Numerosity, Abstraction, and the Emergence of Symbolic Thinking

In this paper we tentatively propose that one of the feral cognitive bases for modern symbolic thinking may be numerosity, that is, the ability to appreciate and understand numbers. We proffer that numerosity appears to be an inherently abstractive process, which is supported by numerous human infant and monkey studies. We also review studies that demonstrate that the neurological substrate for numerosity is primarily the intraparietal sulcus of the parietal lobes, the angular and supramarginal gyri in the inferior parietal lobes, and areas of the prefrontal cortex. We also speculate that the lower level of abstraction involved in numerosity may serve as a basis for higher-level symbolic thinking, such as number and letter symbolism and sequencing. We further speculate that these two levels of abstraction may give rise to highly sophisticated characteristics of modern human language, such as analogizing and metaphorizing.

[1]  R. Dart Australopithecus africanus: The Man-Ape of South Africa , 1925, Nature.

[2]  F. Weidenreich Observations on the form and proportions of the endocranial casts of Sinanthropus Pekinensis, other hominids and the great apes : a comparative study of brain size , 1936 .

[3]  E. L. Kaufman,et al.  The discrimination of visual number. , 1949, The American journal of psychology.

[4]  S. Engel,et al.  Thought and Language , 1964, Dialogue.

[5]  N. Geschwind,et al.  The Development of the Brain and the Evolution of Language , 1974 .

[6]  R. Holloway, Exploring the dorsal surface of hominoid brain endocasts by stereoplotter and discriminant analysis. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[7]  P. Tobias The brain of Homo habilis: A new level of organization in cerebral evolution☆ , 1987 .

[8]  James R. Hurford,et al.  Language and Number: The Emergence of a Cognitive System , 1987 .

[9]  Stevan Harnad,et al.  Symbol grounding problem , 1990, Scholarpedia.

[10]  GrimmJohn C. Marshall,et al.  Aphasia and Acalculia , 1993 .

[11]  D. Blum The Monkey Wars , 1994 .

[12]  David Kirsh,et al.  The Intelligent Use of Space , 1995, Artif. Intell..

[13]  E. Trinkaus Neanderthal mortality patterns , 1995 .

[14]  R. Jackendoff How language helps us think , 1996 .

[15]  David Silbersweig,et al.  Functional anatomy of inner speech and auditory verbal imagery , 1995, Schizophrenia Research.

[16]  T. Deacon The Symbolic Species: The Co-evolution of Language and the Brain , 1998 .

[17]  J. T. Lurito,et al.  Comparison of Rhyming and Word Generation with FMRI , 1998, NeuroImage.

[18]  S. Dehaene,et al.  Abstract representations of numbers in the animal and human brain , 1998, Trends in Neurosciences.

[19]  D. Cummins,et al.  Biological preparedness and evolutionary explanation , 1999, Cognition.

[20]  G. Denes,et al.  The Breakdown of Calculation Procedures in Alzheimer's Disease * * This article is a modified version of a paper presented at the Annual Meeting of the Italian Neuropsychological Society, Bologna, April 1997. , 1999, Cortex.

[21]  E. Spelke,et al.  Sources of mathematical thinking: behavioral and brain-imaging evidence. , 1999, Science.

[22]  Mark J. Lowe,et al.  Comparison of rhyming and word generation with FMRI , 2000 .

[23]  T. Wynn,et al.  Executive Functions of the Frontal Lobes and the Evolutionary Ascendancy of Homo Sapiens , 2001 .

[24]  S. Ambrose Paleolithic Technology and Human Evolution , 2001, Science.

[25]  N. Kanwisher,et al.  Neuroimaging of cognitive functions in human parietal cortex , 2001, Current Opinion in Neurobiology.

[26]  Noam Chomsky,et al.  The faculty of language: what is it, who has it, and how did it evolve? , 2002 .

[27]  G. Lakoff,et al.  Where mathematics comes from : how the embodied mind brings mathematics into being , 2002 .

