Various behavioural paradigms indicate that numbers are represented along a left-to-right oriented 'mental number line'. In the spatial–numerical association of response codes (SNARC) effect, small numbers are responded to faster with the left hand, with saccades to the left or when presented to the left, and large numbers show a similar advantage for right-sided responses.
Patients who neglect the left portion of space show a similar neglect of the left portion of the 'mental number line'. When asked to bisect a physical line, they deviate to the right. Similarly, when asked to bisect a numerical interval, they deviate towards larger values ('to the right' on the mental number line).
Recent functional MRI and single-unit physiology studies indicate that numerical quantity might be represented by neurons in a frontal–parietal network. Because of the specificity and proximity of numerical and spatial representations in the parietal lobe, we suggest that this region might be crucial for behavioural interactions between number and space.
Studies of spatial cognition in the parietal lobe of the macaque monkey indicate several regions that could be involved in spatial cognition in the intraparietal sulcus (IPS), including the lateral intraparietal (LIP), ventral intraparietal (VIP) and anterior intraparietal (AIP) areas. Of particular interest is area LIP, which is involved in saccades, the planning of actions and shifts of attention in space.
Neuroimaging studies indicate possible human homologues of these macaque regions. Although tentative, these homologies are based on common physiological properties and common organization along the IPS.
Interestingly, the regions that have been identified as being involved in numerical tasks in the IPS overlap with regions that have been shown to be involved in spatial cognition. In particular, 'number neurons' are located in the depth of the IPS, in a region that might be homologous to area VIP.
We suggest that behavioural interactions between number and space are due to shifts of attention along the mental number line, mediated by VIP–LIP circuitry. We therefore predict that addition tasks should lead to greater activation of left area LIP, and subtraction tasks to greater activation of right area LIP. Similarly, shifting attention to the left should interfere with addition, and shifting attention to the right should interfere with subtraction.
Given that this circuitry is present in both non-human primates and humans, we propose that the neural architecture might place constraints on the evolution of numerical–spatial interactions in humans.
Since the time of Pythagoras, numerical and spatial representations have been inextricably linked. We suggest that the relationship between the two is deeply rooted in the brain's organization for these capacities. Many behavioural and patient studies have shown that numerical–spatial interactions run far deeper than simply cultural constructions, and, instead, influence behaviour at several levels. By combining two previously independent lines of research, neuroimaging studies of numerical cognition in humans, and physiological studies of spatial cognition in monkeys, we propose that these numerical–spatial interactions arise from common parietal circuits for attention to external space and internal representations of numbers.
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The authors thank M. Sigman, L. E. Williams, A. J. Wilson and three anonymous reviewers for valuable comments on earlier versions of this manuscript. This research was supported by the Institut National de la Santé et de la Recherche Médicale (S.D. and P.P.), a James S. McDonnell Centennial Fellowship (S.D.), a Numeracy and Brain Development (NUMBRA) postdoctoral fellowship (E.M.H.) and a Marie-Curie individual fellowship (M.P.).
The authors declare no competing financial interests.
- INTRAPARIETAL SULCUS (IPS).
A long, deep fissure that cuts through the parietal lobe, dividing the superior and inferior parietal lobules. This sulcus is present in both humans and non-human primates, and accumulating data indicate that its organization might be partially conserved in evolution.
- LATERAL INTRAPARIETAL (LIP).
A region of the lateral bank of the IPS that is involved in visual representations of space in an eye-centred coordinate frame. This region is crucial for attention, intention to make saccadic eye movements and spatial updating.
- VENTRAL INTRAPARIETAL (VIP).
A region in the ventral portion of the IPS that is responsive to motion in visual, auditory and tactile modalities with head-centred receptive fields. Recent studies indicate that number-selective neurons are located in or near this region.
- SPATIAL–NUMERICAL ASSOCIATION OF RESPONSE CODES EFFECT (SNARC effect).
The finding that subjects respond more quickly to larger numbers if the response is on the right side of space, and to the left for smaller numbers, which indicates automatic spatial–numerical associations.
- ANTERIOR INTRAPARIETAL (AIP).
A region in the anterior portion of the IPS that is involved in fine grasping behaviours. Neurons in this area respond to both visual and tactile stimuli, with receptive fields that move with the hand.
- CAUDAL INTRAPARIETAL (CIP).
A region at the posterior end of the IPS that is involved in the analysis of three-dimensional shapes. Signals from area CIP are sent to area AIP, where they are integrated to plan the grasping of three-dimensional objects.
- MEDIAL INTRAPARIETAL (MIP).
A region in the medial bank of the IPS that is involved in visuomotor transformations. Along with area V6A, this region comprises the PRR, which is active in tasks that require reaching to specific locations.
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Hubbard, E., Piazza, M., Pinel, P. et al. Interactions between number and space in parietal cortex. Nat Rev Neurosci 6, 435–448 (2005). https://doi.org/10.1038/nrn1684
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