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:
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:
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.
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:
