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Lixia He, Tiangang Zhou, Jun Zhang, Lin Chen, Yan Zhuo; Connectedness and inside/outside relation affect dot numerical judgment: implications for perceptual objects defined by topological attributes. Journal of Vision 2008;8(6):654. doi: 10.1167/8.6.654.
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A wealth of evidence in behavioral and neurological studies supports that number sense exists not only in normal adults with well-developed symbolic numerical system, but also among non-verbal animals and pre-verbal infants. For instance, monkeys could extract number information from visual dot displays irrespective of their exact physical appearance such as item shape, size, circumference and location. However, one basic question remains open of what properties exactly determine a numerical identity.
The present study first investigated how connectedness (an attribute of topology) affected dot numerical representation. Participants judged the number of dots in random spatial positions with brief visual presentation such that judgment was based on instantaneous impression without overt or covert counting. Several pairs of dots were connected via a thin line. We found that connectedness resulted in numerical underestimation, that is, the more connected pairs, the less dots perceived. This effect remained when changes occurred to local features such as item shape (dot or triangle) and connecting pattern (line segments or irregular curves, dots terminating the lines or merely on the lines). However, when line segments were merely attached to dots without actually connecting them, the underestimation was no longer observed. Further we investigated another attribute of topology, the inside/outside relation using the same paradigm. We found that when dots were enclosed by an arbitrarily-shaped envelop, underestimation occurred comparing to those with no dots enclosed; and this impairment increased with more dots enclosed. However, once the inside/outside relationship was destroyed, for example, the envelop was split into two open curves, the underestimation effect demolished.
To account for these data, we propose that numerical perception of visual items is based on the number of perceptual objects which could be defined by topological attributes characterized by either connectedness or inside/outside relation (Chen, 2005).
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