[28]  G. Orban,et al.  Extracting 3D from Motion: Differences in Human and Monkey Intraparietal Cortex , 2002, Science.

[29]  Noam Chomsky,et al.  The faculty of language: what is it, who has it, and how did it evolve? , 2002, Science.

[30]  Peter Carruthers Human Creativity: Its Evolution, its Cognitive Basis, and its Connections with Childhood Pretence , 2002 .

[31]  J. Arsuaga,et al.  Encephalization and allometric trajectories in the genus Homo: Evidence from the Neandertal and modern lineages , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[32]  H. Wiese Iconic and non-iconic stages in number development: the role of language , 2003, Trends in Cognitive Sciences.

[33]  David J. Freedman,et al.  Neural correlates of categories and concepts , 2003, Current Opinion in Neurobiology.

[34]  François Chollet,et al.  Writing, calculating, and finger recognition in the region of the angular gyrus: a cortical stimulation study of Gerstmann syndrome. , 2003, Journal of neurosurgery.

[35]  M. Vanhaeren,et al.  Middle Stone Age Shell Beads from South Africa , 2004, Science.

[36]  C R Gallistel,et al.  Language and the Origin of Numerical Concepts , 2004, Science.

[37]  E. Bruner Geometric morphometrics and paleoneurology: brain shape evolution in the genus Homo. , 2004, Journal of human evolution.

[38]  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.

[39]  A. Ardila,et al.  Acalculia and Dyscalculia , 2002, Neuropsychology Review.

[40]  Ron Borowsky,et al.  FMRI of two measures of phonological processing in visual word recognition: Ecological validity matters , 2004, Brain and Language.

[41]  A. Ardila,et al.  Toward a Model of Neuropsychological Activity , 1998, Neuropsychology Review.

[42]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

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

[44]  Daniel Ansari,et al.  Neural correlates of symbolic number processing in children and adults , 2005, Neuroreport.

[45]  E. Hutchins Material anchors for conceptual blends , 2005 .

[46]  Frederick L. Coolidge,et al.  Working Memory, its Executive Functions, and the Emergence of Modern Thinking , 2005 .

[47]  E. Brannon The independence of language and mathematical reasoning. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[48]  V Menon,et al.  Cerebral Cortex doi:10.1093/cercor/bhi055 Developmental Changes in Mental Arithmetic: Evidence for Increased Functional Specialization in the Left Inferior Parietal Cortex , 2005 .

[49]  H. Cruz Mathematical symbols as epistemic actions – an extended mind perspective , 2005 .

[50]  D. Everett Cultural Constraints on Grammar and Cognition in Pirahã , 2005, Current Anthropology.

[51]  Nancy Kanwisher,et al.  Non-symbolic arithmetic in adults and young children , 2006, Cognition.

[52]  Frederick L. Coolidge,et al.  The effect of enhanced working memory on language , 2006 .

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

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

[55]  Florian Koppelstaetter,et al.  Neural correlates of the number–size interference task in children , 2006, Neuroreport.

[56]  Guy A. Orban,et al.  Mapping the parietal cortex of human and non-human primates , 2006, Neuropsychologia.

[57]  G. Orban,et al.  Selectivity of Neuronal Adaptation Does Not Match Response Selectivity: A Single-Cell Study of the fMRI Adaptation Paradigm , 2006, Neuron.

[58]  Kewei Chen,et al.  Arithmetic processing in the brain shaped by cultures. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[59]  S. Harnad Symbol grounding problem , 1991, Scholarpedia.

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

[61]  D. Chiappe,et al.  The role of working memory in metaphor production and comprehension. , 2007 .

[62]  Aniruddh D. Patel Music, Language, and the Brain , 2007 .

[63]  D. V. Essen,et al.  Surface-Based and Probabilistic Atlases of Primate Cerebral Cortex , 2007, Neuron.

[64]  Dean Falk,et al.  Evolution of the Primate Brain , 2007 .

