ABSTRACT—Subitizing is the rapid and accurate,enumer- ation of small sets (up to 3–4 items). Alth... more ABSTRACT—Subitizing is the rapid and accurate,enumer- ation of small sets (up to 3–4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying mechanisms remain debated. One hypothesis proposes,that subitizing results from nu- merical estimation mechanisms that, according to Weber’s law, operate with high precision for small numbers. Al- ternatively, subitizing might rely
Evolutionary and Developmental Perspectives on Mind, Brain, and Behavior, 2009
Historically, many mathematical advances have been developed through the use of conceptual mappin... more Historically, many mathematical advances have been developed through the use of conceptual mappings between numbers and space. From the most elementary aspects of mathematics, such as the notion of measurement, all the way up to the concepts of the real number line, Cartesian coordinates, the complex plane, and even the proof of Fermat's Last Theorem, metaphors by which numbers are made to correspond to spatial positions permeate mathematical thinking . The evolution of these culturally defined representations of number has been critical to the development of mathematics. In this chapter, we review and update our previous models ) discussing the neural mechanisms that might underpin these cultural achievements. We begin by reviewing recent behavioral, patient, and transcranial magnetic stimulation (TMS) data showing that certain aspects of numerical understanding depend on spatial representations (for reviews of the behavioral literature, see also . We then turn to neuroimaging data in humans that suggest how the deep connection between numbers and space may be mediated by circuitry in the parietal lobe. Drawing on recent work in monkey physiology and human neuroimaging studies establishing tentative homologies, we then present a refined hypothesis concerning specific neural regions in the intraparietal sulcus (IPS) involved in these numerical and spatial processes, including the human homologues of the lateral intraparietal (hLIP) and ventral intraparietal (hVIP) regions. To date, these two lines of research have been largely independent, as most studies of numerical cognition have been conducted in humans using functional imaging, while the most detailed studies of spatial processing have been conducted in monkeys, using single-unit electrophysiology. However, this division is breaking down, as single-unit data have revealed "number neurons" in the macaque IPS, while many recent human neuroimaging studies have focused on establishing humanmonkey homologies in the parietal lobe. We conclude by discussing the development of numerical-spatial interactions within the context of the "neuronal recycling" hypothesis (Dehaene 2005; Dehaene and Cohen 2007).
Many common tasks require us to individuate in parallel two or more objects out of a complex scen... more Many common tasks require us to individuate in parallel two or more objects out of a complex scene. Although the mechanisms underlying our abilities to count the number of items, remember the visual properties of objects and to make saccadic eye movements towards targets have been studied separately, each of these tasks require selection of individual objects and shows a capacity limit. Here we show that a common factor--salience--determines the capacity limit in the various tasks. We manipulated bottom-up salience (visual contrast) and top-down salience (task relevance) in enumeration and visual memory tasks. As one item became increasingly salient, the subitizing range was reduced and memory performance for all other less-salient items was decreased. Overall, the pattern of results suggests that our abilities to enumerate and remember small groups of stimuli are grounded in an attentional priority or salience map which represents the location of important items.
Patients with frontal lobe damage have been shown to produce implausible answers in cognitive est... more Patients with frontal lobe damage have been shown to produce implausible answers in cognitive estimation, a task requiring approximate answers to quantity-related questions of general semantic knowledge. We investigated a patient with frontal lobe damage who presented executive deficits and difficulties in cognitive estimation. The patient also showed difficulties in verbal numerosity estimation (approximately evaluating the quantity of visually presented sets of items), as he produced extreme answers well outside healthy participants' range of answers. A series of tasks evidenced intact number processing and well preserved semantic representation of numbers. Detailed investigation of estimation processes suggested a deficit at the level of translation from an intact semantic representation of numbers to output, whether verbal or non-symbolic. This case study allows disentangling different processes involved in estimation and contributes to a better understanding of the cognitive estimation deficits frequently reported for patients with frontal lesions.
