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Numbers
Research on arithmetic and the brain

Research on arithmetic and the brain

A survey of our research and main publications in the cognitive neuroscience of arithmetic

 

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Introduction

 

 

In “The Number Sense”, Stanislas Dehaene proposed that the human capacity for arithmetic finds its ultimate roots in a basic cerebral system for perception and mental manipulation of approximate numbers, very ancient in evolution. According to this theory, we share this system with many animal species, and it appears very early in human development, independently of language. Of course, it is a primitive system, capable only of basic computations such as estimation, comparison, addition and subtraction of approximate numbers. On this shared basis, various human cultures invent increasingly elaborate cultural tools such as Arabic symbols, counting routines, algorithms for exact addition, multiplication etc.

 

Thus, the origins of human arithmetic lie in both a universal core system of approximate quantity, and on various cultural tools for exact arithmetic

 

Our laboratory uses several methods to test this theory: neuroimaging, neuronal modelling, mental chronometry, studies of patients with acalculia or dyscalculia, and studies of populations in the Amazon.

 

For accessible reviews of our work, you might consult the following publications:

 

Interview for the Edge website: http://www.edge.org/3rd_culture/dehaene/

 

1. Neuroimaging

 

 

We use brain-imaging techniques such as fMRI to identify the human brain responses during arithmetic tasks. Our research has identified a brain area, the horizontal segment of the intraparietal sulcus, as playing an important role in the quantity representation.

 

The following paper provides a review of this line of research:

 

 

Recent specialized publications on neuroimaging of arithmetic include:

  • Manuela Piazza, Veronique Izard, Philippe Pinel, Denis Le Bihan, and Stanislas Dehaene. Tuning curves for approximate numerosity in the human intraparietal sulcus.. Neuron, 44(3):547-55, October 2004. [WWW ] [PDF ] [Abstract]
  • Philippe Pinel, Manuela Piazza, Denis LeBihan, and Stanislas Dehaene. Distributed and overlapping cerebral representations of number size and luminance during comparative judgements. Neuron, 41(6):983-993, 2004. [PDF ]
  • Manuela Piazza, E. Giacomini, Denis LeBihan, and Stanislas Dehaene. Single-trial classification of parallel pre-attentive and serial attentive processes using functional magnetic resonance imaging. Proceeding of the Royal Society Biological Sciences, 270:1237--1245, 2003. [PDF ]
  • Olivier Simon, Jean-François Mangin, Laurent Cohen, Denis LeBihan, and Stanislas Dehaene. Topographical layout of hand, eye, calculation and language related areas in the human parietal lobe. Neuron, 33:475--487, 2002. [PDF ]
  • Philippe Pinel, Stanislas Dehaene, D. Rivière, and Denis LeBihan. Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage, 14:1013--1026, 2001. [PDF ]
  • Lionel Naccache and Stanislas Dehaene. The priming method : imaging unconscious repetition priming reveals an abstract representation of number in the parietal lobes. Cerebral Cortex, 11:966--974, 2001. [PDF ]
  • R. Stanescu, Philippe Pinel, Pierre-François van de Moortele, Denis LeBihan, Laurent Cohen, and Stanislas Dehaene. Cerebral bases of calculation processes: Impact of number size on the cerebral circuits for exact and approximative calculation. Brain, 123:2240--2255, 2000.
  • Florence Chochon, Laurent Cohen, Pierre-François van de Moortele, and Stanislas Dehaene. Differential contributions of the left and right inferior parietal lobules to number processing. Journal Cognitive Neuroscience, 11:617--630, 1999. [PDF ]
  • Stanislas Dehaene, Elizabeth Spelke, Philippe Pinel, R. Stanescu, and S. Tsivkin. Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284:970--974, 1999. [PDF ]
  • Stanislas Dehaene. The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience, 8:47--68, 1996.
  • Stanislas Dehaene, Nathalie Tzourio, V. Frak, L. Raynaud, Laurent Cohen, Jacques Mehler, and Bernard Mazoyer. Cerebral activations during number multiplication and comparison: a PET study. Neuropsychologia, 34:1097--1106, 1996.

 

2. Neuronal modeling and cross-species comparisons

 

 

In 1993, Stanislas Dehaene and Jean-Pierre Changeux developed a neuronal network model of number processing, which made the prediction that the parietal cortex should contain “numerosity detectors”. These are neurons tuned to a specific number, and thus firing preferentially for instance to sets of 3 objects. The model explained why such a code led to classical behavioral findings such as the distance effect and Weber’s law. The model also predicted that these neurons should have a Gaussian tuning curve when plotted on a logarithmic axis of number size.

  • Stanislas Dehaene and Jean-Pierre Changeux. Development of elementary numerical abilities: A neuronal model. Journal Cognitive Neuroscience, 5:390--407, 1993.

 

In 2002, these predictions were beautifully verified by Andreas Nieder and Earl Miller in the macaque monkey. Their work was published in a landmark series of papers in Science, Neuron, PNAS, and Journal of Cognitive Neuroscience. For accessible descriptions of their work, you may consult:

 

  • Stanislas Dehaene. Single-Neuron Arithmetic. Science, 297:1652--1653, 2002. [PDF ]
  • Stanislas Dehaene. The neural basis of Weber-Fechner's law: Neuronal recordings reveal a logarithmic scale for number. Trends in Cognitive Science, 7:145--147, 2003. [PDF ]

Following Nieder and Miller’s work, we used fMRI to demonstrate a similar sensitivity to numerosity in the human intraparietal sulcus, using an fMRI adaptation method:

 


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