Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Voluntary eye movements direct attention on the mental number space

  • 569 Accesses

  • 16 Citations


Growing evidence suggests that orienting visual attention in space can influence the processing of numerical magnitude, with leftward orienting speeding up the processing of small numbers relative to larger ones and the converse for rightward orienting. The manipulation of eye movements is a convenient way to direct visuospatial attention, but several aspects of the complex relationship between eye movements, attention orienting and number processing remain unexplored. In a previous study, we observed that inducing involuntary, reflexive eye movements by means of optokinetic stimulation affected number processing only when numerical magnitude was task relevant (i.e., during magnitude comparison, but not during parity judgment; Ranzini et al., in J Cogn Psychol 27, 459–470, (2015). Here, we investigated whether processing of task-irrelevant numerical magnitude can be modulated by voluntary eye movements, and whether the type of eye movements (smooth pursuit vs. saccades) would influence this interaction. Participants tracked with their gaze a dot while listening to a digit. The numerical task was to indicate whether the digit was odd or even through non-spatial, verbal responses. The dot could move leftward or rightward either continuously, allowing tracking by smooth pursuit eye movements, or in discrete steps across a series of adjacent locations, triggering a sequence of saccades. Both smooth pursuit and saccadic eye movements similarly affected number processing and modulated response times for large numbers as a function of direction of motion. These findings suggest that voluntary eye movements redirect attention in mental number space and highlight that eye movements should play a key factor in the investigation of number–space interactions.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    In a preliminary analysis we also included the starting position of the dot target (central, peripheral) as within-subjects factor. Starting position did not yield a significant main effect, and it did not enter in any significant interaction with number magnitude (all p > 0.05). Conversely, the critical interaction between number magnitude and movement direction was unaffected [F(1,15) = 5.916, p = 0.028]. Therefore, we collapsed trials from the two conditions and excluded this factor from the analysis.


  1. Adler, S.A., Bala, J., & Krauzlis, R.J. (2002). Primacy of spatial information in guiding target selection for pursuit and saccades. Journal of Vision, 2, 627–644.

  2. Aiello, M., Jacquin-Courtois, S., Merola, S., Ottaviani, T., Tomaiuolo, F., Bueti, D., … Doricchi, F. (2012). No inherent left and right side in human ‘mental number line’: Evidence from right brain damage. Brain, 135, 2492–2505.

  3. Badets, A., & Pesenti, M. (2010). Creating number semantics through finger movement perception. Cognition, 115(1), 46–53.

  4. Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22, 577–609.

  5. Basso, M. A., Krauzlis, R. J., & Wurtz, R. H. (2000). Activation and inactivation of rostral superior colliculus neurons during smooth-pursuit eye movements in monkeys. Journal of Neurophysiology, 84, 892–908.

  6. Berger, A., Henik, A., & Rafal, R. (2005). Competition between endogenous and exogenous orienting of visual attention. Journal of Experimental Psychology: General, 134, 207–221.

  7. Blini, E., Cattaneo, Z., & Vallar, G. (2013). Different effects of numerical magnitude on visual and proprioceptive reference frames. Frontiers in Psychology, 4, 190.

  8. Bonato, M., Priftis, K., Marenzi, R., & Zorzi, M. (2008). Modulation of hemispatial neglect by directional and numerical cues in the line bisection task. Neuropsychologia, 46, 426–433.

  9. Bonato, M., Priftis, K., Marenzi, R., & Zorzi, M. (2009). Normal and impaired reflexive orienting of attention following central non-predictive cues. Journal of Cognitive Neuroscience, 21, 745–759.

  10. Bremmer, F., Distler, C., & Hoffmann, K. P. (1997). Eye position effects in monkey cortex. II. Pursuit- and fixation-related activity in posterior parietal areas LIP and 7A. Jouranl of Neurophysiology, 77, 962–977.

  11. Casarotti, M., Lisi, M., Umiltà, C., & Zorzi, M. (2012). Paying attention through eye movements: A computational investigation of the premotor theory of spatial attention. Journal of Cognitive Neuroscience, 24, 1519–1531.

  12. Casarotti, M., Michielin, M., Zorzi, M., & Umiltà, C. (2007). Temporal order judgment reveals how number magnitude affects visuospatial attention. Cognition, 102(1), 101–117.