ABSTRACT The application of multivariate approaches to neuroimaging data analysis is providing co... more ABSTRACT The application of multivariate approaches to neuroimaging data analysis is providing cognitive neuroscientists with a new perspective on the neural substrate of conceptual knowledge. In this paper we show how the combined use of decoding models and of representational similarity analysis (RSA) can enhance our ability to investigate the inter-categorical distinctions as well as the intra-categorical similarities of neural semantic representations. By means of a linear decoding model, we have been able to predict the category of the words subjects were seeing while undergoing a functional magnetic resonance images (fMRI) acquisition. Moreover, RSA in anatomically defined region of interest (ROIs) revealed a significant correlation with length of words and real item size in primary and secondary visual areas (V1 and V2), while a semantic distance effect was significant in inferotemporal areas (BA37 and BA20). Together, these findings illustrate the possibility to decode the distinctive neural patterns of semantic categories and to investigate the peculiar aspects of the neural representations of each single category. We have in fact been able to show a significant correlation between cognitive and neural semantic distance and to describe the gradient of information coding that characterizes the ventral path: from purely perceptual to purely conceptual. These results would not have been possible without a double exploration of the same dataset by means of decoding models and RSA.
Studies of endogenous (cue-directed) attention have traditionally assumed that such shifts must b... more Studies of endogenous (cue-directed) attention have traditionally assumed that such shifts must be volitional. However, recent behavioural experiments have shown that participants make automatic endogenous shifts of attention when presented with symbolic cues that are systematically associated with particular spatial directions, such as arrows and numerals, even when such cues were not behaviourally relevant. Here we used event-related potentials (ERPs) to test whether these automatic shifts of attention use the same mechanisms as volitional shifts of attention. We presented participants with non-predictive (50% valid) task-irrelevant arrow and numeral cues while measuring cue-and targetlocked ERPs. Although the cues were task-irrelevant, they elicited attention-related ERP components previously found in studies that used informative and/or task-relevant cues. These findings further substantiate the dissociation between endogenous and volitional attentional control, and suggest that the same fronto-parietal networks involved in volitional shifts of attention are also involved in reflexive endogenous shifts of attention.
Numerosity (the number of objects in a set), like color or movement, is a basic property of the e... more Numerosity (the number of objects in a set), like color or movement, is a basic property of the environment. Animal and human brains have been endowed by evolution by mechanisms based on parietal circuitry for representing numerosity in an highly abstract, although approximate fashion. These mechanisms are functional at a very early age in humans and spontaneously deployed in the wild by animals of different species. The recent years have witnessed terrific advances in unveiling the neural code(s) underlying numerosity representations and showing similarities as well as differences across species. In humans, during development, with the introduction of symbols for numbers and the implementation of the counting routines, the parietal system undergoes profound (yet still largely mysterious) modifications, such that the neural machinery previously evolved to represent approximate numerosity gets partially "recycled" to support the representation of exact number.
Subitizing is the rapid and accurate enumeration of small sets (up to 3-4 items). Although subiti... more Subitizing is the rapid and accurate enumeration of small sets (up to 3-4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying mechanisms remain debated. One hypothesis proposes that subitizing results from numerical estimation mechanisms that, according to Weber's law, operate with high precision for small numbers. Alternatively, subitizing might rely on a distinct process dedicated to small numerosities. In this study, we tested the hypothesis that there is a shared estimation system for small and large quantities in human adults, using a masked forced-choice paradigm in which participants named the numerosity of displays taken from sets matched for discrimination difficulty; one set ranged from 1 through 8 items, and the other ranged from 10 through 80 items. Results showed a clear violation of Weber's law (much higher precision over numerosities 1-4 than over numerosities 10-40), thus refuting the single-estimationsystem hypothesis and supporting the notion of a dedicated mechanism for apprehending small numerosities.
