THREE PARIETAL CIRCUITS FOR NUMBER
PROCESSING
Stanislas Dehaene, Manuela Piazza, Philippe Pinel, and Laurent Cohen
INSERM-CEA, Service Hospitalier Frédéric Joliot, Orsay, France
Did evolution endow the human brain with a predisposition to represent and acquire knowledge about
numbers? Although the parietal lobe has been suggested as a potential substrate for a domain-specific
representation of quantities, it is also engaged in verbal, spatial, and attentional functions that may
contribute to calculation. To clarify the organisation of number-related processes in the parietal lobe,
we examine the three-dimensional intersection of fMRI activations during various numerical tasks, and
also review the correspondingneuropsychologicalevidence. On this basis, we propose a tentative tripar
-
tite organisation. The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible can
-
didate for domain specificity: It is systematically activated whenever numbers are manipulated,
independently of number notation, and with increasing activation as the task puts greater emphasis on
quantity processing. Depending on task demands, we speculate that this core quantity system, analo-
gous to an internal “number line,” can be supplemented by two other circuits. A left angular gyrus area,
in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in
verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the
mental number line, just like on any other spatial dimension.
INTRODUCTION
Did evolution endow the human brain with a pre-
disposition to represent dedicated domains of
knowledge? We have previously argued that the
number domain provides a good candidate for such
a biologically determined semantic domain
(Dehaene, 1997; Dehaene, Dehaene-Lambertz, &
Cohen, 1998a). Three criteria for domain specific
-
ity suggest that number and arithmetic are more
than cultural inventions, and may have their ulti
-
mate roots in brain evolution. First, a capacity to
attend to numerosity, and to manipulate it inter
-
nally in elementary computations, is present in ani
-
mals even in the absence of training (Hauser,
Carey, & Hauser, 2000). Second, a similar capacity
for elementary number processing is found early on
in human development, prior to schooling or even
to the development of language skills (Spelke &
Dehaene, 1999; Xu & Spelke, 2000). This suggests
that numerical development follows a distinct
developmental trajectory based on mechanisms
with a long prior evolutionary history.
Third, it has been suggested that number pro
-
cessing rests on a distinct neural circuitry, which
can be reproducibly identified in different subjects
with various neuroimaging, neuropsychological,
and brain stimulation methods (Dehaene et al.,
1998a). The present paper focuses on this last issue,
taking into account the considerable progress that
has recently been made in neuroimaging methods.
The involvement of parietal cortex in number pro
-
cessing was initially discovered on the basis of lesion
data (Gerstmann, 1940; Hécaen, Angelergues, &
COGNITIVE NEUROPSYCHOLOGY, 2003, 20 (3/4/5/6), 487–506
2003 Psychology Press Ltd
http://www.tandf.co.uk/journals/pp/02643294.html DOI:10.1080/02643290244000239
487
Requests for reprints should be addressed to Stanislas Dehaene, INSERM Unit 562, Service Hospitalier Frédéric Joliot, CEA/
DRM/DSV, 4 place du Général Leclerc, 91401 Orsay cedex, France (Email: dehaene@shfj.cea.fr).
Q1520–CNSI 4 / May 28, 03 (Wed)/ [20 pages, 1 tables, 2 figures, 0 footnotes] – S endings, c.f. [no comma].
Houillier, 1961; Henschen, 1919). Subsequently, a
systematic activation of the parietal lobes during
calculation, together with precentral and prefrontal
cortices, was discovered (Roland & Friberg, 1985)
and extensively replicated using positron emission
tomography (PET) (Dehaene et al., 1996; Pesenti,
Thioux, Seron, & De Volder, 2000; Zago, Pesenti,
Mellet, Crivello, Mazoyer, & Tzourio-Mazoyer,
2001) and later fMRI (Burbaud, Camus, Guehl,
Bioulac, Caille, & Allard, 1999; Rueckert et al.,
1996). On this basis, some of us proposed that the
parietal lobe contributes to the representation of
numerical quantity on a mental “number line”
(Dehaene & Cohen, 1995). Unfortunately, due to
poor spatial resolution and limits on experimental
designs, those studies did not permit a finer explo
-
ration of the regions involved in different kinds of
numerical tasks. This has become critical, however,
because recent behavioural studies have made it
clear that mental arithmetic relies on a highly com-
posite set of processes, many of which are probably
not specific to the number domain. For instance,
studies of language interference in normal subjects
suggest that language-based processes play an
important role in exact but not approximate calcu-
lation (Spelke & Tsivkin, 2001). Likewise, concur-
rent performance of a spatial task interferes with
subtraction, but not multiplication, while concur-
rent performance of a language task interferes with
multiplication, but not subtraction (Lee & Kang,
2002). Such behavioural dissociations suggest
that the neural bases of calculation must be
heterogeneous.