  13. Corbetta, M., Akbudak, E., Conturo, T. E., Snyder, A. Z., Ollinger, J. M., Drury, H. A., … Shulman, G. L. (1998). A common network of functional areas for attention and eye movements. Neuron, 21, 761–773.

  14. Corbetta, M., Kincade, J. M., Ollinger, J. M., McAvoy, M. P., & Shulman, G. L. (2000). Voluntary orienting is dissociated from target detection in human posterior parietal cortex. Nature Neuroscience, 3, 292–297.

  15. Corbetta, M., Patel, G., & Shulman, G. L. (2008). The reorienting system of the human brain: From environment to theory of mind. Neuron, 58, 306–324.

  16. Corbetta, M., & Shulman, G. L. (2002). Control of goal directed and stimulus-driven attention in the brain. Nature Reviews Neuroscience, 3, 201–215.

  17. Cutini, S., Scarpa, F., Scatturin, P., Dell’Acqua, R., & Zorzi, M. (2014). Number-space interactions in the human parietal cortex: Enlightening the SNARC effect with functional near-infrared spectroscopy. Cerebral Cortex, 24(2), 444-451.

  18. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371–396.

  19. Di Luca, S., Pesenti, M., Vallar, G., & Girelli, L. (2013). Numbers reorient visuo-spatial attention during cancellation tasks. Experimental Brain Research, 225, 549–557.

  20. Dodd, M. D., Van der Stigchel, S., Adil Leghari, M., Fung, G., & Kingstone, A. (2008). Attentional SNARC: There’s something special about numbers (let us count the ways). Cognition, 108, 810–818.

  21. Engbert, R., & Mergenthaler, K. (2006). Microsaccades are triggered by low retinal image slip. Proceedings of the National Academy of Sciences of the United States of America, 103, 7192–7197.

  22. Fischer, M. H. (2001). Number processing induces spatial performance biases. Neurology, 57, 822–826.

  23. Fischer, M. H., & Brugger, P. (2011). When digits help digits: Spatial–numerical associations point to finger counting as prime example of embodied cognition. Frontiers in Psychology, 2, 260.

  24. Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555–556.

  25. Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor bias induced by number perception. Experimental Psychology, 51, 91–97.

  26. Galfano, G., Rusconi, E., & Umiltà, C. (2006). Number magnitude orients attention, but not against one’s will. Psychonomic Bulletin & Review, 13, 869–874.

  27. Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal–spatial and visuospatial coding of number–space interactions. Journal of Experimental Psychology: General, 139, 180–190.

  28. Göbel, S. M., Shaki, S., & Fischer, M. H. (2011). The cultural number line: A review of cultural and linguistic influences on the development of number processing. Journal of Cross-Cultural Psychology, 42, 543–565.

  29. Grade, S., Lefèvre, N., & Pesenti, M. (2013). Influence of gaze observation on random number generation. Experimental Psychology, 60, 122–130.

  30. Grant, E. R., & Spivey, M. J. (2003). Eye movements and problem solving guiding attention guides thought. Psychological Science, 14, 462–466.

  31. Halligan, P. W., Fink, G. R., Marshall, J. C., & Vallar, G. (2003). Spatial cognition: Evidence from visual neglect. Trends in Cognitive Sciences, 7, 125–133.

  32. Hartmann, M. (2015). Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition? Cognitive Processing, 1, 245–248.

  33. Hartmann, M., Mast, F. W., & Fischer, M. H. (2015). Spatial biases during mental arithmetic: Evidence from eye movements on a blank screen. Frontiers in Psychology, 6, 12.

  34. Hartmann, M., Mast, F. W., & Fischer, M. H. (2015). Counting is a spatial process: Evidence from eye movements. Psychological Research. doi:10.1007/s00426-015-0722-5

  35. Herrera, A., Macizo, P., & Semenza, C. (2008). The role of working memory in the association between number magnitude and space. Acta Psychologica, 128, 225–237.

  36. Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448.

  37. Kincade, J. M., Abrams, R. A., Astafiev, S. V., Shulman, G. L., & Corbetta, M. (2005). An event-related functional magnetic resonance imaging study of voluntary and stimulus-driven orienting of attention. The Journal of Neuroscience, 25, 4593–4604.

