On the functional independence of numerical acuity and visual working memory

Roberto Dell’Acqua; Sessa, Paola; Brigadoi, Sabrina; Gervain, Judit; Luria, Roy; Doro, Mattia · 2024 · Crossref

DOI: 10.3389/fpsyg.2024.1335857

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Summary

This study investigates the functional relationship between visual working memory (VWM) capacity and numerical acuity, specifically addressing whether these two cognitive domains share underlying processing mechanisms. While VWM is a central construct in cognitive models, its capacity is limited and predictive of many high-level cognitive efficiencies. Numerical acuity, the ability to approximate the numerosity of large sets without counting, is considered a primordial, likely pre-attentive ability. Previous research by Piazza et al. (2011) suggested these systems are independent, but the current authors identified methodological flaws in that study, including suboptimal timing parameters in the change detection task and the use of an inappropriate formula for calculating VWM capacity. The present research aims to provide a more rigorous test of this dissociation by correcting these design issues. The experiment involved 41 university students who completed two tasks: a whole-display change detection task to measure VWM capacity and a dot-comparison task to assess numerical acuity. In the change detection task, participants memorized arrays of 2, 3, or 5 colored squares displayed for 150 ms, followed by a 900 ms retention interval, and then identified if one color had changed in a test array. This timing was designed to prevent foveation and verbal rehearsal strategies. VWM capacity (K) was calculated using Pashler’s (1988) formula, which is theoretically appropriate for whole-display tasks, rather than Cowan’s (2001) formula used previously. Numerical acuity was measured using a dot-comparison task where participants judged which of two arrays contained more dots. Crucially, stimuli were generated using the CUSTOM toolbox to decorrelate numerosity from continuous perceptual variables like density and total surface area, ensuring the task tapped into number processing rather than sensory cues. The results demonstrated that VWM capacity increased with set-size, plateauing at set-size 5, with mean K values of 1.9, 2.8, and 4.4 for set-sizes 2, 3, and 5, respectively. Construct validity checks confirmed that K values correlated across different set-sizes. Numerical acuity was quantified by Weber fractions, with participants showing an average acuity index of 0.80 (derived from 1 – ω). The core finding was a null correlation between individual maximum VWM capacity (K at set-size 5) and numerical acuity. This absence of correlation was supported by both classical statistics and Bayesian analysis, which provided substantial evidence for the null hypothesis. The authors concluded that the lack of correlation persists even when methodological confounds are strictly controlled. The significance of these findings lies in the strong support for the functional independence of visual working memory and the approximate number system. The results suggest that VWM operates as a high-level central hub for information maintenance, while numerical acuity relies on lower-level, likely sensory, processing stages that do not consume VWM resources. This distinction clarifies the architecture of human cognition, indicating that not all cognitive abilities are constrained by working memory limits. By employing rigorous experimental controls and appropriate analytical formulas, the study reinforces the view that numerosity approximation is a distinct, automatic process separate from the attention-demanding mechanisms of visual working memory.

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• cognitive capacity variation