Neural foundations and functional specificity of number representations

Number is a complex category, as with the word "number" we may refer to different entities. First, it is a perceptual property that characterizes any set of individual items, namely its cardinality. The ability to extract the (approximate) cardinality of sets is almost universal in the animal domain and present in humans since birth. In primates, posterior parietal cortex seems to be a crucial site for this ability, even if the degree of selectivity of numerical representations in parietal cortex reported to date appears much lower compared to that of other semantic categories in the ventral stream. Number can also be intended as a mathematical object, which we humans use to count, measure, and order: a (verbal or visual) symbol that stands for the cardinality of a set, the intensity of a continuous quantity or the position of an item on a list. Evidence points to a convergence towards parietal cortex for the semantic coding of numerical symbols and to the bilateral occipitotemporal cortex for the shape coding of Arabic digits and other number symbols.

[1]  G. Orban,et al.  Parietal Representation of Symbolic and Nonsymbolic Magnitude , 2003, Journal of Cognitive Neuroscience.

[2]  P. Gordon Numerical Cognition Without Words: Evidence from Amazonia , 2004, Science.

[3]  Bert Reynvoet,et al.  The magnitude representation of small and large symbolic numbers in the left and right hemisphere: An event-related fMRI study , 2010 .

[4]  Daniel Ansari,et al.  Age-related Changes in the Activation of the Intraparietal Sulcus during Nonsymbolic Magnitude Processing: An Event-related Functional Magnetic Resonance Imaging Study , 2006, Journal of Cognitive Neuroscience.

[5]  M. Pesenti,et al.  Numerosity-duration interference: a Stroop experiment. , 2006, Acta psychologica.

[6]  Geraint Rees,et al.  Commonalities for Numerical and Continuous Quantity Skills at Temporo-parietal Junction , 2014, Journal of Cognitive Neuroscience.

[7]  Justin Halberda,et al.  Individual differences in non-verbal number acuity correlate with maths achievement , 2008, Nature.

[8]  S. Dehaene,et al.  [Reading numbers in pure alexia: effects of the task and hemispheric specialization]. , 1995, Revue neurologique.

[9]  Daniel Ansari,et al.  The Evolution of Numerical Cognition: From Number Neurons to Linguistic Quantifiers , 2008, The Journal of Neuroscience.

[10]  G. Aguirre,et al.  Different spatial scales of shape similarity representation in lateral and ventral LOC. , 2009, Cerebral cortex.

[11]  Wim Fias,et al.  Distinct representations of numerical and non-numerical order in the human intraparietal sulcus revealed by multivariate pattern recognition , 2011, NeuroImage.

[12]  Daniel Ansari,et al.  Developmental Cognitive Neuroscience Developmental Specialization of the Left Parietal Cortex for the Semantic Representation of Arabic Numerals: an Fmr-adaptation Study , 2022 .

[13]  Brian Butterworth,et al.  Exact and Approximate Judgements of Visual and Auditory Numerosity: an Fmri Study , 2006 .

[14]  David C. Burr,et al.  A generalized sense of number , 2014, Proceedings of the Royal Society B: Biological Sciences.

[15]  Jonathan Winawer,et al.  A Brain Area for Visual Numerals , 2013, The Journal of Neuroscience.

[16]  Paul B. Buckley,et al.  Comparisons of digits and dot patterns. , 1974, Journal of experimental psychology.

[17]  F. Piras,et al.  Word and number reading in the brain: Evidence from a Voxel-based Lesion-symptom Mapping study , 2009, Neuropsychologia.

[18]  Avishai Henik,et al.  Notation-Dependent and -Independent Representations of Numbers in the Parietal Lobes , 2007, Neuron.

[19]  Karen Wynn,et al.  Addition and subtraction by human infants , 1992, Nature.

[20]  Andreas Nieder,et al.  Semantic Associations between Signs and Numerical Categories in the Prefrontal Cortex , 2007, PLoS biology.

[21]  Sylvie Droit-Volet,et al.  Time and number discrimination in a bisection task with a sequence of stimuli: a developmental approach. , 2003, Journal of experimental child psychology.

[22]  S. Dehaene,et al.  Event-related fMRI analysis of the cerebral circuit for number comparison. , 1999, Neuroreport.

