Skip to main content
Log in

How does number magnitude influence temporal and spatial parameters of eye movements?

  • Research Article
  • Published:
Experimental Brain Research Aims and scope Submit manuscript

Abstract

The influence of numerical processing on individuals’ behavior is now well documented. The spatial representation of numbers on a left-to-right mental line (i.e., SNARC effect) has been shown to have sensorimotor consequences, the majority of studies being mainly concerned with its impact on the response times. Its impact on the motor programming stage remains less documented, although swiping movement amplitudes have recently been shown to be modulated by number magnitude. Regarding saccadic eye movements, the few available studies have not provided clear-cut conclusions. They showed that spatial–numerical associations modulated ocular drifts, but not the amplitude of memory-guided saccades. Because these studies held saccadic coordinates constant, which might have masked potential numerical effects, we examined whether spontaneous saccadic eye movements (with no saccadic target) could reflect numerical effects. Participants were asked to look either to the left or to the right side of an empty screen to estimate the magnitude (< or > 5) of a centrally presented digit. Latency data confirmed the presence of the classical SNARC and distance effects. More critically, saccade amplitude reflected a numerical effect: participants’ saccades were longer for digits far from the standard (1 and 9) and were shorter for digits close to it (4 and 6). Our results suggest that beyond response times, kinematic parameters also offer valuable information for the understanding of the link between numerical cognition and motor programming.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Andres M, Ostry DJ, Nicol F, Paus T (2008) Time course of number magnitude interference during grasping. Cortex 44(4):414–419

    Article  PubMed  Google Scholar 

  • Bueti D, Walsh V (2009) The parietal cortex and the representation of time, space, number and other magnitudes. Philos Trans R Soc B: Biol Sci 364(1525):1831–1840

    Article  Google Scholar 

  • Burr DC, Ross J, Binda P, Morrone MC (2010) Saccades compress space, time, and number. Trends Cogn Sci 14(12):528–533

    Article  PubMed  Google Scholar 

  • Cantlon JF, Platt ML, Brannon EM (2009) Beyond the number domain. Trends Cogn Sci 13(2):83–91

    Article  PubMed  PubMed Central  Google Scholar 

  • Colby CL, Goldberg ME (1992) The updating of the representation of visual space in parietal cortex by intended eye movements. Science 255(5040):90–92

    Article  PubMed  Google Scholar 

  • Daar M, Pratt J (2008) Digits affect actions: the SNARC effect and response selection. Cortex 44(4):400–405

    Article  PubMed  Google Scholar 

  • Dehaene S (1997) The number sense: how the mind creates mathematics. Oxford University Press, New York

    Google Scholar 

  • Dehaene S, Bossini S, Giraux P (1993) The mental representation of parity and number magnitude. J Exp Psychol Gen 122(3):371

    Article  Google Scholar 

  • Didino D, Breil C, Knops A (2019) The influence of semantic processing and response latency on the SNARC effect. Acta Physiol (Oxf) 196:75–86

    Google Scholar 

  • Dotan D, Dehaene S (2013) How do we convert a number into a finger trajectory? Cognition 129(3):512–529

    Article  PubMed  Google Scholar 

  • Fernández SR, Rahona JJ, Hervás G, Vázquez C, Ulrich R (2011) Number magnitude determines gaze direction: spatial–numerical association in a free-choice task. Cortex 47(5):617–620

    Article  Google Scholar 

  • Fias W (1996) The importance of magnitude information in numerical processing: evidence from the SNARC effect. Math Cogn 2(1):95–110

    Article  Google Scholar 

  • Fias W, Lauwereyns J, Lammertyn J (2001) Irrelevant digits affect feature-based attention depending on the overlap of neural circuits. Cogn Brain Res 12(3):415–423

    Article  CAS  Google Scholar 

  • Findlay JM, Walker R (1999) A model of saccade generation based on parallel processing and competitive inhibition. Behav Brain Sci 22(4):661–674

    Article  CAS  PubMed  Google Scholar 

  • Fischer MH, Warlop N, Hill RL, Fias W (2004) Oculomotor bias induced by number perception. Exp Psychol 51(2):91–97