The triple-code model of number processing
predicts that, depending on the task, three distinct
systems of representation may be recruited: a quan
-
tity system (a nonverbal semantic representation of
the size and distance relations between numbers,
which may be category specific), a verbal system
(where numerals are represented lexically, phono
-
logically, and syntactically, much like any other type
of word), and a visual system (in which numbers can
be encoded as strings of Arabic numerals)
(Dehaene, 1992; Dehaene & Cohen, 1995). We
initially proposed that the parietal activations dur
-
ing number processing reflected solely the contri
-
bution of the quantity system. However, it is now
clear that this hypothesis requires further elabora
-
tion. First, the left perisylvian language network
clearly extends into the inferior parietal lobe.
Second, the posterior superior parietal lobes are
strongly engaged in visual attention processes that
may contribute to the visual processing of numbers.
It is thus crucial to distinguish, within the observed
parietal lobe activations during number processing,
which activation sites, if any, are associated with a
semantic representation of numerical quantity and
which correspond to nonspecific verbal or visual/
attentional systems.
Fortunately, functional magnetic resonance
imaging (fMRI) has recently allowed much finer-
grained studies of the neuroanatomy of number
processing, using paradigms adapted from cogni
-
tive psychology. The present review focuses
entirely on the parietal lobe activations identified
by those recent neuroimaging studies. We use
three-dimensional visualisation software to inves-
tigate how the parietal activations reported by
various studies relate to one another in cortical
space. On this basis, we propose that three circuits
coexist in the parietal lobe and capture most of the
observed differences between arithmetic tasks: a
bilateral intraparietal system associated with a core
quantity system, a region of the left angular gyrus
associated with verbal processing of numbers, and
a posterior superior parietal system of spatial and
nonspatial attention.
It should be emphasised that our description
provides only a tentative model. Although it is
based on a synthesis of the existing literature, this
model remains speculative and will require further
validation by direct experimentation. For each
postulated circuit, we first examine the relevant
neuroimaging literature, and then consider how
those brain-imaging results impinge on our under
-
standing of neuropsychological impairments of
number processing. Our account predicts that
depending on lesion localisation, three different
categories of numerical impairments should be
observed: genuine semantic impairments of the
numerical domain following intraparietal lesions;
impairments of verbal fact retrieval following
lesions to the left perisylvian cortices, including the
left angular gyrus; and impairments of spatial
DEHAENE ET AL.
488 COGNITIVE NEUROPSYCHOLOGY, 2003, 20 (3/4/5/6)
attention on the number line following lesions to
the dorsal parietal attention system.
THE BILATERAL HORIZONTAL
SEGMENT OF THE
INTRAPARIETAL SULCUS AND
QUANTITY PROCESSING
Neuroimaging evidence
The horizontal segment of the intraparietal sulcus
(hereafter HIPS) is a major site of activation in
neuroimaging studies of number processing. As
shown in Figure 1a, this region lies at the intersec
-
tion of the activations observed in many different
number processing tasks (see Table 1). What seems
to be common to those tasks is the requirement to
access a semantic representation of the quantity
that the numbers represent. We propose that a
nonverbal representation of numerical quantity,
perhaps analogous to a spatial map or “number
line,” is present in the HIPS of both hemispheres.
This representation would underlie our intuition of
what a given numerical size means, and of the prox-
imity relations between numbers. In support of this
view, several features of its responsiveness to experi-
mental conditions are worth noting.