[23]  Stefan Heim,et al.  Are numbers special? Comparing the generation of verbal materials from ordered categories (months) to numbers and other categories (animals) in an fMRI study , 2008, Human brain mapping.

[24]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

[25]  S. Kastner,et al.  Topographic maps in human frontal and parietal cortex , 2009, Trends in Cognitive Sciences.

[26]  Shachar Maidenbaum,et al.  A number-form area in the blind , 2015, Nature Communications.

[27]  D G Gadian,et al.  Calculation difficulties in children of very low birthweight: a neural correlate. , 2001, Brain : a journal of neurology.

[28]  David C. Burr,et al.  The effects of cross-sensory attentional demand on subitizing and on mapping number onto space , 2012, Vision Research.

[29]  Neil Marlow,et al.  Individual Differences in Inhibitory Control, Not Non-Verbal Number Acuity, Correlate with Mathematics Achievement , 2013, PloS one.

[30]  G. Fink,et al.  REVIEW: The functional organization of the intraparietal sulcus in humans and monkeys , 2005, Journal of anatomy.

[31]  M. Livingstone,et al.  Behavioral and Anatomical Consequences of Early versus Late Symbol Training in Macaques , 2012, Neuron.

[32]  S. Dehaene,et al.  A Magnitude Code Common to Numerosities and Number Symbols in Human Intraparietal Cortex , 2007, Neuron.

[33]  Wim Fias,et al.  Salience maps in parietal cortex: Imaging and computational modeling , 2010, NeuroImage.

[34]  Marie-Pascale Noël,et al.  The isolation of numerals at the semantic level , 1998 .

[35]  Elizabeth M. Brannon,et al.  Improving arithmetic performance with number sense training: An investigation of underlying mechanism , 2014, Cognition.

[36]  Marco Zorzi,et al.  Selective impairment for reading numbers and number words: a single case study , 2004, Neuropsychologia.

[37]  K. Wynn,et al.  Large-Number Addition and Subtraction by 9-Month-Old Infants , 2004, Psychological science.

[38]  Andreas Nieder,et al.  A Labeled-Line Code for Small and Large Numerosities in the Monkey Prefrontal Cortex , 2007, The Journal of Neuroscience.

[39]  Richard F. Thompson,et al.  Number Coding in Association Cortex of the Cat , 1970, Science.

[40]  S. Dehaene,et al.  Interactions between number and space in parietal cortex , 2005, Nature Reviews Neuroscience.

[41]  Valérie Dormal,et al.  A common right fronto‐parietal network for numerosity and duration processing: An fMRI study , 2012, Human brain mapping.

[42]  M. Behrmann,et al.  Number reading in pure alexia—A review , 2011, Neuropsychologia.

[43]  Stanislas Dehaene,et al.  Distinct Cerebral Pathways for Object Identity and Number in Human Infants , 2008, PLoS biology.

[44]  Kenneth F. Valyear,et al.  Human parietal cortex in action , 2006, Current Opinion in Neurobiology.

[45]  Bert Reynvoet,et al.  The interplay between nonsymbolic number and its continuous visual properties. , 2012, Journal of experimental psychology. General.

[46]  Margot J. Taylor,et al.  Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations , 2011, NeuroImage.

[47]  A. Kleinschmidt,et al.  A Supramodal Number Representation in Human Intraparietal Cortex , 2003, Neuron.

[48]  Stanislas Dehaene,et al.  Development of Elementary Numerical Abilities: A Neuronal Model , 1993, Journal of Cognitive Neuroscience.

[49]  S. Dehaene Varieties of numerical abilities , 1992, Cognition.

[50]  E. J. Carter,et al.  Functional Imaging of Numerical Processing in Adults and 4-y-Old Children , 2006, PLoS biology.

[51]  M. Farah,et al.  Neural Specialization for Letter Recognition , 2002, Journal of Cognitive Neuroscience.

[52]  E. Brannon,et al.  Monotonic Coding of Numerosity in Macaque Lateral Intraparietal Area , 2007, PLoS biology.

[53]  Elizabeth M. Brannon,et al.  Beyond the number domain , 2009, Trends in Cognitive Sciences.