    Article  PubMed  Google Scholar 

  • Fischer U, Fischer MH, Huber S, Strauß S, Moeller K (2018) The influence of number magnitude on continuous swiping movements. J Numer Cogn 4:297–316

    Article  Google Scholar 

  • Ganor-Stern D, Goldman R (2015) Reaching towards an end: numerical end and distance effects in motor movements. J Cogn Psychol 27(4):490–498

    Article  Google Scholar 

  • Gevers W, Verguts T, Reynvoet B, Caessens B, Fias W (2006) Numbers and space: a computational model of the SNARC effect. J Exp Psychol Hum Percept Perform 32(1):32

    Article  PubMed  Google Scholar 

  • Grefkes C, Fink GR (2005) The functional organization of the intraparietal sulcus in humans and monkeys. J Anat 207(1):3–17

    Article  PubMed  PubMed Central  Google Scholar 

  • Hartmann M, Mast FW, Fischer MH (2015) Spatial biases during mental arithmetic: evidence from eye movements on a blank screen. Front Psychol 6:12

    Article  PubMed  PubMed Central  Google Scholar 

  • Hartmann M, Sommer NR, Diana L, Müri RM, Eberhard-Moscicka AK (2019) Further to the right: viewing distance modulates attentional asymmetries (‘pseudoneglect’) during visual exploration. Brain Cognit 129:40–48

    Article  Google Scholar 

  • Hartmann M, Mast FW, Fischer MH (2016) Counting is a spatial process: evidence from eye movements. Psychol Res 80(3):399–409

    Article  PubMed  Google Scholar 

  • Hesse PN, Fiehler K, Bremmer F (2016) SNARC effect in different effectors. Perception 45(1–2):180–195

    Article  PubMed  Google Scholar 

  • Hubbard EM, Piazza M, Pinel P, Dehaene S (2005) Interactions between number and space in parietal cortex. Nat Rev Neurosci 6(6):435

    Article  CAS  PubMed  Google Scholar 

  • Hung YH, Hung DL, Tzeng OJL, Wu DH (2008) Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition 106(3):1441–1450

    Article  PubMed  Google Scholar 

  • Irwin DE, Thomas LE (2007) The effect of saccades on number processing. Percept Psychophys 69(3):450–458

    Article  PubMed  Google Scholar 

  • Klein E, Huber S, Nuerk HC, Moeller K (2014) Operational momentum affects eye fixation behaviour. Q J Exp Psychol 67(8):1614–1625

    Article  CAS  Google Scholar 

  • Knops A, Thirion B, Hubbard EM, Michel V, Dehaene S (2009) Recruitment of an area involved in eye movements during mental arithmetic. Science 324(5934):1583–1585

    Article  CAS  PubMed  Google Scholar 

  • Lindemann O, Abolafia JM, Girardi G, Bekkering H (2007) Getting a grip on numbers: numerical magnitude priming in object grasping. J Exp Psychol Hum Percept Perform 33(6):1400

    Article  PubMed  Google Scholar 

  • Loetscher T, Schwarz U, Schubiger M, Brugger P (2008) Head turns bias the brain’s internal random generator. Curr Biol 18(2):R60–R62

    Article  CAS  PubMed  Google Scholar 

  • Loetscher T, Bockisch CJ, Nicholls ME, Brugger P (2010) Eye position predicts what number you have in mind. Curr Biol 20(6):R264–R265

    Article  CAS  PubMed  Google Scholar 

  • Masson N, Letesson C, Pesenti M (2018) Time course of overt attentional shifts in mental arithmetic: evidence from gaze metrics. Q J Exp Psychol 71(4):1009–1019

    Article  Google Scholar 

  • Mock J, Huber S, Klein E, Moeller K (2016) Insights into numerical cognition: considering eye-fixations in number processing and arithmetic. Psychol Res 80(3):334–359

    Article  CAS  PubMed  Google Scholar 

  • Moyer RS, Landauer TK (1967) Time required for judgements of numerical inequality. Nature 215(5109):1519

