The neural signature of numerosity by separating numerical and continuous magnitude extraction in visual cortex with frequency-tagged EEG

Significance Approximating large quantities has been identified as a building block of mathematical cognition. Despite its importance from both a fundamental and an educational perspective, the mechanism behind this ability is still not fully understood. The remaining gap comes from the fact that a set is not only characterized by its number of objects but additionally by nonnumerical features naturally correlating with numerosity (e.g., a more numerous set occupies a larger surface). The current frequency-tagging EEG paradigm isolates specific responses to number and to nonnumerical dimensions. We demonstrate that when numerosity and the other dimensions are totally decorrelated in stimulus sequences, changes of each are automatically discriminated in early visual cortex, highlighting the status of numerosity as a primary visual feature. The ability to handle approximate quantities, or number sense, has been recurrently linked to mathematical skills, although the nature of the mechanism allowing to extract numerical information (i.e., numerosity) from environmental stimuli is still debated. A set of objects is indeed not only characterized by its numerosity but also by other features, such as the summed area occupied by the elements, which often covary with numerosity. These intrinsic relations between numerosity and nonnumerical magnitudes led some authors to argue that numerosity is not independently processed but extracted through a weighting of continuous magnitudes. This view cannot be properly tested through classic behavioral and neuroimaging approaches due to these intrinsic correlations. The current study used a frequency-tagging EEG approach to separately measure responses to numerosity as well as to continuous magnitudes. We recorded occipital responses to numerosity, total area, and convex hull changes but not to density and dot size. We additionally applied a model predicting primary visual cortex responses to the set of stimuli. The model output was closely aligned with our electrophysiological data, since it predicted discrimination only for numerosity, total area, and convex hull. Our findings thus demonstrate that numerosity can be independently processed at an early stage in the visual cortex, even when completely isolated from other magnitude changes. The similar implicit discrimination for numerosity as for some continuous magnitudes, which correspond to basic visual percepts, shows that both can be extracted independently, hence substantiating the nature of numerosity as a primary feature of the visual scene.

[1]  Mathieu Guillaume,et al.  NASCO: A New Method and Program to Generate Dot Arrays for Non-Symbolic Number Comparison Tasks , 2020, J. Numer. Cogn..

[2]  Nicholas K DeWind,et al.  Numerical encoding in early visual cortex , 2019, Cortex.

[3]  J. Affeldt,et al.  The feasibility study , 2019, The Information System Consultant’s Handbook.

[4]  Stanislas Dehaene,et al.  Attentional amplification of neural codes for number independent of other quantities along the dorsal visual stream , 2019, bioRxiv.

[5]  P. Lemaire,et al.  Strategy variability in numerosity comparison task: a study in young and older adults , 2019, Open Psychology.

[6]  A. Knops,et al.  Evidence for a Posterior Parietal Cortex Contribution to Spatial but not Temporal Numerosity Perception. , 2018, Cerebral cortex.

[7]  André Mouraux,et al.  Fast periodic visual stimulation to study tool-selective processing in the human brain , 2018, Experimental Brain Research.

[8]  Bruno Rossion,et al.  A rapid, objective and implicit measure of visual quantity discrimination , 2018, Neuropsychologia.

[9]  David C. Burr,et al.  Psychophysical evidence for the number sense , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

[10]  Elizabeth M. Brannon,et al.  Numerosity processing in early visual cortex , 2017, NeuroImage.

[11]  B. Rossion,et al.  The non-linear development of the right hemispheric specialization for human face perception , 2017, Neuropsychologia.

[12]  Joonkoo Park,et al.  A neural basis for the visual sense of number and its development: A steady-state visual evoked potential study in children and adults , 2017, Developmental Cognitive Neuroscience.

[13]  Yarden Gliksman,et al.  Size Perception and the Foundation of Numerical Processing , 2017 .

[14]  D. Ansari,et al.  Are numbers grounded in a general magnitude processing system? A functional neuroimaging meta-analysis , 2017, Neuropsychologia.

[15]  Julian Jara-Ettinger,et al.  Universal and uniquely human factors in spontaneous number perception , 2017, Nature Communications.

[16]  P. Bressan,et al.  Commentary: From ‘sense of number’ to ‘sense of magnitude’ – The role of continuous magnitudes in numerical cognition , 2017, Front. Psychol..

[17]  R. Cohen Kadosh,et al.  Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. , 2016, Acta psychologica.

[18]  S. Dumoulin,et al.  A network of topographic numerosity maps in human association cortex , 2016, Nature Human Behaviour.