Proceedings of the Royal Society B: Biological Sciences, 2003
Theories of perception have proposed a basic distinction between parallel pre-attentive and seria... more Theories of perception have proposed a basic distinction between parallel pre-attentive and serial attentive modes of processing. However, chronometric measures are often ambiguous in separating parallel and serial processes. We have used the activity of attention-related regions of the human brain, measured with functional magnetic resonance imaging, to separate parallel from serial processes at the single-trial level in a visual quantification task. In this task, some have suggested the deployment of two qualitatively different processes, a fast parallel 'subitizing' for sets of one, two or three objects and a slow serial counting for larger sets. Our results indicate that attention-related regions of the posterior parietal and frontal cortices show a sudden increase in activity only from numerosity four onwards, confirming the parallelserial dichotomy of subitizing and counting. Moreover, using the presence or absence of attentional shifts, as inferred from the activation of posterior parietal regions, we successfully predict whether, on a given trial, subjects deployed a serial exploration of the display or a parallel apprehension. Beyond the subitizing/counting debate, this approach may prove useful to probe the attentional demands of other cognitive tasks.
are distributed on a logarithmic scale, thus permitting a wide range of quantities to be encoded ... more are distributed on a logarithmic scale, thus permitting a wide range of quantities to be encoded with a small population of cells. This compressive property implies Unité INSERM 562 "Cognitive Neuroimaging" an increasingly coarser encoding of larger numbers. 2 Unité de Neuroimagerie Anatomo-Fonctionnelle Thus, it can explain the behavioral observation that, as Service Hospitalier Fré dé ric Joliot the numbers increase, it takes a proportionally larger CEA/DSV difference between them for discrimination performance 91401 Orsay Cedex to remain at a constant level (Weber's law).
How are comparative judgments performed in the human brain? We scanned subjects with fMRI while t... more How are comparative judgments performed in the human brain? We scanned subjects with fMRI while they compared stimuli for size, luminance, or number. Regions involved in comparative judgments were identified using three criteria: task-related activation, presence of a distance effect, and interference of one dimension onto the other. We observed considerable overlap in the neural substrates of the three comparison tasks. Interestingly, the amount of overlap predicted the amount of cross-dimensional interference: in both behavior and fMRI, number interfered with size, and size with luminance, but number did not interfere with luminance. The results suggest that during comparative judgments, the relevant continuous quantities are represented in distributed and overlapping neural populations, with number and size engaging a common parietal spatial code, while size and luminance engage shared occipito-temporal perceptual representations.
Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in vari... more Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distancedependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.
The history of mathematics is traversed by a deep connection between numbers and space. From the ... more The history of mathematics is traversed by a deep connection between numbers and space. From the most elementary aspects of mathematics, such as the notion of measurement, all the way up to the concepts of the real number line, Cartesian coordinates, the complex plane and even the proof of Fermat's Last Theorem, metaphors by which numbers are made to correspond to spatial positions permeate mathematical thinking 1-3 . The evolution of these culturally-defined representations of numbers has been crucial to the development of mathematics. In this review, we discuss the neural mechanisms that might underpin these cultural achievements. We begin by reviewing recent behavioural and patient data that show that certain aspects of numerical understanding depend on spatial representations. We then turn to neuroimaging data in humans, which indicate that the deep connection between numbers and space might be mediated by the neural circuitry in the parietal lobe. Drawing on recent work in monkey physiology and neuroimaging studies that established tentative monkey-human homologies, we then present a refined hypothesis about the specific neural regions in the INTRAPARIETAL SULCUS (IPS) that might be involved in these numerical and spatial processes, including the LATERAL INTRAPARIETAL (LIP) and VENTRAL INTRAPARIETAL (VIP) regions.