[54]  D. Ansari Effects of development and enculturation on number representation in the brain , 2008, Nature Reviews Neuroscience.

[55]  S. Dehaene,et al.  The priming method: imaging unconscious repetition priming reveals an abstract representation of number in the parietal lobes. , 2001, Cerebral cortex.

[56]  Stephan Eliez,et al.  Functional brain imaging study of mathematical reasoning abilities in velocardiofacial syndrome (del22q11.2) , 2001, Genetics in Medicine.

[57]  Doris Y. Tsao,et al.  Mechanisms of face perception. , 2008, Annual review of neuroscience.

[58]  S. Dehaene,et al.  Topographical Layout of Hand, Eye, Calculation, and Language-Related Areas in the Human Parietal Lobe , 2002, Neuron.

[59]  F. Durgin Texture density adaptation and visual number revisited , 2008, Current Biology.

[60]  F. Kingdom,et al.  A common visual metric for approximate number and density , 2011, Proceedings of the National Academy of Sciences.

[61]  S. Dehaene,et al.  Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. , 1990, Journal of experimental psychology. Human perception and performance.

[62]  K. Kucian,et al.  Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study , 2006, Behavioral and Brain Functions.

[63]  Ivilin Peev Stoianov,et al.  Number skills are maintained in healthy ageing , 2014, Cognitive Psychology.

[64]  Curren Katz,et al.  Dissociating estimation from comparison and response eliminates parietal involvement in sequential numerosity perception , 2015, NeuroImage.

[65]  Marinella Cappelletti,et al.  rTMS over the intraparietal sulcus disrupts numerosity processing , 2007, Experimental Brain Research.

[66]  Yale E. Cohen,et al.  A common reference frame for movement plans in the posterior parietal cortex , 2002, Nature Reviews Neuroscience.

[67]  Stanislas Dehaene,et al.  Approximate quantities and exact number words: dissociable systems , 2003, Neuropsychologia.

[68]  E. Spelke,et al.  Newborn infants perceive abstract numbers , 2009, Proceedings of the National Academy of Sciences.

[69]  Andreas Nieder,et al.  Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex , 2007, Proceedings of the National Academy of Sciences.

[70]  Joonkoo Park,et al.  Rapid and Direct Encoding of Numerosity in the Visual Stream. , 2015, Cerebral cortex.

[71]  Mohammad Dastjerdi,et al.  Numerical processing in the human parietal cortex during experimental and natural conditions , 2013, Nature Communications.

[72]  S Dehaene,et al.  Spatially invariant coding of numerical information in functionally defined subregions of human parietal cortex. , 2015, Cerebral cortex.

[73]  T. Allison,et al.  Human extrastriate visual cortex and the perception of faces, words, numbers, and colors. , 1994, Cerebral cortex.

[74]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

[75]  N. Kanwisher,et al.  Interpreting fMRI data: maps, modules and dimensions , 2008, Nature Reviews Neuroscience.

[76]  S Ullman,et al.  Shifts in selective visual attention: towards the underlying neural circuitry. , 1985, Human neurobiology.

[77]  Justin Halberda,et al.  Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). , 2011, Child development.

[78]  J. Duncan The multiple-demand (MD) system of the primate brain: mental programs for intelligent behaviour , 2010, Trends in Cognitive Sciences.

[79]  E. Brannon,et al.  The difficulties of representing continuous extent in infancy: using number is just easier. , 2008, Child development.

[80]  Elizabeth S. Spelke,et al.  Symbolic arithmetic knowledge without instruction , 2007, Nature.

[81]  J. Bulthé,et al.  Format-dependent representations of symbolic and non-symbolic numbers in the human cortex as revealed by multi-voxel pattern analyses , 2014, NeuroImage.

[82]  T. Matsuzawa Symbolic representation of number in chimpanzees , 2009, Current Opinion in Neurobiology.

[83]  Z. Pylyshyn Visual indexes, preconceptual objects, and situated vision , 2001, Cognition.

[84]  David C Burr,et al.  Subitizing but not estimation of numerosity requires attentional resources. , 2010, Journal of vision.