[65]  Chaitanya Ramineni,et al.  Predicting First–Grade Math Achievement from Developmental Number Sense Trajectories , 2007 .

[66]  Susan Carey,et al.  One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles , 2007, Cognition.

[67]  M. Tomasello,et al.  Shared intentionality. , 2007, Developmental science.

[68]  R. Haier,et al.  The Parieto-Frontal Integration Theory (P-FIT) of intelligence: Converging neuroimaging evidence , 2007, Behavioral and Brain Sciences.

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

[70]  Luigi Cattaneo,et al.  Numbers within Our Hands: Modulation of Corticospinal Excitability of Hand Muscles during Numerical Judgment , 2007, Journal of Cognitive Neuroscience.

[71]  From numerical concepts to concepts of number , 2008, Behavioral and Brain Sciences.

[72]  M. Bright The diversity of species , 2008 .

[73]  L. Malafouris Beads for a Plastic Mind: the ‘Blind Man's Stick’ (BMS) Hypothesis and the Active Nature of Material Culture , 2008, Cambridge Archaeological Journal.

[74]  H. D. Cruz,et al.  An Extended Mind Perspective on Natural Number Representation , 2008 .

[75]  D. Biro,et al.  Chimpanzee Numerical Competence: Cardinal and Ordinal Skills , 2008 .

[76]  Michael C. Frank,et al.  Number as a cognitive technology: Evidence from Pirahã language and cognition , 2008, Cognition.

[77]  Derek C. Penn,et al.  Darwin's mistake: Explaining the discontinuity between human and nonhuman minds , 2008, Behavioral and Brain Sciences.

[78]  S. Dehaene,et al.  Numerical and spatial intuitions: a role for posterior parietal cortex? , 2008 .

[79]  R. Botha Prehistoric shell beads as a window on language evolution , 2008 .

[80]  A. Nieder,et al.  Complementary Contributions of Prefrontal Neuron Classes in Abstract Numerical Categorization , 2008, The Journal of Neuroscience.

[81]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

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

[83]  Michael Andres,et al.  Finger counting: The missing tool? , 2008, Behavioral and Brain Sciences.

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

[85]  Ronald R. Peeters,et al.  Parietal regions processing visual 3D shape extracted from disparity , 2009, NeuroImage.

[86]  M. Seghier,et al.  An anatomical signature for literacy , 2009, Nature.

[87]  C. Gilmore,et al.  Children's mapping between symbolic and nonsymbolic representations of number. , 2009, Journal of experimental child psychology.

[88]  M. Delazer,et al.  Neuroscience of learning arithmetic—Evidence from brain imaging studies , 2009, Neuroscience & Biobehavioral Reviews.

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

[90]  S. Dehaene,et al.  Representation of number in the brain. , 2009, Annual review of neuroscience.

[91]  Manuela Piazza,et al.  How Humans Count: Numerosity and the Parietal Cortex , 2009, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[92]  A. Nieder Prefrontal cortex and the evolution of symbolic reference , 2009, Current Opinion in Neurobiology.

[93]  R. Cohen Kadosh,et al.  Numerical representation in the parietal lobes: abstract or not abstract? , 2009, The Behavioral and brain sciences.

[94]  L. Wadley,et al.  Implications for complex cognition from the hafting of tools with compound adhesives in the Middle Stone Age, South Africa , 2009, Proceedings of the National Academy of Sciences.

[95]  G. Orban,et al.  The Representation of Tool Use in Humans and Monkeys: Common and Uniquely Human Features , 2009, The Journal of Neuroscience.

[96]  Daniel Ansari,et al.  Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement. , 2009, Journal of experimental child psychology.

[97]  Elizabeth M. Brannon,et al.  The Neural Development of an Abstract Concept of Number , 2009, Journal of Cognitive Neuroscience.

[98]  Daniel Ansari,et al.  Challenging the reliability and validity of cognitive measures: the case of the numerical distance effect. , 2010, Acta psychologica.