In the primate brain, sensory information is processed along two partially segregated cortical st... more In the primate brain, sensory information is processed along two partially segregated cortical streams: the ventral stream, mainly coding for objects' shape and identity, and the dorsal stream, mainly coding for objects' quantitative information (including size, number, and spatial position). Neurophysiological measures indicate that such functional segregation is present early on in infancy, and that the two streams follow independent maturational trajectories during childhood. Here we collected, in a large sample of young children and adults, behavioural measures on an extensive set of functions typically associated with either the dorsal or the ventral stream. We then used a correlational approach to investigate the presence of inter-individual variability resulting in clustering of functions. Results show that dorsal- and ventral-related functions follow two uncorrelated developmental trajectories. Moreover, within each stream, some functions show age-independent correlations: finger gnosis, non-symbolic numerical abilities and spatial abilities within the dorsal stream, and object and face recognition abilities within the ventral stream. This pattern of clear within-stream cross-task correlation seems to be lost in adults, with two notable exceptions: performance in face and object recognition on one side, and in symbolic and non-symbolic comparison on the other, remain correlated, pointing to distinct shape recognition and quantity comparison systems.
Children's sense of numbers before formal education is thought to rely on an approximate number s... more Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear representation and decrease their use of an intuitive, logarithmic one. We investigated the development of numerical estimation in a younger population (3.5-6.5 y.o.) using 0-to-100 and two novel sets of 1-to-10 and 1-to-20 number lines. Children's estimates shifted from logarithmic to linear in the small number range, whereas they became more accurate but increasingly logarithmic on the larger interval. Estimation accuracy was correlated with knowledge of Arabic numerals and numerical order. These results suggest that the development of numerical estimation is built on a logarithmic coding of numbers -the hallmark of the approximate number system -and is subsequently shaped by the acquisition of cultural practices with numbers.
E.M. Hubbard). a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o ... more E.M. Hubbard). a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o r t e x 0010-9452/$ -see front matter ª c o r t e x 4 5 ( 2 0 0 9 ) 1 2 0 0 -1 2 1 6 c o r t e x 4 5 ( 2 0 0 9 ) 1 2 0 0 -1 2 1 6
ABSTRACT—Subitizing is the rapid and accurate,enumer- ation of small sets (up to 3–4 items). Alth... more ABSTRACT—Subitizing is the rapid and accurate,enumer- ation of small sets (up to 3–4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying mechanisms remain debated. One hypothesis proposes,that subitizing results from nu- merical estimation mechanisms that, according to Weber’s law, operate with high precision for small numbers. Al- ternatively, subitizing might rely
Evolutionary and Developmental Perspectives on Mind, Brain, and Behavior, 2009
Historically, many mathematical advances have been developed through the use of conceptual mappin... more Historically, many mathematical advances have been developed through the use of conceptual mappings between numbers and space. From the most elementary aspects of mathematics, such as the notion of measurement, all the way up to the concepts of the real number line, Cartesian coordinates, the complex plane, and even the proof of Fermat's Last Theorem, metaphors by which numbers are made to correspond to spatial positions permeate mathematical thinking . The evolution of these culturally defined representations of number has been critical to the development of mathematics. In this chapter, we review and update our previous models ) discussing the neural mechanisms that might underpin these cultural achievements. We begin by reviewing recent behavioral, patient, and transcranial magnetic stimulation (TMS) data showing that certain aspects of numerical understanding depend on spatial representations (for reviews of the behavioral literature, see also . We then turn to neuroimaging data in humans that suggest how the deep connection between numbers and space may be mediated by circuitry in the parietal lobe. Drawing on recent work in monkey physiology and human neuroimaging studies establishing tentative homologies, we then present a refined hypothesis concerning specific neural regions in the intraparietal sulcus (IPS) involved in these numerical and spatial processes, including the human homologues of the lateral intraparietal (hLIP) and ventral intraparietal (hVIP) regions. To date, these two lines of research have been largely independent, as most studies of numerical cognition have been conducted in humans using functional imaging, while the most detailed studies of spatial processing have been conducted in monkeys, using single-unit electrophysiology. However, this division is breaking down, as single-unit data have revealed "number neurons" in the macaque IPS, while many recent human neuroimaging studies have focused on establishing humanmonkey homologies in the parietal lobe. We conclude by discussing the development of numerical-spatial interactions within the context of the "neuronal recycling" hypothesis (Dehaene 2005; Dehaene and Cohen 2007).
