Costs of manipulating representations of approximate visual magnitudes stored in visual working memory

Rapid extraction of numerical information from visual arrays is supported by the Approximate Number System (ANS). ANS representations are noisy, and storing and/or manipulating these representations in visual working memory (VWM) may result in additional representational noise. We asked how different types of mental manipulations of ANS representations in VWM may impact the precision of their outputs. In Experiment 1, adults (n=47) manipulated representations of two sets of dots that appeared sequentially (by recalling one of the two memorized sets (Storage), summing two sets (Addition), taking the difference between two sets (Subtraction), and performing an inverse subtraction (Unknown-addend)), and then to judge whether the output of that manipulation was larger than a comparison set (ratios between output and comparison set ranged from .75 to .88). Accuracy decreased as ratio increased (consistent with ANS), and participants were more accurate in Storage and Addition conditions compared to the two subtractive conditions, suggesting that different types of mental manipulations of ANS representations in VWM have a differential impact on precision. We also observed significantly higher reaction time in the Storage condition (in which participants had to store two sets in VWM) compared to the other three conditions (in which participants could store the first set, and then perform the manipulation upon viewing the second set). In Experiment 2 we equated VWM load in the Storage and Addition conditions: participants (n=44) were asked to hold two sets of dots in VWM and then perform a manipulation (Storage or Addition) based on a cue that appeared before the onset of the comparison array. We again found similar accuracy but higher reaction time for Storage versus Addition, suggesting that inhibiting a VWM representation (the uncued set in the Storage condition) may impose greater VWM cost than combining two stored representations.