Behavioral evidence for format-dependent processes in approximate numerosity representation

A genuinely abstract number representation is thought to be capable of representing the numerosity of any set of discrete elements, whether they are sequentially or simultaneously presented. Recent neuroimaging studies, however, have demonstrated that different areas of intraparietal sulcus play a role in extracting numerosity across simultaneous or sequential presentation during a quantification process, suggesting the existence of a format-dependent numerical system. To test whether behavioral evidence exists for format-dependent numerical processing in adult humans, we measured the Weber fractions of numerosity discrimination for sequential stimuli, simultaneous stimuli, and cross-format stimuli with a carefully controlled experimental procedure. The results showed distinct differences between the performance in the simultaneous and sequential conditions, supporting the existence of format-dependent processes for numerosity representation. Moreover, the performance on cross-format trials differed among participants, with the exception that performance was always worse than in the simultaneous condition. Taken together, our findings suggest that numerical representation may involve a complex set of multiple stages.

[1]  T. Simon,et al.  The foundations of numerical thinking in a brain without numbers , 1999, Trends in Cognitive Sciences.

[2]  Roi Cohen Kadosh,et al.  Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation , 2008, Progress in Neurobiology.

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

[4]  Timothy Edward John Behrens,et al.  Response-Selection-Related Parietal Activation during Number Comparison , 2004, Journal of Cognitive Neuroscience.

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

[6]  Midori Tokita,et al.  How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled? , 2010, Attention, perception & psychophysics.

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

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

[9]  H. B. Barlow,et al.  The precision of numerosity discrimination in arrays of random dots , 1983, Vision Research.

[10]  Marc D Hauser,et al.  Evolutionary foundations of number: spontaneous representation of numerical magnitudes by cotton–top tamarins , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[11]  R. Church,et al.  A mode control model of counting and timing processes. , 1983, Journal of experimental psychology. Animal behavior processes.

[12]  Z. Pylyshyn,et al.  Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. , 1994, Psychological review.

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

[14]  Elizabeth M Brannon,et al.  The multisensory representation of number in infancy. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

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

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

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

[18]  Catherine Sophian,et al.  How do people apprehend large numerosities? , 2008, Cognition.

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

[20]  Rochel Gelman,et al.  Variability signatures distinguish verbal from nonverbal counting for both large and small numbers , 2001, Psychonomic bulletin & review.

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

[22]  Kazuo Hiraki,et al.  Auditory-visual intermodal matching of small numerosities in 6-month-old infants. , 2005, Developmental science.

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

[24]  Frank H. Durgin,et al.  Texture density adaptation and the perceived numerosity and distribution of texture. , 1995 .

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

[26]  Elizabeth M. Brannon,et al.  Monkeys Match the Number of Voices They Hear to the Number of Faces They See , 2005, Current Biology.

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

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

[29]  J. Cantlon,et al.  Shared System for Ordering Small and Large Numbers in Monkeys and Humans , 2006, Psychological science.

[30]  C. Gallistel,et al.  Nonverbal Counting in Humans: The Psychophysics of Number Representation , 1999 .

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

[32]  Z. Pylyshyn,et al.  Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. , 1994, Psychological review.

[33]  Fei Xu,et al.  Linking Visual Attention and Number Processing in the Brain: The Role of the Temporo-parietal Junction in Small and Large Symbolic and Nonsymbolic Number Comparison , 2007, Journal of Cognitive Neuroscience.

[34]  Midori Tokita,et al.  Temporal information affects the performance of numerosity discrimination: Behavioral evidence for a shared system for numerosity and temporal processing , 2011, Psychonomic bulletin & review.

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