Numerals do not need numerosities: robust evidence for distinct numerical representations for symbolic and non-symbolic numbers

In numerical cognition research, it has traditionally been argued that the processing of symbolic numerals (e.g., digits) is identical to the processing of the non-symbolic numerosities (e.g., dot arrays), because both number formats are represented in one common magnitude system—the Approximate Number System (ANS). In this study, we abandon this deeply rooted assumption and investigate whether the processing of numerals and numerosities can be dissociated, using an audio-visual paradigm in combination with various experimental manipulations. In Experiment 1, participants performed four comparison tasks with large symbolic and non-symbolic numbers: (1) number word–digit (2) tones–dots, (3) number word–dots, (4) tones–digit. In Experiment 2, we manipulated the number range (small vs. large) and the presentation modality (visual–auditory vs. auditory–visual). Results demonstrated ratio effects (i.e., the signature of ANS being addressed) in all tasks containing numerosities, but not in the task containing numerals only. Additionally, a cognitive cost was observed when participants had to integrate symbolic and non-symbolic numbers. Therefore, these results provide robust (i.e., independent of presentation modality or number range) evidence for distinct processing of numerals and numerosities, and argue for the existence of two independent number processing systems.

[1]  Jennifer Wiley,et al.  What Are the Odds? A Practical Guide to Computing and Reporting Bayes Factors , 2014, J. Probl. Solving.

[2]  Bert Reynvoet,et al.  Evidence for distinct magnitude systems for symbolic and non-symbolic number , 2017, Psychological research.

[3]  S Dehaene,et al.  Attention, automaticity, and levels of representation in number processing. , 1995, Journal of experimental psychology. Learning, memory, and cognition.

[4]  Emmy Defever,et al.  Association between basic numerical abilities and mathematics achievement. , 2012, The British journal of developmental psychology.

[5]  Bert Reynvoet,et al.  The Processing of Two-Digit Numbers Depends on Task Instructions , 2011 .

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

[7]  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.

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

[9]  A. Nieder.  The neuronal code for number , 2016, Nature Reviews Neuroscience.

[10]  S. Dehaene.  Symbols and quantities in parietal cortex: elements of a mathematical theory of number representation and manipulation , 2007 .

[11]  Edgar Erdfelder,et al.  G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences , 2007, Behavior research methods.

[12]  Midori Tokita,et al.  Precision and Bias in Approximate Numerical Judgment in Auditory, Tactile, and Cross-modal Presentation , 2016, Perception.

[13]  Midori Tokita,et al.  Behavioral evidence for format-dependent processes in approximate numerosity representation , 2012, Psychonomic bulletin & review.

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

[15]  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.

[16]  Jan B. F. van Erp,et al.  Multisensory temporal numerosity judgment , 2008, Brain Research.

[17]  Leif D. Nelson,et al.  A 21 Word Solution , 2012 .

[18]  W. Gevers,et al.  The role of general and number-specific order processing in adults’ arithmetic performance , 2017 .

[19]  R. Núñez,et al.  Is There Really an Evolved Capacity for Number? , 2017, Trends in Cognitive Sciences.

[20]  C. Gallistel,et al.  Preverbal and verbal counting and computation , 1992, Cognition.

[21]  S. Dehaene,et al.  Cross-linguistic regularities in the frequency of number words , 1992, Cognition.

[22]  Klaus Willmes,et al.  On the Magnitude Representations of Two-Digit Numbers , 2005 .

[23]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[24]  Marc Brysbaert,et al.  The syllable-length effect in number processing is task-dependent , 1991, Perception & psychophysics.

[25]  Midori Tokita,et al.  Is approximate numerical judgment truly modality-independent? Visual, auditory, and cross-modal comparisons , 2013, Attention, perception & psychophysics.

[26]  Jeffrey N. Rouder,et al.  Bayesian inference for psychology. Part II: Example applications with JASP , 2017, Psychonomic Bulletin & Review.

[27]  E. Spelke,et al.  The construction of large number representations in adults , 2003, Cognition.

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

[29]  Bert Reynvoet,et al.  Symbolic estrangement or symbolic integration of numerals with quantities: Methodological pitfalls and a possible solution , 2018, PloS one.

[30]  H. Jeffreys,et al.  Theory of probability , 1896 .

[31]  K Moeller,et al.  Two-digit number processing: holistic, decomposed or hybrid? A computational modelling approach , 2011, Psychological research.

[32]  Florian Mormann,et al.  Single Neurons in the Human Brain Encode Numbers , 2018, Neuron.

[33]  Stanislas Dehaene,et al.  Précis of The Number Sense , 2001 .

[34]  Jeffrey N. Rouder,et al.  Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications , 2017, Psychonomic Bulletin & Review.

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

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

[37]  Michaël A. Stevens,et al.  A model of exact small-number representation , 2005, Psychonomic bulletin & review.

[38]  B. Reynvoet,et al.  Children's representation of symbolic and nonsymbolic magnitude examined with the priming paradigm. , 2011, Journal of experimental child psychology.

[39]  Marc Brysbaert,et al.  Power Analysis and Effect Size in Mixed Effects Models: A Tutorial , 2018, Journal of cognition.

[40]  E. Kroesbergen,et al.  On the Difference Between Numerosity Processing and Number Processing , 2018, Front. Psychol..

[41]  Attila Krajcsi,et al.  The Source of the Symbolic Numerical Distance and Size Effects , 2016, Front. Psychol..

[42]  Bert Reynvoet,et al.  The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol–Symbol Associations , 2016, Front. Psychol..

[43]  Justin Halberda,et al.  Developmental change in the acuity of the "Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. , 2008, Developmental psychology.

[44]  J. H. Steiger,et al.  Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. , 2004, Psychological methods.

[45]  Bert Reynvoet,et al.  Generating nonsymbolic number stimuli , 2011, Behavior research methods.

[46]  Daniel Ansari,et al.  Evidence against a strong association between numerical symbols and the quantities they represent , 2012, CogSci.

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

[48]  Gábor Lengyel,et al.  Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects , 2018, Front. Psychol..