Many common tasks require us to individuate in parallel two or more objects out of a complex scen... more Many common tasks require us to individuate in parallel two or more objects out of a complex scene. Although the mechanisms underlying our abilities to count the number of items, remember the visual properties of objects and to make saccadic eye movements towards targets have been studied separately, each of these tasks require selection of individual objects and shows a capacity limit. Here we show that a common factor--salience--determines the capacity limit in the various tasks. We manipulated bottom-up salience (visual contrast) and top-down salience (task relevance) in enumeration and visual memory tasks. As one item became increasingly salient, the subitizing range was reduced and memory performance for all other less-salient items was decreased. Overall, the pattern of results suggests that our abilities to enumerate and remember small groups of stimuli are grounded in an attentional priority or salience map which represents the location of important items.
Patients with frontal lobe damage have been shown to produce implausible answers in cognitive est... more Patients with frontal lobe damage have been shown to produce implausible answers in cognitive estimation, a task requiring approximate answers to quantity-related questions of general semantic knowledge. We investigated a patient with frontal lobe damage who presented executive deficits and difficulties in cognitive estimation. The patient also showed difficulties in verbal numerosity estimation (approximately evaluating the quantity of visually presented sets of items), as he produced extreme answers well outside healthy participants' range of answers. A series of tasks evidenced intact number processing and well preserved semantic representation of numbers. Detailed investigation of estimation processes suggested a deficit at the level of translation from an intact semantic representation of numbers to output, whether verbal or non-symbolic. This case study allows disentangling different processes involved in estimation and contributes to a better understanding of the cognitive estimation deficits frequently reported for patients with frontal lesions.
ABSTRACT The application of multivariate approaches to neuroimaging data analysis is providing co... more ABSTRACT The application of multivariate approaches to neuroimaging data analysis is providing cognitive neuroscientists with a new perspective on the neural substrate of conceptual knowledge. In this paper we show how the combined use of decoding models and of representational similarity analysis (RSA) can enhance our ability to investigate the inter-categorical distinctions as well as the intra-categorical similarities of neural semantic representations. By means of a linear decoding model, we have been able to predict the category of the words subjects were seeing while undergoing a functional magnetic resonance images (fMRI) acquisition. Moreover, RSA in anatomically defined region of interest (ROIs) revealed a significant correlation with length of words and real item size in primary and secondary visual areas (V1 and V2), while a semantic distance effect was significant in inferotemporal areas (BA37 and BA20). Together, these findings illustrate the possibility to decode the distinctive neural patterns of semantic categories and to investigate the peculiar aspects of the neural representations of each single category. We have in fact been able to show a significant correlation between cognitive and neural semantic distance and to describe the gradient of information coding that characterizes the ventral path: from purely perceptual to purely conceptual. These results would not have been possible without a double exploration of the same dataset by means of decoding models and RSA.
Studies of endogenous (cue-directed) attention have traditionally assumed that such shifts must b... more Studies of endogenous (cue-directed) attention have traditionally assumed that such shifts must be volitional. However, recent behavioural experiments have shown that participants make automatic endogenous shifts of attention when presented with symbolic cues that are systematically associated with particular spatial directions, such as arrows and numerals, even when such cues were not behaviourally relevant. Here we used event-related potentials (ERPs) to test whether these automatic shifts of attention use the same mechanisms as volitional shifts of attention. We presented participants with non-predictive (50% valid) task-irrelevant arrow and numeral cues while measuring cue-and targetlocked ERPs. Although the cues were task-irrelevant, they elicited attention-related ERP components previously found in studies that used informative and/or task-relevant cues. These findings further substantiate the dissociation between endogenous and volitional attentional control, and suggest that the same fronto-parietal networks involved in volitional shifts of attention are also involved in reflexive endogenous shifts of attention.
