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Chen Cheng, Melissa Kibbe; Different types of mental manipulation of visual number representations differentially impact representational precision. Journal of Vision 2020;20(11):1135. doi: https://doi.org/10.1167/jov.20.11.1135.
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Humans (and many animals) can rapidly extract approximate numerical information from visual arrays (e.g. sets of objects, dots, etc.). We also can update these numerical representations as new visual information comes in, summing over new input (akin to incrementing an “accumulator”). However, it is currently unknown whether manipulation of visual number representations is confined to accumulator operations, or whether different types of manipulations may differentially impact the precision of the outputs of those manipulations. We asked participants (n=24) to perform different manipulations over visual number representations. These manipulations involved representing an occluded array (Basic condition), summing two sequentially-presented arrays (Summation condition), or separately representing two arrays and then taking their difference (Difference condition) (see Figure 1a). Crucially, both the Summation and Difference conditions required participants to manipulate two arrays, but only the Summation manipulation could be accomplished using an accumulator operation. We measured the precision of the outputs of these manipulations by asking participants to compare the outputs to a visible array of items, manipulating the difficulty of the comparison within each condition using five ratios (0.75, 0.8, 0.83, 0.86, 0.88). We observed a main effect of Ratio (F(4,92)=14.07, p<.001); participants were above chance (50%) for the first four ratios across conditions (ps<.001), but performance declined as the difficulty of the comparison increased. There was no main effect of Condition (F(2,46)=.152, p=.859), but there was a significant Ratio X Condition interaction (F(8,184)=7.97, p<.001); participants performed worse on Difference trials compared to both Basic and Summation trials when ratios were easier, with performance converging across the conditions as the task became more difficult (Figure 1b). These results suggest that visual number representations support a range of mental manipulations, but that the nature of the manipulation impacts the representational precision of its output.
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