Mental arithmetic. The HIPS seems to be active
whenever an arithmetic operation calls upon a
quantitative representation of numbers. For ex
-
ample, it is more active when subjects calculate than
when they merely have to read numerical symbols
(Burbaud et al., 1999; Chochon, Cohen, Van de
Moortele, & Dehaene, 1999; Pesenti et al., 2000),
suggesting that it plays a role in the semantic
manipulation of numbers. Its activation increases,
at least in the right hemisphere, when subjects have
to compute two addition or subtraction operations
instead of one (Menon, Rivera, White, Glover, &
Reiss, 2000). Furthermore, even within calculation,
the HIPS is more active when subjects estimate the
approximate result of an addition problem than
when they compute its exact solution (Dehaene,
Spelke, Stanescu, Pinel, & Tsivkin, 1999). Finally,
it shows greater activation for subtraction than for
multiplication (Chochon et al., 1999; Lee, 2000).
Multiplication tables and small exact addition facts
can be stored in rote verbal memory, and hence
place minimal requirements on quantity manipula
-
tion. Contrariwise, although some subtraction
problems may be stored in verbal memory, many
are not learned by rote and therefore require genu
-
ine quantity manipulations. In another study, rela
-
tive to five different visuospatial and phonological
non-numerical tasks, subtraction was the only task
that led to increased activation of the HIPS
(Simon, Cohen, Mangin, Bihan, & Dehaene,
2002).
Number comparison. The HIPS is also active when
-
ever a comparative operation that needs access to a
numerical scale is called for. For instance, it is more
active when comparing the magnitudes of two
numbers than when simply reading them
(Chochon et al., 1999). The systematic contribu-
tion of this region to number comparison processes
is replicated in many paradigms using tomographic
imaging (Le Clec’H et al., 2000; Pesenti et al.,
2000; Pinel, Dehaene, Riviere, & LeBihan, 2001;
Thioux, Pesenti, Costes, De Volder, & Seron,
2002) as well as scalp recordings of event-related
potentials (Dehaene, 1996). Parietal activation in
number comparison is often larger in the right than
in the left hemisphere (Chochon et al., 1999;
Dehaene, 1996; Pinel et al., 2001). This may point
to a possible right-hemispheric advantage in com
-
parison and in other tasks requiring an abstraction
of numerical relations (Langdon & Warrington,
1997; Rosselli & Ardila, 1989). However, in com
-
parison, the parietal activation, although it may be
asymmetric, is always present in both hemispheres,
compatible with the observation that numerical
comparison is accessible to both hemispheres in
split-brain patients (Cohen & Dehaene, 1996;
Seymour, Reuter-Lorenz, & Gazzaniga, 1994).
Specificity for the number domain. Several studies
have reported greater HIPS activation when
processing numbers than when processing other
categories of objects on non-numerical scales (such
as comparing the ferocity of animals, the relative
positions of body parts, or the orientation of two
COGNITIVE NEUROPSYCHOLOGY, 2003, 20 (3/4/5/6) 489
PARIETAL NUMBER PROCESSING CIRCUITS
DEHAENE ET AL.
490 COGNITIVE NEUROPSYCHOLOGY, 2003, 20 (3/4/5/6)
z=44
x=39x=-48
x=54
x=-49
z=30
x=12
A.
B.
C.
50
%
22 %
z=49
z=61x=-26
Figure 1. Regions of overlapping activity for three groups of studies, superimposed on axial and sagittal slices of a normalised single-subject
anatomical image. The overlap was calculated by averaging binarised contrast images indicating which voxels were significant for a given
contrast (studies and contrasts are listed in Table 1). The colour scale indicates the percentage of studies showing activation in a given voxel.
The same colour scale (from 22% to 50% of overlap) is applied to all images. Although no single voxel was shared by 100% of studies in a
group, probably due to variability across groups of subjects, laboratories, and imaging methods, Table 1 revealed a high consistency of
activations. (A) The horizontal segment of the intraparietal sulcus (HIPS) was activated bilaterally in a variety of contrasts sharing a
component of numerical quantity manipulation. The barycentre of the region of maximum overlap (>50%) was at Talairach Coordinates
(TC) 41, –42, 49 in the left hemisphere, and –48, –41, 43 in the right hemisphere. Activation overlap is also visible in the precentral gyrus.
