterinary Medicine Vienna, Savoyenstrasse 1a, Vienna 1160, Austria
| | - Jeffrey R Stevens
- Department of Psychology and Center for Brain, Biology and Behavior, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
| | | | - Dorottya J Ujfalussy
- MTA-ELTE Comparative Ethology Research Group, Eötvös Loránd University of Sciences (ELTE), Budapest 1117, Hungary.,Department of Ethology, Eötvös Loránd University of Sciences (ELTE), Budapest 1117, Hungary
| | - Jennifer Vonk
- Department of Psychology, Oakland University, Rochester, MI 48309, USA
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7
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Fornaciai M, Park J. Disentangling feedforward versus feedback processing in numerosity representation. Cortex 2020; 135:255-267. [PMID: 33412370 DOI: 10.1016/j.cortex.2020.11.013] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Revised: 07/26/2020] [Accepted: 11/16/2020] [Indexed: 11/18/2022]
Abstract
Numerosity is a fundamental aspect of the external environment, needed to guide our behavior in an effective manner. Previous studies show that numerosity processing involves at least two temporal stages (~100 and ~150 msec after stimulus onset) in early visual cortex. One possibility is that the two stages reflect an initial feedforward processing followed by feedback signals from higher-order cortical areas that underlie segmentation of visual inputs into perceptual units that define numerosity. Alternatively, multiple stages of feedforward processing might progressively refine the input leading to the segmented representation. Here, we distinguish these two hypotheses by exploiting the connectedness illusion (i.e., the systematic underestimation of pairwise-connected dots), backward masking (to suppress feedback signals), and serial dependence (i.e., a perceptual bias making a stimulus appear to be more similar to its preceding one). Our results show that a connected dot array biases the numerosity representation of the subsequent dot array based on its illusory perception, irrespective of whether it is visible or suppressed by masking. These findings demonstrate that feedback processing is not strictly necessary for the perceptual segmentation that gives rise to perceived numerosity, and instead suggest that different stages of feedforward activity presumably carrying low and high spatial frequency information are sufficient to create a numerosity representation in early visual areas.
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Affiliation(s)
- Michele Fornaciai
- Department of Psychological and Brain Sciences, University of Massachusetts Amherst, MA, USA.
| | - Joonkoo Park
- Department of Psychological and Brain Sciences, University of Massachusetts Amherst, MA, USA; Commonwealth Honors College, University of Massachusetts Amherst, MA, USA
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8
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Cheyette SJ, Piantadosi ST. A unified account of numerosity perception. Nat Hum Behav 2020; 4:1265-1272. [PMID: 32929205 DOI: 10.1038/s41562-020-00946-0] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 08/07/2020] [Indexed: 01/29/2023]
Abstract
People can identify the number of objects in sets of four or fewer items with near-perfect accuracy but exhibit linearly increasing error for larger sets. Some researchers have taken this discontinuity as evidence of two distinct representational systems. Here, we present a mathematical derivation showing that this behaviour is an optimal representation of cardinalities under a limited informational capacity, indicating that this behaviour can emerge from a single system. Our derivation predicts how the amount of information accessible to viewers should influence the perception of quantity for both large and small sets. In a series of four preregistered experiments (N = 100 each), we varied the amount of information accessible to participants in number estimation. We find tight alignment between the model and human performance for both small and large quantities, implicating efficient representation as the common origin behind key phenomena of human and animal numerical cognition.
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9
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Nieder A. Absolute Numerosity Discrimination as a Case Study in Comparative Vertebrate Intelligence. Front Psychol 2020; 11:1843. [PMID: 32849085 PMCID: PMC7426444 DOI: 10.3389/fpsyg.2020.01843] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2020] [Accepted: 07/06/2020] [Indexed: 01/29/2023] Open
Abstract
The question of whether some non-human animal species are more intelligent than others is a reoccurring theme in comparative psychology. To convincingly address this question, exact comparability of behavioral methodology and data across species is required. The current article explores one of the rare cases in which three vertebrate species (humans, macaques, and crows) experienced identical experimental conditions during the investigation of a core cognitive capability – the abstract categorization of absolute numerical quantity. We found that not every vertebrate species studied in numerical cognition were able to flexibly discriminate absolute numerosity, which suggests qualitative differences in numerical intelligence are present between vertebrates. Additionally, systematic differences in numerosity judgment accuracy exist among those species that could master abstract and flexible judgments of absolute numerosity, thus arguing for quantitative differences between vertebrates. These results demonstrate that Macphail’s Null Hypotheses – which suggests that all non-human vertebrates are qualitatively and quantitatively of equal intelligence – is untenable.
