Interactions Between Number and Space in Parietal Cortex Edward M. Hubbard, Manuela Piazza, Philippe Pinel and Stanislas Dehaene INSERM Unit 562, Service Hospitalier Frédéric Joliot Orsay, France

Homologies Between Humans and Macaques

Introduction Various behavioral paradigms indicate that numbers are represented along a left-to-right oriented ‘mental number line1,2: • 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 responses3. • In the Attention Bias Effect, a number presented at fixation biases attention to the left for small numbers and to the right for large numbers4. • In the Line Bisection Effect, lines composed of numbers bias bisection to the left or right, depending on numerical size5. • In the Lateralized Presentation Effect, small numbers reaction times are faster when small numbers are presented to the left, and large numbers to the right6.

AIP

LIP

VIP

Spatial Updating in the Lateral Intraparietal

Intraparietal sulcus Right LIP Right LIP

Left LIP Left LIP

Subtraction task

1,2

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Left LIP

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Right LIP

1 0,6

Z = 43 mm

% BOLD

Z = 49 mm

0,8 0,6

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0,4 0,2

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1st sac

2nd sac

1st sac

2nd sac

Right – Left Hand Reaction Time Difference

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Left-Left Left-Right

40 20 0 -20 -40 -60 0

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Number habituation (Piazza 2004)

Shape habituation (Piazza 2004)

Saccades (Simon 2002)

Size distance effect (Pinel 2004)

Grasping (Simon 2002)

Numerical tasks (Dehaene 2003)

9

Attention Bias Effect 8

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 may be crucial for behavioral interactions between number and space.

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1-irrelevant number

2-attentional bias

3-target detection

Line Bisection Effect

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Far number

Right – Left Visual Field Reaction Time Difference

Right – Left Visual Field Reaction Time Difference

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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) areas10,11. 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.

Lateralized Presentation Effect

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70 > reference 50 30 10 -10 -30

Close number > reference

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30 Close number 10

< reference

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Neural Overlap Between Spatial and Numerical Processes

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AIP-related areas 1- Binkofsky 1998 2- Shikata 2004 3- Buccino 2001 4- Simon 2002 5- Culham 2003

VIP-related areas 1- Bremmer 2002 cIP-related area 1- Shikata 2004

LIP-related areas 1- Simon 2002 2- Sereno 2001 3- Medendorp 2005 4- Medendorp 2003 5- Simon 2002

• Number comparison task (Pinel et al. 2004)

5 4

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Given that this circuitry is present in both non-human primates and humans, we further propose that the neural architecture might place constraints on the evolution of numerical– spatial interactions in humans.

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1 7 6 3

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Subtraction task (Chochon 1999) Subtraction task (Chochon etetal.al.1999)

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Left functional landmarks

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AIP-related areas 1- Mühlau 2005 2- Culham 2003 3- Bonda 1995 4- Binkofsky 1998 5- Grefkes 2002 6- Shikata 2004 7- Simon 2002 8- Chao 2000 9- Buccino 2001 10- Culham 2003

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70 reference

90

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References

Approximate addition task (Dehaene et al. 2002)

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reference

Patients who neglect the left portion of representational space show a similar neglect of the left portion of the ‘mental number line’9. When asked to bisect a physical line, they deviate rightward. Similarly, when asked to bisect a numerical interval, they deviate towards larger values (‘to the right’ on the mental number line). Similar effects can be obtained by TMS.

Shifts of attention along the number line may make use of the same area LIP–VIP neural circuitry involved in the development of multisensory, world-centered representations of space. When subjects compute additions or subtractions on numerical symbols, they should shift their attention to the left for subtraction problems, and to the right for addition problems, leading to increased activation of contralateral area LIP. Behavioral protocols in which attention is shifted to the left should interfere with addition, whereas rightward attentional shifts should interfere with subtraction. In number–form synaesthetes, presentation of, or thinking about, numerical quantities and their transformations should lead to greater activation of area LIP than in nonsynaesthetes, given their strong numerical–spatial associations. Once ‘number’ neurons can be recorded in animals during the performance of simple addition and subtraction tasks, we predict that it should be possible to observe numerical equivalents of the partially shifting receptive fields and gain fields observed in the spatial domain.