(B) The angular gyrus (AG) was activated with a strong left lateralisation (TC –48, –59, 30) in 5 studies of arithmetic tasks with a strong
verbal component. Posterior cingulate as well as superior frontal regions also show some degrees of overlap. (C) The posterior superior
parietal lobule (PSPL) was activated bilaterally in a few numerical tasks (left and right barycentres at TC –26, –69, 61 and 12, –69, 61;
and see Table 1). To emphasise the nonspecificity of this region, the image shows the intersection of the overlap between four numerical tasks
with an image of posterior parietal activity during a non-numerical visual attention shift task (Simon et al., 2002).
visually presented characters: Le Clec’H et al.,
2000; Pesenti et al., 2000; Thioux et al., 2002).
Event-related potentials have also revealed greater
parietal activation for numbers than for other
categories of words such as action verbs, names of
animals, or names of famous persons (Dehaene,
1995). In this study, the first point in time in which
category-specific semantic effects emerge during
visual word processing was found to be 250–280 ms
following stimulus onset.
One study directly tested the specificity of the
HIPS for the numerical domain in multiple tasks
(Thioux et al., 2002). Subjects were presented with
number words and names of animals matched for
length. The HIPS showed greater activation, bilat
-
erally, to numbers than to animal names. This was
true whether subjects were engaged in a comparison
task (larger or smaller than 5; more or less ferocious
than a dog), a categorisation task (odd or even;
mammal or bird), or even a visual judgement of
character shape. Thus, the HIPS shows category
specificity independently of task context. Further
research will be needed, however, to decide whether
it is strictly specific for numbers or whether it
COGNITIVE NEUROPSYCHOLOGY, 2003, 20 (3/4/5/6) 491
PARIETAL NUMBER PROCESSING CIRCUITS
Table 1. Studies and contrasts used to isolate the three parietal regions in Figures 1 and 2
a
Coordinates of maxima
————————————–
Left Right
————— —————
Reference Contrast x y z x y z
Horizontal segment of intraparietal sulcus (HIPS)
Chochon et al. (1999) Comparison of one-digit numbers vs. letter naming –45 –42 39 39 –42 42
Chochon et al. (1999) Subtraction of one-digit numbers from 11 vs. comparison –42 –48 48 39 –42 42
Dehaene et al. (1999) Approximate vs. exact addition of one-digit numbers –56 –44 52 44 –36 52
Lee (2000) Subtraction vs. multiplication of one-digit numbers –31 –52 49 28 –54 52
Naccache and Dehaene (2001) Subliminal quantity priming across notations –44 –56 56 36 –44 44
Piazza et al. (2002
b
) Numerosity estimation vs. physical matching n.s. 44 –56 54
Pinel et al. (2001) Distance effect in comparison of two-digit numbers –40 –44 36 44 –56 48
Simon et al. (2002) Subtraction of one-digit numbers from 11 vs. letter naming –48 –44 52 52 –44 52
Stanescu-Cosson et al. ( 2000) Size effect in exact addition of one-digit numbers –44 –52 48 n.s.
Mean –44 –48 47 41 –47 48
SD 756 775
Angular gyrus (AG)
Chochon et al. (1999) Multiplication vs. comparison of one-digit numbers –30 –69 39 n.s.
Dehaene et al. (1999) Exact vs. approximate addition of one-digit numbers –44 –72 36 40 –76 20
Lee (2000) Multiplication vs. subtraction of one-digit numbers –49 –54 31 n.s.
Simon et al. (2002) Intersection of subtraction and phoneme detection tasks –31 –70 43 n.s.
Stanescu-Cosson et al. (2000) Inverse size effect in exact addition of one-digit numbers –52 –68 32 n.s.
Mean –41 –66 36
SD 964
Posterior superior parietal lobule (PSPL)
Dehaene et al. (1999) Approximate vs. exact addition of one-digit numbers –32 –68 56 20 –60 60
Lee (2000) Subtraction vs. multiplication of one-digit numbers –29 –64 69 21 –61 65
Naccache and Dehaene (2001) Subliminal quantity priming across notations n.s. 12 –60 48
Pinel et al. (2001) Distance effect in comparison of two-digit numbers –4 –72 44 8 –72 52
Mean –22 –68 56 15 –63 56
SD 15412668
a
In each case, we report the coordinates of activation maxima, their mean, and their standard deviation (n.s. = not significant).
b
In some studies, we report the coordinates of subpeaks not reported in the digital papers, which only reported a single global
maximum for each cluster.