[19]  Bruno Rossion,et al.  At a Single Glance: Fast Periodic Visual Stimulation Uncovers the Spatio-Temporal Dynamics of Brief Facial Expression Changes in the Human Brain , 2016, Cerebral cortex.

[20]  Guido Marco Cicchini,et al.  Spontaneous perception of numerosity in humans , 2016, Nature Communications.

[21]  Tobias Kluth,et al.  Numerosity as a topological invariant. , 2016, Journal of vision.

[22]  Guido Marco Cicchini,et al.  Number As a Primary Perceptual Attribute: A Review , 2016, Perception.

[23]  S. Dumoulin,et al.  Topographic representations of object size and relationships with numerosity reveal generalized quantity processing in human parietal cortex , 2015, Proceedings of the National Academy of Sciences.

[24]  Tiangang Zhou,et al.  Topology-defined units in numerosity perception , 2015, Proceedings of the National Academy of Sciences.

[25]  Elizabeth M. Brannon,et al.  Modeling the approximate number system to quantify the contribution of visual stimulus features , 2015, Cognition.

[26]  Justin M. Ales,et al.  The steady-state visual evoked potential in vision research: A review. , 2015, Journal of vision.

[27]  Guido Marco Cicchini,et al.  Mechanisms for perception of numerosity or texture-density are governed by crowding-like effects. , 2015, Journal of vision.

[28]  Nicholas K DeWind,et al.  Rapid and Direct Encoding of Numerosity in the Visual Stream. , 2015, Cerebral cortex.

[29]  A. Norcia,et al.  An objective index of individual face discrimination in the right occipito-temporal cortex by means of fast periodic oddball stimulation , 2014, Neuropsychologia.

[30]  Jonathan Winawer,et al.  A Two-Stage Cascade Model of BOLD Responses in Human Visual Cortex , 2013, PLoS Comput. Biol..

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

[32]  L. Feigenson,et al.  Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance , 2011, PloS one.

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

[34]  Stella F. Lourenco,et al.  General Magnitude Representation in Human Infants , 2010, Psychological science.

[35]  Marie-Pascale Noël,et al.  Symbolic and nonsymbolic number comparison in children with and without dyscalculia , 2010, Cognition.

[36]  S. Heinrich,et al.  Frequency-domain analysis of fast oddball responses to visual stimuli: a feasibility study. , 2009, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[37]  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.

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

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

[40]  Stephen F. Goodwin,et al.  Sexual Dimorphism: Can You Smell the Difference? , 2008, Current Biology.

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

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

[43]  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.

[44]  Denis G. Pelli,et al.  ECVP '07 Abstracts , 2007, Perception.

[45]  R. Gregory The Most Expensive Painting in the World , 2007, Perception.

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

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

[48]  Vincent Walsh A theory of magnitude: common cortical metrics of time, space and quantity , 2003, Trends in Cognitive Sciences.

[49]  David J. Freedman,et al.  Representation of the Quantity of Visual Items in the Primate Prefrontal Cortex , 2002, Science.

[50]  Kelly S. Mix,et al.  Multiple cues for quantification in infancy: is number one of them? , 2002, Psychological bulletin.

[51]  Charles Chubb,et al.  Texture luminance judgments are approximately veridical , 2000, Vision Research.

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

[53]  T. Tsukada,et al.  Effect of number of elements and size of stimulus field on recordability of pattern reversal visual evoked response. , 1988, Investigative ophthalmology & visual science.

[54]  A E Kertesz,et al.  Effect of stimulus size on fusion and vergence. , 1981, Journal of the Optical Society of America.

[55]  D. Regan Steady-state evoked potentials. , 1977, Journal of the Optical Society of America.

[56]  S. S. Stevens Duration, luminance, and the brightness exponent , 1966 .

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

[58]  C. Aring,et al.  A CRITICAL REVIEW , 1939, Journal of neurology and psychiatry.

[59]  David Brink,et al.  : A Review of the , 2018 .

[60]  Edward F. Ester,et al.  Substitution and pooling in visual crowding induced by similar and dissimilar distractors. , 2015, Journal of vision.

[61]  C. Morón,et al.  Transcranial Magnetic Stimulation Study , 2013 .

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

[63]  M. Bach,et al.  On the statistical significance of electrophysiological steady-state responses , 2004, Documenta Ophthalmologica.

[64]  D H Brainard,et al.  The Psychophysics Toolbox. , 1997, Spatial vision.