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Affiliation(s)
- Andreas Nieder
- Animal Physiology Unit, Institute of Neurobiology, University of Tübingen, Tübingen, Germany
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10
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Nieder A. The Adaptive Value of Numerical Competence. Trends Ecol Evol 2020; 35:605-617. [DOI: 10.1016/j.tree.2020.02.009] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2019] [Revised: 02/08/2020] [Accepted: 02/14/2020] [Indexed: 01/25/2023]
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11
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Aulet LS, Chiu VC, Prichard A, Spivak M, Lourenco SF, Berns GS. Canine sense of quantity: evidence for numerical ratio-dependent activation in parietotemporal cortex. Biol Lett 2019; 15:20190666. [PMID: 31847744 PMCID: PMC6936025 DOI: 10.1098/rsbl.2019.0666] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
The approximate number system (ANS), which supports the rapid estimation of quantity, emerges early in human development and is widespread across species. Neural evidence from both human and non-human primates suggests the parietal cortex as a primary locus of numerical estimation, but it is unclear whether the numerical competencies observed across non-primate species are subserved by similar neural mechanisms. Moreover, because studies with non-human animals typically involve extensive training, little is known about the spontaneous numerical capacities of non-human animals. To address these questions, we examined the neural underpinnings of number perception using awake canine functional magnetic resonance imaging. Dogs passively viewed dot arrays that varied in ratio and, critically, received no task-relevant training or exposure prior to testing. We found evidence of ratio-dependent activation, which is a key feature of the ANS, in canine parietotemporal cortex in the majority of dogs tested. This finding is suggestive of a neural mechanism for quantity perception that has been conserved across mammalian evolution.
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Affiliation(s)
- Lauren S Aulet
- Department of Psychology, Emory University, Atlanta, GA 30322, USA
| | - Veronica C Chiu
- Department of Psychology, Emory University, Atlanta, GA 30322, USA
| | - Ashley Prichard
- Department of Psychology, Emory University, Atlanta, GA 30322, USA
| | - Mark Spivak
- Comprehensive Pet Therapy, Atlanta, GA 30328, USA
| | | | - Gregory S Berns
- Department of Psychology, Emory University, Atlanta, GA 30322, USA
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12
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Nieder A. Neural constraints on human number concepts. Curr Opin Neurobiol 2019; 60:28-36. [PMID: 31810008 DOI: 10.1016/j.conb.2019.10.003] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Revised: 10/09/2019] [Accepted: 10/11/2019] [Indexed: 01/29/2023]
Abstract
True counting and arithmetic abilities are unique to humans and are inextricably linked to symbolic competence. However, our unprecedented numerical skills are deeply rooted in our neuronal heritage as primates and vertebrates. In this article, I argue that numerical competence in humans is the result of three neural constraints. First, I propose that the neuronal mechanisms of quantity estimation are part of our evolutionary heritage and can be witnessed across primate and vertebrate phylogeny. Second, I suggest that a basic understanding of number, what numerical quantity means, is innately wired into the brain and gives rise to an intuitive number sense, or number instinct. Third and finally, I argue that symbolic counting and arithmetic in humans is rooted in an evolutionarily and ontogenetically primeval neural system for non-symbolic number representations. These three neural constraints jointly determine the basic processing of number concepts in the human mind.
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Affiliation(s)
- Andreas Nieder
- Animal Physiology Unit, Institute of Neurobiology, University of Tübingen, Auf der Morgenstelle 28, 72076 Tübingen, Germany.
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13
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Cheyette SJ, Piantadosi ST. A primarily serial, foveal accumulator underlies approximate numerical estimation. Proc Natl Acad Sci U S A 2019; 116:17729-17734. [PMID: 31427541 PMCID: PMC6731650 DOI: 10.1073/pnas.1819956116] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The approximate number system (ANS) has attracted broad interest due to its potential importance in early mathematical development and the fact that it is conserved across species. Models of the ANS and behavioral measures of ANS acuity both assume that quantity estimation is computed rapidly and in parallel across an entire view of the visual scene. We present evidence instead that ANS estimates are largely the product of a serial accumulation mechanism operating across visual fixations. We used an eye-tracker to collect data on participants' visual fixations while they performed quantity-estimation and -discrimination tasks. We were able to predict participants' numerical estimates using their visual fixation data: As the number of dots fixated increased, mean estimates also increased, and estimation error decreased. A detailed model-based analysis shows that fixated dots contribute twice as much as peripheral dots to estimated quantities; people do not "double count" multiply fixated dots; and they do not adjust for the proportion of area in the scene that they have fixated. The accumulation mechanism we propose explains reported effects of display time on estimation and earlier findings of a bias to underestimate quantities.