[85]  Andreas Nieder,et al.  A parieto-frontal network for visual numerical information in the monkey. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[86]  V. Dormal,et al.  Common and Specific Contributions of the Intraparietal Sulci to Numerosity and Length Processing , 2009, NeuroImage.

[87]  Steven C. Dakin,et al.  A texture-processing model of the ‘visual sense of number’ , 2014, Proceedings of the Royal Society B: Biological Sciences.

[88]  G. Orban,et al.  Processing of Abstract Ordinal Knowledge in the Horizontal Segment of the Intraparietal Sulcus , 2007, The Journal of Neuroscience.

[89]  V. Walsh,et al.  The parietal cortex and the representation of time, space, number and other magnitudes , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[90]  Bahador Bahrami,et al.  Human Neuroscience , 2022 .

[91]  Philippe Pinel,et al.  Distributed and Overlapping Cerebral Representations of Number, Size, and Luminance during Comparative Judgments , 2004, Neuron.

[92]  Pooja Viswanathan,et al.  Neuronal correlates of a visual “sense of number” in primate parietal and prefrontal cortices , 2013, Proceedings of the National Academy of Sciences.

[93]  Alain Content,et al.  Judgement of discrete and continuous quantity in adults: Number counts! , 2012, Quarterly journal of experimental psychology.

[94]  Wim Fias,et al.  Representation of Number in Animals and Humans: A Neural Model , 2004, Journal of Cognitive Neuroscience.

[95]  David C. Burr,et al.  Separate Mechanisms for Perception of Numerosity and Density , 2014, Psychological science.

[96]  Bertrand Thirion,et al.  Deciphering Cortical Number Coding from Human Brain Activity Patterns , 2009, Current Biology.

[97]  G. Denes,et al.  A specific deficit for numbers in a case of dense acalculia. , 1991, Brain : a journal of neurology.

[98]  Arlette Streri,et al.  Dissociation between small and large numerosities in newborn infants. , 2014, Developmental science.

[99]  David Melcher,et al.  A Shared, Flexible Neural Map Architecture Reflects Capacity Limits in Both Visual Short-Term Memory and Enumeration , 2014, The Journal of Neuroscience.

[100]  Stanislas Dehaene,et al.  Primed numbers : Exploring the modularity of numerical representations with masked and unmasked semantic priming , 1999 .

[101]  Bert De Smedt,et al.  Visual Number Beats Abstract Numerical Magnitude: Format-dependent Representation of Arabic Digits and Dot Patterns in Human Parietal Cortex , 2015, Journal of Cognitive Neuroscience.

[102]  S. Dimond The disconnection syndromes. , 1975, Modern trends in neurology.

[103]  D. Melcher,et al.  Subitizing reflects visuo-spatial object individuation capacity , 2011, Cognition.

[104]  M S Gazzaniga,et al.  The disconnection syndrome. Basic findings reaffirmed. , 1994, Brain : a journal of neurology.

[105]  M. Just,et al.  Decoding the representation of numerical values from brain activation patterns , 2013, Human brain mapping.

[106]  S. Dehaene,et al.  The enigma of Gerstmann's syndrome revisited: a telling tale of the vicissitudes of neuropsychology. , 2010, Brain : a journal of neurology.

[107]  M. Livingstone,et al.  The benefit of symbols: monkeys show linear, human-like, accuracy when using symbols to represent scalar value , 2010, Animal Cognition.

[108]  Brian Butterworth,et al.  Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[109]  Daniel Ansari,et al.  Semantic and Perceptual Processing of Number Symbols: Evidence from a Cross-linguistic fMRI Adaptation Study , 2013, Journal of Cognitive Neuroscience.

[110]  Andrea Facoetti,et al.  Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia , 2010, Cognition.

[111]  Marinella Cappelletti,et al.  Category specificity in reading and writing: the case of number words , 2001, Nature Neuroscience.

[112]  S. Dehaene,et al.  Functional and Structural Alterations of the Intraparietal Sulcus in a Developmental Dyscalculia of Genetic Origin , 2003, Neuron.

[113]  David A. Boas,et al.  Near-infrared spectroscopy shows right parietal specialization for number in pre-verbal infants , 2010, NeuroImage.