Numerosity (the number of objects in a set), like color or movement, is a basic property of the e... more Numerosity (the number of objects in a set), like color or movement, is a basic property of the environment. Animal and human brains have been endowed by evolution by mechanisms based on parietal circuitry for representing numerosity in an highly abstract, although approximate fashion. These mechanisms are functional at a very early age in humans and spontaneously deployed in the wild by animals of different species. The recent years have witnessed terrific advances in unveiling the neural code(s) underlying numerosity representations and showing similarities as well as differences across species. In humans, during development, with the introduction of symbols for numbers and the implementation of the counting routines, the parietal system undergoes profound (yet still largely mysterious) modifications, such that the neural machinery previously evolved to represent approximate numerosity gets partially "recycled" to support the representation of exact number.
Subitizing is the rapid and accurate enumeration of small sets (up to 3-4 items). Although subiti... more Subitizing is the rapid and accurate enumeration of small sets (up to 3-4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying mechanisms remain debated. One hypothesis proposes that subitizing results from numerical estimation mechanisms that, according to Weber's law, operate with high precision for small numbers. Alternatively, subitizing might rely on a distinct process dedicated to small numerosities. In this study, we tested the hypothesis that there is a shared estimation system for small and large quantities in human adults, using a masked forced-choice paradigm in which participants named the numerosity of displays taken from sets matched for discrimination difficulty; one set ranged from 1 through 8 items, and the other ranged from 10 through 80 items. Results showed a clear violation of Weber's law (much higher precision over numerosities 1-4 than over numerosities 10-40), thus refuting the single-estimationsystem hypothesis and supporting the notion of a dedicated mechanism for apprehending small numerosities.
Proceedings of the Royal Society B: Biological Sciences, 2003
Theories of perception have proposed a basic distinction between parallel pre-attentive and seria... more Theories of perception have proposed a basic distinction between parallel pre-attentive and serial attentive modes of processing. However, chronometric measures are often ambiguous in separating parallel and serial processes. We have used the activity of attention-related regions of the human brain, measured with functional magnetic resonance imaging, to separate parallel from serial processes at the single-trial level in a visual quantification task. In this task, some have suggested the deployment of two qualitatively different processes, a fast parallel 'subitizing' for sets of one, two or three objects and a slow serial counting for larger sets. Our results indicate that attention-related regions of the posterior parietal and frontal cortices show a sudden increase in activity only from numerosity four onwards, confirming the parallelserial dichotomy of subitizing and counting. Moreover, using the presence or absence of attentional shifts, as inferred from the activation of posterior parietal regions, we successfully predict whether, on a given trial, subjects deployed a serial exploration of the display or a parallel apprehension. Beyond the subitizing/counting debate, this approach may prove useful to probe the attentional demands of other cognitive tasks.
are distributed on a logarithmic scale, thus permitting a wide range of quantities to be encoded ... more are distributed on a logarithmic scale, thus permitting a wide range of quantities to be encoded with a small population of cells. This compressive property implies Unité INSERM 562 "Cognitive Neuroimaging" an increasingly coarser encoding of larger numbers. 2 Unité de Neuroimagerie Anatomo-Fonctionnelle Thus, it can explain the behavioral observation that, as Service Hospitalier Fré dé ric Joliot the numbers increase, it takes a proportionally larger CEA/DSV difference between them for discrimination performance 91401 Orsay Cedex to remain at a constant level (Weber's law).