54 2

Number comparison task

750

• •

MIP-related area 1- Grekes 2004

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-1

800

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Quantity estimation task (Piazza et al. 2001)

R.H.

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Representational Neglect A hemineglect patient does not describe the left side of the scene (in this case, the front of the house), even during mental imagery.

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Right functional landmarks

-70

Numerical bisection task

5

Conclusions and Predictions On the basis of our prediction of VIP–LIP interactions during number processing, we propose specific, testable hypotheses about the effects that we would expect to find with regard to numerical and spatial interactions:

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Neuropsychological Studies

3

One important function of VIP-LIP circuitry is spatial updating12,13 so that objects in the world are perceived as stable despite large changes in retinal position. Another is attention to specific locations in space, and multisensory integration. We suggest that behavioral interactions between number and space are due to shifts of attention along the mental number line, mediated by similar VIP–LIP circuitry.

70

Far number < reference

50

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’ Z = 53 mm

Behavioral Studies

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Grasping task

Taken together, these data suggest that numerical-spatial interactions may be based on effector-independent representations of space in LIP7,8.

SNARC Effect

after 1st saccade

before 1st saccade

Left-Right Left-Left

’ Ocular saccade

LIP-related areas 1- Simon 2002 2- Sereno 2001 3- Medendorp 2005 4- Medendorp 2003 5- Simon 2002

VIP-related areas 1- Bremmer 2002 cIP-related area 1- Shikata 2004 MIP-related area 1- Grekes 2004

Left cortical flat map

Right cortical flat map

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 with space. In particular, ‘number neurons’ are located in the depth of the IPS, in a region that might be homologous to area VIP (see ref. 1 and references contained therein).

1. Hubbard, E.M., Piazza, M. Pinel, P. and Dehaene, S. (2005). Interactions between numbers and space in parietal cortex. Nature Reviews Neuroscience, 6(6): 435-448. 2. Fias, W. & Fischer, M. H. in Handbook of Mathematical Cognition (ed Campbell, J. I. D.) 43-54 (Psychology Press, New York, 2005). 3. Dehaene, S., Bossini, S. & Giraux, P. The mental representation of parity and numerical magnitude. J. Exp. Psych. Gen. 122, 371396 (1993). 4. Fischer, M. H., Castel, A. D., Dodd, M. D. & Pratt, J. Perceiving numbers causes spatial shifts of attention. Nat. Neurosci. 6, 555-556 (2003). 5. Fischer, M. H. Number processing induces spatial performance biases. Neurology 57, 822-826 (2001). 6. Lavidor, M., Brinksman, V. & Göbel, S. M. Hemispheric asymmetry and the mental number line: comparison of double-digit numbers. Neuropsychologia 42, 1927-1933 (2004). 7. Astafiev, S. V. et al. Functional organization of human intraparietal and frontal cortex for attending, looking, and pointing. J. Neurosci. 23, 4689-4699 (2003). 8. Medendorp, W. P., Goltz, H. C., Crawford, J. D. & Villis, T. Integration of target and effector information in human posterior parietal cortex for the planning of action. J. Neurophys. 93, 954-962 (2005). 9. Zorzi, M., Priftis, K. & Umilta, C. Neglect disrupts the mental number line. Nature 417, 138-139 (2002). 10. Colby, C. L. & Goldberg, M. E. Space and attention in parietal cortex. Ann. Rev. Neurosci. 22, 319-349 (1999). 11. Cohen, Y. E. & Andersen, R. A. A common reference frame for movement plans in the posterior parietal cortex. Nat. Rev. Neurosci. 3, 553-562 (2002). 12. Duhamel, J. R., Colby, C. L. & Goldberg, M. E. The updating of the representation of visual space in parietal cortex by intended eye movements. Science 255, 90-92(1992). 13. Medendorp, W. P., Goltz, H. C., Villis, T. & Crawford, J. D. Gaze-centered updating of visual space in human parietal cortex. J. Neurosci. 23, 6209-6214 (2003).