  38. Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585.

  39. Kramer, P., Stoianov, I., Umiltà, C., & Zorzi, M. (2011). Interactions between perceptual and numerical space. Psychonomic Bulletin & Review, 18, 722–728.

  40. Krauzlis, R. J. (2004). Recasting the smooth pursuit eye movement system. Journal of Neurophysiology, 91(2), 591–603. doi:10.1152/jn.00801.2003.

  41. Krauzlis, R. J., & Miles, F. A. (1996). Release of fixation for pursuit and saccades in humans: Evidence for shared inputs acting on different neural substrates. Journal of Neurophysiology, 76, 2822–2833.

  42. Krauzlis, R. J., Zivotofsky, A. Z., & Miles, F. A. (1999). Target selection for pursuit and saccadic eye movements in humans. Journal of Cognitive Neuroscience, 11, 641–649.

  43. Lisberger, S. G., Morris, E. J., & Tychsen, L. (1987). Visual motion processing and sensory-motor integration for smooth pursuit eye movements. Annual Review of Neuroscience, 10, 97–129.

  44. Loetscher, T., Bockisch, C. J., & Brugger, P. (2008). Looking for the answer: The mind’s eye in number space. Neuroscience, 151, 725–729.

  45. Loetscher, T., Bockisch, C. J., Nicholls, M. E. R., & Brugger, P. (2010). Eye position predicts what number you have in mind. Current Biology, 20, R264–R265.

  46. Masson, N., & Pesenti, M. (2014). Attentional bias induced by solving simple and complex addition and subtraction problems. Quarterly Journal of Experimental Psychology, 67 (8), 1514-1526.

  47. Moore, T., Armstrong, K. M., & Fallah, M. (2003). Visuomotor origins of covert spatial attention. Neuron, 40, 671–683.

  48. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519–1520.

  49. Myachykov, A., Ellis, R., Cangelosi, A., & Fischer, M. H. (2016). Ocular drift along the mental number line. Psychological Research. doi:10.1007/s00426-015-0731-4

  50. Nakayama, K., & Mackeben, M. (1989). Sustained and transient components of focal visual attention. Vision Research, 29, 1631–1647.

  51. Nicholls, M. E. R., Loftus, A. M., & Gevers, W. (2008). Look, no hands: A perceptual task shows that number magnitude induces shifts of attention. Psychonomic Bulletin & Review, 15, 413–418.

  52. Pizzamiglio, L., Antonucci, G., Guariglia, C., Judica, A., Montenero, P., Razzano, C., & Zoccolotti, P. (1992). Cognitive rehabilitation of the hemineglect disorders in chronic patients with unilateral right brain damage. Journal of Clinical and Experimental Neuropsychology, 14, 901–923.

  53. Pizzamiglio, L., Frasca, R., Guariglia, C., Incoccia, C., & Antonucci, G. (1990). Effect of optokinetic stimulation in patients with visual neglect. Cortex, 26, 535–541.

  54. Posner, M. I. (1980). Orienting of attention. The Quarterly Journal of Experimental Psychology, 32, 2–25.

  55. Posner, M. I., & Petersen, S. E. (1990). The attention system of the human brain. Annual Reviews in Neuroscience, 13, 25–42.

  56. Priftis, K., Zorzi, M., Meneghello, F., Marenzi, R., & Umiltà, C. (2006). Explicit versus implicit processing of representational space in neglect: Dissociations in accessing the mental number line. Journal of Cognitive Neuroscience, 18, 680–688.

  57. Prifts, K., Pitteri, M., Meneghello, F., Umiltà, C., & Zorzi, M. (2012). Optokinetic stimulation modulates neglect for the number space: Evidence from mental number interval bisection. Frontiers in Human Neuroscience, 6, 23.

  58. Ranzini, M., Dehaene, S., Piazza, M., & Hubbard, E. M. (2009). Neural mechanisms of attentional shifts due to irrelevant spatial and numerical cues. Neuropsychologia, 47, 2615–2624.