How are comparative judgments performed in the human brain? We scanned subjects with fMRI while t... more How are comparative judgments performed in the human brain? We scanned subjects with fMRI while they compared stimuli for size, luminance, or number. Regions involved in comparative judgments were identified using three criteria: task-related activation, presence of a distance effect, and interference of one dimension onto the other. We observed considerable overlap in the neural substrates of the three comparison tasks. Interestingly, the amount of overlap predicted the amount of cross-dimensional interference: in both behavior and fMRI, number interfered with size, and size with luminance, but number did not interfere with luminance. The results suggest that during comparative judgments, the relevant continuous quantities are represented in distributed and overlapping neural populations, with number and size engaging a common parietal spatial code, while size and luminance engage shared occipito-temporal perceptual representations.
Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in vari... more Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distancedependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.
The history of mathematics is traversed by a deep connection between numbers and space. From the ... more The history of mathematics is traversed by a deep connection between numbers and space. From the most elementary aspects of mathematics, such as the notion of measurement, all the way up to the concepts of the real number line, Cartesian coordinates, the complex plane and even the proof of Fermat's Last Theorem, metaphors by which numbers are made to correspond to spatial positions permeate mathematical thinking 1-3 . The evolution of these culturally-defined representations of numbers has been crucial to the development of mathematics. In this review, we discuss the neural mechanisms that might underpin these cultural achievements. We begin by reviewing recent behavioural and patient data that show that certain aspects of numerical understanding depend on spatial representations. We then turn to neuroimaging data in humans, which indicate that the deep connection between numbers and space might be mediated by the neural circuitry in the parietal lobe. Drawing on recent work in monkey physiology and neuroimaging studies that established tentative monkey-human homologies, we then present a refined hypothesis about the specific neural regions in the INTRAPARIETAL SULCUS (IPS) that might be involved in these numerical and spatial processes, including the LATERAL INTRAPARIETAL (LIP) and VENTRAL INTRAPARIETAL (VIP) regions.
In the primate brain, sensory information is processed along two partially segregated cortical st... more In the primate brain, sensory information is processed along two partially segregated cortical streams: the ventral stream, mainly coding for objects' shape and identity, and the dorsal stream, mainly coding for objects' quantitative information (including size, number, and spatial position). Neurophysiological measures indicate that such functional segregation is present early on in infancy, and that the two streams follow independent maturational trajectories during childhood. Here we collected, in a large sample of young children and adults, behavioural measures on an extensive set of functions typically associated with either the dorsal or the ventral stream. We then used a correlational approach to investigate the presence of inter-individual variability resulting in clustering of functions. Results show that dorsal- and ventral-related functions follow two uncorrelated developmental trajectories. Moreover, within each stream, some functions show age-independent correlations: finger gnosis, non-symbolic numerical abilities and spatial abilities within the dorsal stream, and object and face recognition abilities within the ventral stream. This pattern of clear within-stream cross-task correlation seems to be lost in adults, with two notable exceptions: performance in face and object recognition on one side, and in symbolic and non-symbolic comparison on the other, remain correlated, pointing to distinct shape recognition and quantity comparison systems.
Children's sense of numbers before formal education is thought to rely on an approximate number s... more Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear representation and decrease their use of an intuitive, logarithmic one. We investigated the development of numerical estimation in a younger population (3.5-6.5 y.o.) using 0-to-100 and two novel sets of 1-to-10 and 1-to-20 number lines. Children's estimates shifted from logarithmic to linear in the small number range, whereas they became more accurate but increasingly logarithmic on the larger interval. Estimation accuracy was correlated with knowledge of Arabic numerals and numerical order. These results suggest that the development of numerical estimation is built on a logarithmic coding of numbers -the hallmark of the approximate number system -and is subsequently shaped by the acquisition of cultural practices with numbers.
E.M. Hubbard). a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o ... more E.M. Hubbard). a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o r t e x 0010-9452/$ -see front matter ª c o r t e x 4 5 ( 2 0 0 9 ) 1 2 0 0 -1 2 1 6 c o r t e x 4 5 ( 2 0 0 9 ) 1 2 0 0 -1 2 1 6
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