Skip to main content
Log in

Voluntary eye movements direct attention on the mental number space

  • Original Article
  • Published:
Psychological Research Aims and scope Submit manuscript

Abstract

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 via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  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.

References

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  PubMed Central  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  PubMed  PubMed Central  Google Scholar 

  • 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

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    Google Scholar 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    PubMed  PubMed Central  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

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

    PubMed  PubMed Central  Google Scholar 

  • 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.

  • 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.

    Article  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Zorzi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. 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). https://doi.org/10.1007/s00426-015-0741-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00426-015-0741-2

Keywords

Navigation