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Affiliation(s)
- Samuel J Cheyette
- Department of Psychology, University of California, Berkeley, CA 94720
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14
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Looking for more food or more people? Task context influences basic numerosity perception. Cortex 2019; 114:67-75. [DOI: 10.1016/j.cortex.2018.05.021] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2017] [Revised: 05/12/2018] [Accepted: 05/28/2018] [Indexed: 11/22/2022]
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15
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Why are conversations limited to about four people? A theoretical exploration of the conversation size constraint. EVOL HUM BEHAV 2019. [DOI: 10.1016/j.evolhumbehav.2018.09.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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16
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Fornaciai M, Park J. Early Numerosity Encoding in Visual Cortex Is Not Sufficient for the Representation of Numerical Magnitude. J Cogn Neurosci 2018; 30:1788-1802. [DOI: 10.1162/jocn_a_01320] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Recent studies have demonstrated that the numerosity of visually presented dot arrays is represented in low-level visual cortex extremely early in latency. However, whether or not such an early neural signature reflects the perceptual representation of numerosity remains unknown. Alternatively, such a signature may indicate the raw sensory representation of the dot-array stimulus before becoming the perceived representation of numerosity. Here, we addressed this question by using the connectedness illusion, whereby arrays with pairwise connected dots are perceived to be less numerous compared with arrays containing isolated dots. Using EEG and fMRI in two independent experiments, we measured neural responses to dot-array stimuli comprising 16 or 32 dots, either isolated or pairwise connected. The effect of connectedness, which reflects the segmentation of the visual stimulus into perceptual units, was observed in the neural activity after 150 msec post stimulus onset in the EEG experiment and in area V3 in the fMRI experiment using a multivariate pattern analysis. In contrast, earlier neural activity before 100 msec and in area V2 was strictly modulated by numerosity regardless of connectedness, suggesting that this early activity reflects the sensory representation of a dot array before perceptual segmentation. Our findings thus demonstrate that the neural representation for numerosity in early visual cortex is not sufficient for visual number perception and suggest that the perceptual encoding of numerosity occurs at or after the segmentation process that takes place later in area V3.
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17
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Kim D, Opfer JE. Dynamics and development in number-to-space mapping. Cogn Psychol 2018; 107:44-66. [PMID: 30439563 DOI: 10.1016/j.cogpsych.2018.10.001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Revised: 05/17/2018] [Accepted: 10/11/2018] [Indexed: 01/29/2023]
Abstract
Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic encoding mechanism that is sensitive to previously encountered stimuli. Here we examine trial-to-trial changes in logarithmicity of numerosity estimates to test an alternative dynamic model (D-MLLM) with both a strong logarithmic component and a weak response to previous stimuli. In support of D-MLLM, first-trial numerosity estimates in both adults (Study 1, 2, 3, and 4) and children (Study 4) were strongly logarithmic, despite zero previous stimuli. Additionally, although numerosity of a previous trial affected adults' estimates, the influence of previous numbers always accompanied the logarithmic-to-linear shift predicted by D-MLLM. We conclude that a dynamic encoding mechanism is not necessary for compressive mapping, but sequential effects on response scaling are a possible source of linearity in adults' numerosity estimation.
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Affiliation(s)
- Dan Kim
- The Ohio State University, 255 Psychology Building, Columbus, OH 43210, USA.
| | - John E Opfer
- The Ohio State University, 255 Psychology Building, Columbus, OH 43210, USA.
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18
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Abstract
The types of cognitive and neural mechanisms available to children for making concepts depend on the problems their brains evolved to solve over the past millions of years. Comparative research on numerical cognition with humans and nonhuman primates has revealed a system for quantity representation that lays the foundation for quantitative development. Nonhuman primates in particular share many human abilities to compute quantities, and are likely to exhibit evolutionary continuity with humans. While humans conceive of quantity in ways that are similar to other primates, they are unique in their capacity for symbolic counting and logic. These uniquely human constructs interact with primitive systems of numerical reasoning. In this article, I discuss how evolution shapes human numerical concepts through evolutionary constraints on human object-based perception and cognition, neural homologies among primates, and interactions between uniquely human concepts and primitive logic.
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19
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