Looking for the answer: The mind's eye in number space
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)
- et al.
Interactions between attention and working memory
Neuroscience
(2006) - et al.
Stimulus-response compatibility in representational space
Neuropsychologia
(1998) - et al.
Pseudoneglect: effects of hemispace on a tactile line bisection task
Neuropsychologia
(1980) - et al.
Temporal order judgment reveals how number magnitude affects visuospatial attention
Cognition
(2007) - et al.
The role of parietal cortex in visuomotor control: What have we learned from neuroimaging?
Neuropsychologia
(2006) - et al.
Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic
Cortex
(1997) - et al.
Saccade target selection and object recognition: Evidence for a common attentional mechanism
Vision Res
(1996) - et al.
Looking for answers: Eye movements in non-visual cognitive tasks
Brain Cogn
(2007) - et al.
Human gaze stability in the horizontal vertical and torsional direction during voluntary head movements, evaluated with a three-dimensional scleral induction coil technique
Vision Res
(1987) - et al.
Parietal rTMS distorts the mental number line: Simulating “spatial” neglect in healthy subjects
Neuropsychologia
(2006)
From thought to action: The parietal cortex as a bridge between perception, action, and cognition
Neuron
Pseudoneglect: a review and meta-analysis of performance factors in line bisection tasks
Neuropsychologia
Eye scanpaths during visual imagery reenact those of perception of the same visual scene
Cognit Sci
Cognitive control of attention in the human brain: insights from orienting attention to mental representations
Brain Res
Spatial attention and the mental number line: Evidence for characteristic biases and compression
Neuropsychologia
A lateralized bias in mental imagery: Evidence for representational pseudoneglect
Neurosci Lett
Covert visual spatial orienting and saccades: overlapping neural systems
Neuroimage
Why your “head is in the clouds” during thinking: The relationship between cognition and upper space
Acta Psychol
Reorienting attention across the horizontal and vertical meridians: evidence in favor of a premotor theory of attention
Neuropsychologia
Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe
Neuron
Functional organization of human intraparietal and frontal cortex for attending, looking, and pointing
J Neurosci
Three-dimensional Hess screen test with binocular dual search coils in a three-field magnetic system
Invest Ophthalmol Vis Sci
Spontaneous eye movements during visual imagery reflect the content of the visual scene
J Cogn Neurosci
A common reference frame for movement plans in the posterior parietal cortex
Nat Rev Neurosci
Space and attention in parietal cortex
Annu Rev Neurosci
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
Cited by (53)
Summing up: A functional role of eye movements along the mental number line for arithmetic
2022, Acta PsychologicaNeurocognitive and physiological measurment of STEM learning processes
2022, International Encyclopedia of Education: Fourth EditionContribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection
2017, NeuropsychologiaCitation 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 ReviewsCitation 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 oculomotor resonance effect in spatial-numerical mapping
2015, Acta PsychologicaThe effect of hand movements on numerical bisection judgments in early blind and sighted individuals
2015, CortexCitation 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.