Elsevier

Neuroscience

Volume 151, Issue 3, 6 February 2008, Pages 725-729
Neuroscience

Looking for the answer: The mind's eye in number space

https://doi.org/10.1016/j.neuroscience.2007.07.068Get rights and content

Abstract

Human subjects' answer to questions like “what number is halfway between 2 and 8” provides insights into spatial attention mechanisms involved in numerical processing. Here we show that mental numerical bisections are accompanied by a systematic pattern of horizontal eye movements: processing of a large number followed by a small number is accompanied with leftward eye movements, a tendency less pronounced or even reversed for the processing of a small number followed by a large number. The eyes thus appear to move along a left-to-right-oriented number line, indicating that shifts of attention in representational space are accompanied by an ocular motor orienting response. These results add to the growing evidence for a convergence of numerical processing, spatial attention, and movement planning in the parietal and frontal lobes. They also demonstrate the homologous relationship between our internal representations of numbers and space, and show that the concept of “number space” is more than a mere metaphor.

Section snippets

Experimental procedures

Nine healthy right-handed men (mean age 29, S.D. 6) participated in the experiment. Sitting in a dark room, subjects verbally indicated the median number of pre-recorded, orally presented numerical intervals and were instructed to respond as fast as possible in order to prevent any calculation strategy. Eleven ascending (e.g. 1–7) and 11 descending (e.g. 7-1) one digit number pairs were read from tape as “halfway between x and y?” in a pseudo-randomized order. The interval varied between 2

Results

There were 20.5% errors (1, 7, and 12.5% errors; for small, medium and large intervals respectively). There was neither a difference in the number of errors for ascending and descending intervals (chi-square=1.2, P>0.27) nor a pseudoneglect, i.e. more deviation errors toward the smaller number (Wilcoxon z=1.0, P>0.29). All further analyses are based on correct responses.

To test the modulation of eye movements by the distance between stimulus numbers, taking into consideration their presentation

Discussion

In a numerical bisection task, subjects showed larger leftward eye movements to number pairs presented in a descending (e.g. 6-2) compared with an ascending order (e.g. 2–6). This result demonstrates that the search for the number lying halfway between two stimulus numbers is accompanied by a systematic pattern of involuntary horizontal eye movements. The eyes appear to move along a left-to-right-oriented number line, indicating that shifts of attention in representational space are accompanied

Conclusion

To summarize, cognitive processes as different as attentional orienting, memorizing, the formation of mental images and numerical processing are all reported to be at least accompanied, if not influenced, by eye movements. It has been speculated that these seemingly dissimilar processes may have evolved from common visual perceptual functions (Jonides et al., 2005, Ehrlichman et al., 2007), thus providing a possible basis for the observed ocular–cognitive interactions. Our study illustrates

Acknowledgments

This study was supported by a grant from the Betty and David Koetser Foundation to P.B. We thank Tanja Schmückle-Meier for assistance in data collection, Albert Züger for technical support and Domink Straumann for helpful comments on an early draft.

References (52)

  • J. Gottlieb

    From thought to action: The parietal cortex as a bridge between perception, action, and cognition

    Neuron

    (2007)
  • G. Jewell et al.

    Pseudoneglect: a review and meta-analysis of performance factors in line bisection tasks

    Neuropsychologia

    (2000)
  • B. Laeng et al.

    Eye scanpaths during visual imagery reenact those of perception of the same visual scene

    Cognit Sci

    (2002)
  • J. Lepsien et al.

    Cognitive control of attention in the human brain: insights from orienting attention to mental representations

    Brain Res

    (2006)
  • M.R. Longo et al.

    Spatial attention and the mental number line: Evidence for characteristic biases and compression

    Neuropsychologia

    (2007)
  • P. McGeorge et al.

    A lateralized bias in mental imagery: Evidence for representational pseudoneglect

    Neurosci Lett

    (2007)
  • A.C. Nobre et al.

    Covert visual spatial orienting and saccades: overlapping neural systems

    Neuroimage

    (2000)
  • F.H. Previc et al.

    Why your “head is in the clouds” during thinking: The relationship between cognition and upper space

    Acta Psychol

    (2005)
  • G. Rizzolatti et al.

    Reorienting attention across the horizontal and vertical meridians: evidence in favor of a premotor theory of attention

    Neuropsychologia

    (1987)
  • O. Simon et al.

    Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe

    Neuron

    (2002)
  • S.V. Astafiev et al.

    Functional organization of human intraparietal and frontal cortex for attending, looking, and pointing

    J Neurosci

    (2003)
  • O. Bergamin et al.

    Three-dimensional Hess screen test with binocular dual search coils in a three-field magnetic system

    Invest Ophthalmol Vis Sci

    (2001)
  • S.A. Brandt et al.

    Spontaneous eye movements during visual imagery reflect the content of the visual scene

    J Cogn Neurosci

    (1997)
  • Y.E. Cohen et al.

    A common reference frame for movement plans in the posterior parietal cortex

    Nat Rev Neurosci

    (2002)
  • C.L. Colby et al.

    Space and attention in parietal cortex

    Annu Rev Neurosci

    (1999)
  • M. Corbetta

    Frontoparietal cortical networks for directing attention and the eye to visual locations: identical, independent, or overlapping neural systems?

    Proc Natl Acad Sci U S A

    (1998)
  • Cited by (53)

    • Neurocognitive and physiological measurment of STEM learning processes

      2022, International Encyclopedia of Education: Fourth Edition
    • Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection

      2017, Neuropsychologia
      Citation Excerpt :

      Indeed, evidence exists suggesting that eye movements and orienting of attention share the same mechanisms (e.g., Casarotti et al., 2012; Rizzolatti et al., 1987). Importantly, the choice of using eye movements to orient attention in space is also supported by a study by Loetscher et al. (2008) showing that spontaneous gaze shifts were generated while performing number interval bisection, and more in general by an increasing number of studies showing interactions between eye movements and number processing (for a review see, Hartmann, 2015). Using a similar approach, previous studies were able to establish the link between visuospatial attention and number processing in numerical tasks such as parity judgment or number comparison, showing that orienting of attention in physical space induced biases at the cognitive numerical level (e.g., Kramer et al., 2011; Stoianov et al., 2008; Ranzini et al., 2015; Ranzini et al., 2016).

    • Mental number space in three dimensions

      2015, Neuroscience and Biobehavioral Reviews
      Citation Excerpt :

      Here, participants are asked to call out a sequence of numbers as randomly as possible while performing a spatial task. When doing this while simultaneously performing horizontal head movements, they generate relatively larger numbers when looking to the right, and smaller numbers when looking to the left (Loetscher et al., 2008a). Similarly, when participants perform random number generation while walking, they produce larger numbers before taking an instructed right turn instead of an instructed left turn, and they spontaneously turn left more often than right when they say small compared to large numbers (Shaki and Fischer, 2014).

    • The effect of hand movements on numerical bisection judgments in early blind and sighted individuals

      2015, Cortex
      Citation Excerpt :

      The different number pairs were recorded as a single sound file (3.5 sec in duration) and presented in random order using E-prime2 (Psychology Software Tools, Pittsburgh, PA). Ascending and descending pairs were intermixed in the same block, in line with prior studies (Cattaneo, Fantino, Silvanto, Tinti, et al., 2011; Loetscher, Bockisch, & Brugger, 2008; Longo & Lourenco, 2007, Experiment 2). Participants were instructed to quickly estimate and verbally report the number laying in the middle of the given number pair (for instance, for the interval “352 368”, the correct answer is “360”) without making any arithmetic calculation.

    View all citing articles on Scopus
    View full text