[114]  Thad A. Polk,et al.  Neural Dissociation of Number from Letter Recognition and Its Relationship to Parietal Numerical Processing , 2012, Journal of Cognitive Neuroscience.

[115]  E. Brannon,et al.  Attending to One of Many: When Infants are Surprisingly Poor at Discriminating an Item's Size , 2011, Front. Psychology.

[116]  N. Kanwisher Functional specificity in the human brain: A window into the functional architecture of the mind , 2010, Proceedings of the National Academy of Sciences.

[117]  C. Koch,et al.  Computational modelling of visual attention , 2001, Nature Reviews Neuroscience.

[118]  Andreas Nieder,et al.  Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices , 2012, Proceedings of the National Academy of Sciences.

[119]  Marinella Cappelletti,et al.  Spared numerical abilities in a case of semantic dementia , 2001, Neuropsychologia.

[120]  Roland Bammer,et al.  Arithmetic ability and parietal alterations: a diffusion tensor imaging study in velocardiofacial syndrome. , 2005, Brain research. Cognitive brain research.

[121]  Michael Andres,et al.  Mode-dependent and mode-independent representations of numerosity in the right intraparietal sulcus , 2010, NeuroImage.

[122]  Marie-Pascale Noël,et al.  The development of automatic numerosity processing in preschoolers: evidence for numerosity-perceptual interference. , 2008, Developmental psychology.

[123]  D. Burr,et al.  A Visual Sense of Number , 2007, Current Biology.

[124]  Hilary Barth,et al.  Abstract number and arithmetic in preschool children. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[125]  Bert Reynvoet,et al.  The neural origin of the priming distance effect: Distance‐dependent recovery of parietal activation using symbolic magnitudes , 2009, Human brain mapping.

[126]  Marie-Pascale Noël,et al.  Neural Correlates of Symbolic Number Comparison in Developmental Dyscalculia , 2010, Journal of Cognitive Neuroscience.

[127]  D. Ariely Seeing Sets: Representation by Statistical Properties , 2001, Psychological science.

[128]  Elizabeth M Brannon,et al.  Training the Approximate Number System Improves Math Proficiency , 2013, Psychological science.

[129]  Michael Andres,et al.  Dissociation of numerosity and duration processing in the left intraparietal sulcus: A transcranial magnetic stimulation study , 2008, Cortex.

[130]  A. Sack,et al.  The cross-functional role of frontoparietal regions in cognition: internal attention as the overarching mechanism , 2014, Progress in Neurobiology.

[131]  Wim Fias,et al.  Number Processing Pathways in Human Parietal Cortex , 2009, Cerebral cortex.

[132]  Philippe Pinel,et al.  Tuning Curves for Approximate Numerosity in the Human Intraparietal Sulcus , 2004, Neuron.

[133]  Andreas Nieder,et al.  Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex , 2006, Science.

[134]  B. P. Klein,et al.  Topographic Representation of Numerosity in the Human Parietal Cortex , 2013, Science.

[135]  Nancy Kanwisher,et al.  Broad domain generality in focal regions of frontal and parietal cortex , 2013, Proceedings of the National Academy of Sciences.

[136]  J. Tanji,et al.  Numerical representation for action in the parietal cortex of the monkey , 2002, Nature.

[137]  J. Démonet,et al.  Cortical areas involved in Arabic number reading , 2008, Neurology.

[138]  M. Sereno,et al.  Multisensory maps in parietal cortex☆ , 2014, Current Opinion in Neurobiology.

[139]  A. Nieder Counting on neurons: the neurobiology of numerical competence , 2005, Nature Reviews Neuroscience.

[140]  Pierre Pica,et al.  Education Enhances the Acuity of the Nonverbal Approximate Number System , 2013, Psychological science.

[141]  Marinella Cappelletti,et al.  Numbers and time doubly dissociate , 2011, Neuropsychologia.

[142]  Manuela Piazza,et al.  Neurocognitive start-up tools for symbolic number representations , 2010, Trends in Cognitive Sciences.

[143]  M. Pinsk,et al.  Visuotopic Organization of Macaque Posterior Parietal Cortex: A Functional Magnetic Resonance Imaging Study , 2011, The Journal of Neuroscience.