  59. Ranzini, M., Lisi, M., Blini, E. A., Pitteri, M., Treccani, B., Priftis, K., & Zorzi, M. (2015). Larger, smaller, odd or even? Task-specific effects of optokinetic stimulation on the mental number space. Journal of Cognitive Psychology, 27(4), 459–470.

  60. Ranzini, M., Lugli, L., Anelli, F., Carbone, R., Nicoletti, R., & Borghi, A. M. (2011). Graspable objects shape number processing. Frontiers in Human Neuroscience, 5, 147.

  61. Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 274–278.

  62. Ristic, J., Wright, A., & Kingstone, A. (2006). The number line reflects top-down control. Psychonomic Bulletin & Review, 13(5), 862–868.

  63. Rizzolatti, G., Riggio, L., Dascola, I., & Umiltà, C. (1987). Reorienting attention across the horizontal and vertical meridians: Evidence in favor of a premotor theory of attention. Neuropsychologia, 25(1), 31–40.

  64. Ruiz Fernández, S., Rahona, J. J., Hervás, G., Vázquez, G., & Ulrich, R. (2011). Number magnitude determines gaze direction: Spatial–numerical association in a free-choice task. Cortex, 5, 617–620.

  65. Schneider, E., Maruyama, M., Dehaene, S., & Sigman, M. (2012). Eye gaze reveals a fast, parallel extraction of the syntax of arithmetic formulas. Cognition, 125, 475–490.

  66. Schwarz, W., & Keus, I. (2004). Moving the eyes along the mental number line: Comparing SNARC effects with manual and saccadic responses. Perception and Psychophysics, 66, 651-664.

  67. Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits of both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review, 16, 328–331.

  68. Simon, O., Mangin, J.-F., Cohen, L., Le Bihan, D. D., & Dehaene, S. (2002). Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron, 33, 475–487.

  69. Spivey, M. J., & Geng, J. J. (2001). Oculomotor mechanisms activated by imagery and memory: Eye movements to absent objects. Psychological Research, 65(235), 241.

  70. Stoianov, I., Kramer, P., Umiltà, C., & Zorzi, M. (2008). Visuospatial priming of the mental number line. Cognition, 106, 770–779.

  71. Tanaka, M., & Lisberger, S. G. (2001). Regulation of the gain of visually guided smooth-pursuit eye movements by frontal cortex. Nature, 409, 191–194.

  72. Tanaka, M., & Lisberger, S. G. (2002). Role of arcuate frontal cortex of monkeys in smooth pursuit eye movements. I. Basic response properties to retinal image motion and position. Journal of Neurophysiology, 87, 2684–2699.

  73. Ulrich, R., & Miller, J. (1994). Effects of truncation on reaction time analysis. Journal of Experimental Psychology: General, 123, 34–80.

  74. Umiltà, C., Priftis, K., & Zorzi, M. (2009). The spatial representation of numbers: Evidence from neglect and pseudoneglect. Experimental Brain Research, 192, 561–569.

  75. Van Dijck, J.-P., Gevers, W., & Fias, W. (2009). Numbers are associated with different types of spatial information depending on the task. Cognition, 113, 248–253.

  76. Van Dijck, J.-P., Gevers, W., Lafosse, C., & Fias, W. (2012). The heterogeneous nature of number–space interactions. Frontiers in Human Neuroscience, 5, 182.

  77. Yu, X., Liu, J., Li, D., Cui, J., & Zhou, X. (2015). Dynamic mental number line in simple arithmetic. Psychological Research. doi:10.1007/s00426-015-0730-5.

  78. Zorzi, M., Bonato, M., Treccani, B., Scalambrin, G., Marenzi, R., & Priftis, K. (2012). Neglect impairs explicit processing of the mental number line. Frontiers in Human Neuroscience, 6, 125.

  79. Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417, 138–139.

Download references


This study was supported by University of Padova Strategic Grant “NEURAT” to M.Z.

Author information

Correspondence to Marco Zorzi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ranzini, M., Lisi, M. & Zorzi, M. Voluntary eye movements direct attention on the mental number space. Psychological Research 80, 389–398 (2016).

Download citation


  • Smooth Pursuit
  • Number Processing
  • Numerical Magnitude
  • Attention Orienting
  • Visuospatial Attention