[99]  Giorgio Vallortigara,et al.  Origins of spatial, temporal and numerical cognition: Insights from comparative psychology , 2010, Trends in Cognitive Sciences.

[100]  Frank Domahs,et al.  Embodied numerosity: Implicit hand-based representations influence symbolic number processing across cultures , 2010, Cognition.

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

[102]  E. Bruner Morphological Differences in the Parietal Lobes within the Human Genus , 2010, Current Anthropology.

[103]  R. Colom,et al.  Human midsagittal brain shape variation: patterns, allometry and integration , 2010, Journal of anatomy.

[104]  M. Vanhaeren,et al.  Symbolic use of marine shells and mineral pigments by Iberian Neandertals , 2010, Proceedings of the National Academy of Sciences.

[105]  E. Reuland Imagination, Planning, and Working Memory , 2010, Current Anthropology.

[106]  Emiliano Bruner,et al.  A bivariate approach to the widening of the frontal lobes in the genus Homo. , 2010, Journal of human evolution.

[107]  Andreas Nieder,et al.  Basic mathematical rules are encoded by primate prefrontal cortex neurons , 2010, Proceedings of the National Academy of Sciences.

[108]  P. Gunz,et al.  Brain development after birth differs between Neanderthals and modern humans , 2010, Current Biology.

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

[110]  Kim Sterelny,et al.  Minds: extended or scaffolded? , 2010 .

[111]  Lambros Malafouris,et al.  The brain-artefact interface (BAI): a challenge for archaeology and cultural neuroscience. , 2010, Social cognitive and affective neuroscience.

[112]  Elizabeth S. Spelke,et al.  Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling , 2010, Cognition.

[113]  A. Ardila On the Evolution of Calculation Abilities , 2010, Front. Evol. Neurosci..

[114]  Thomas Wynn,et al.  Recursion: what is it, who has it, and how did it evolve? , 2011, Wiley interdisciplinary reviews. Cognitive science.

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

[116]  A. Ardila,et al.  There are Two Different Language Systems in the Brain , 2011 .

[117]  Karen Wynn,et al.  Tracking and quantifying objects and non-cohesive substances. , 2011, Developmental science.

[118]  Karenleigh A. Overmann,et al.  The prehistory of number concept , 2011, Behavioral and Brain Sciences.

[119]  Melissa E. Libertus,et al.  Preschool acuity of the approximate number system correlates with school math ability. , 2011, Developmental science.

[120]  R. Colom,et al.  Midsagittal brain shape correlation with intelligence and cognitive performance , 2011 .

[121]  C. Price,et al.  The neural correlates of inner speech defined by voxel-based lesion–symptom mapping , 2011, Brain : a journal of neurology.

[122]  Marie-Pascale Noël,et al.  Is Finger-counting Necessary for the Development of Arithmetic Abilities? , 2011, Front. Psychology.

[123]  Wim Fias,et al.  Stages of Nonsymbolic Number Processing in Occipitoparietal Cortex Disentangled by fMRI Adaptation , 2011, The Journal of Neuroscience.

[124]  José Manuel de la Cuétara,et al.  A Bivariate Approach to the Variation of the Parietal Curvature in the Genus Homo , 2011, Anatomical record.

[125]  G. Orban The extraction of 3D shape in the visual system of human and nonhuman primates. , 2011, Annual review of neuroscience.

[126]  Susan C. Johnson,et al.  An association between understanding cardinality and analog magnitude representations in preschoolers , 2011, Cognition.

[127]  Helen De Cruz,et al.  The role of material culture in human time representation: Calendrical systems as extensions of mental time travel , 2011, Adapt. Behav..

[128]  Wim Fias,et al.  Passive Hand Movements Disrupt Adults’ Counting Strategies , 2011, Front. Psychology.

[129]  Frank Domahs,et al.  The Influence of Implicit Hand-Based Representations on Mental Arithmetic , 2011, Front. Psychology.