    Article  CAS  PubMed  Google Scholar 

  • Myachykov A, Cangelosi A, Ellis R, Fischer MH (2015) The oculomotor resonance effect in spatial–numerical mapping. Acta Physiol (Oxf) 161:162–169

    Google Scholar 

  • Myachykov A, Ellis R, Cangelosi A, Fischer MH (2016) Ocular drift along the mental number line. Psychol Res 80(3):379–388

    Article  PubMed  PubMed Central  Google Scholar 

  • Nuerk HC, Iversen W, Willmes K (2004) Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect. Q J Exp Psychol Sect A 57(5):835–863

    Article  Google Scholar 

  • Pressigout A, Charvillat A, Mersad K, Doré-Mazars K (2018) Time dependency of the SNARC effect for different number formats: evidence from saccadic responses. Psychol Res 83:1–11

    Google Scholar 

  • Ranzini M, Lisi M, Zorzi M (2016) Voluntary eye movements direct attention on the mental number space. Psychol Res 80(3):389–398

    Article  PubMed  Google Scholar 

  • Rugani R, Sartori L (2016) Numbers in action. Front Hum Neurosci 10:388

    PubMed  PubMed Central  Google Scholar 

  • Schwarz W, Keus IM (2004) Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses. Percept Psychophys 66(4):651–664

    Article  PubMed  Google Scholar 

  • Seegelke C, Wühr P (2018) Compatibility between object size and response side in grasping: the left hand prefers smaller objects, the right hand prefers larger objects. PeerJ 6:e6026

    Article  PubMed  PubMed Central  Google Scholar 

  • Shaki S, Fischer MH, Petrusic WM (2009) Reading habits for both words and numbers contribute to the SNARC effect. Psychon Bull Rev 16(2):328–331

    Article  PubMed  Google Scholar 

  • Shuman M, Kanwisher N (2004) Numerical magnitude in the human parietal lobe: tests of representational generality and domain specificity. Neuron 44(3):557–569

    Article  CAS  PubMed  Google Scholar 

  • Simon O, Mangin JF, Cohen L, Le Bihan D, Dehaene S (2002) Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron 33(3):475–487

    Article  CAS  PubMed  Google Scholar 

  • Song JH, Nakayama K (2008) Target selection in visual search as revealed by movement trajectories. Vision Res 48(7):853–861

    Article  PubMed  Google Scholar 

  • Team R (2015) RStudio: integrated development for R. RStudio, Inc., Boston, MA, 42, 14. http://www.rstudio.com

  • Walsh V (2003) A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn Sci 7(11):483–488

    Article  PubMed  Google Scholar 

  • Whalen J, Gallistel CR, Gelman R (1999) Nonverbal counting in humans: the psychophysics of number representation. Psychol Sci 10(2):130–137

    Article  Google Scholar 

  • Winter B, Marghetis T, Matlock T (2015) Of magnitudes and metaphors: explaining cognitive interactions between space, time, and number. Cortex 64:209–224

    Article  PubMed  Google Scholar 

  • Wood G, Willmes K, Nuerk HC, Fischer MH (2008) On the cognitive link between space and number: a meta-analysis of the SNARC effect. Psychol Sci Q 4(4):489–525

    Google Scholar 

  • Zebian S (2005) Linkages between number concepts, spatial thinking, and directionality of writing: the SNARC effect and the reverse SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. J Cogn Cult 5(1–2):165–190

    Article  Google Scholar 

Download references

Acknowledgements

We thank the editor and reviewers for considering this manuscript. This research received funding from a scholarship from the Ministry of Research (Alexandra Pressigout). We thank Agnes Charvillat for her help with the English version and Leo-Jun Leroy for his contribution to data collection.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Pressigout.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee (local Ethics Committee of Paris Descartes University, No. CER-PD: 2018-62) and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Communicated by Melvyn A. Goodale.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pressigout, A., Dore-Mazars, K. How does number magnitude influence temporal and spatial parameters of eye movements?. Exp Brain Res 238, 101–109 (2020). https://doi.org/10.1007/s00221-019-05701-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00221-019-05701-0

Keywords

Navigation