General discussion
Based on the Gestalt theory of perceptual grouping, the phenomenon of “groupitizing” is considered a valuable strategy in numerosity perception, along with subitizing, counting, and estimation ( Anobile et al., 2020a ; Anobile et al., 2020b ; Ciccione & Dehaene, 2020 ). Groupitizing involves perceiving visually grouped arrays as a single entity, which enhances the speed and precision of numerosity perception. The “A Theory of Magnitude” (ATOM) framework, suggests a close link between number and action. Motor adaptation, a cognitive process through which our motor system adjusts to changes in the environment or our own body, plays a role in numerosity perception by influencing how the brain processes numerical information and perceives numerosities ( Debats, Heuer & Kayser, 2023 ; Franklin et al., 2023 ).

Previous studies have used motor adaptation technology to investigate the effects of motor adaptation on numerosity perception. It has been found that high-frequency motor adaptation leads to underestimation of numerosity perception, while low-frequency adaptation leads to overestimation. This phenomenon of motor adaptation, where prolonged exposure to a stimulus can result in perceptual changes, has been well-documented in numerosity perception tasks ( Anobile et al., 2016 ; Anobile et al., 2020a ; Anobile et al., 2020b ). However, the interaction between motor adaptation and “groupitizing” in numerosity perception has not been thoroughly investigated. This raises the question of how groupitizing may interact with motor adaptation and affect numerosity perception.

The results of our study provide valuable insights into the interaction between motor adaptation and grouping strategies in numerosity estimation tasks. Experiment 1 replicated previous findings that adaptation to fast hand tapping led to an underestimation of numerosity, while adaptation to slow hand tapping resulted in overestimation, consistent with previous research ( Anobile et al., 2020a ; Anobile et al., 2020b ; Anobile et al., 2016 ). However, contrary to previous findings, our results did not reveal a significant grouping effect on perception precision, indicating that motor adaptation may have modulated the grouping advantage. Interestingly, our data did show a grouping advantage in reaction time, with faster reaction times observed in the grouping condition compared to the no-grouping condition. This suggests that grouping may influence the speed of numerosity perception but not necessarily the precision.

However, surprisingly, adaptation effects persist even when presenting grouped stimuli after motor adaptation, showing a stronger impact under grouping conditions ( Figure 2A ). This finding presents an intriguing and complex phenomenon. Firstly, previous neuroscientific research suggests that motor adaptation induces neural adaptation to features such as motion direction and speed, thereby altering the responsiveness of the perceptual system ( Kohn & Movshon, 2004 ). This adaptation may affect numerosity perception by reducing the sensitivity of the perceptual system to grouping information. Considering that neurons may have different functions in different tasks and conditions, motor adaptation and grouping effects may share some neural populations ( Kanai & Verstraten, 2005 ; Krekelberg, Boynton & Wezel, 2006 ), leading to more intricate interactions between the two effects. Secondly, participants, when presented with grouped stimuli after motor adaptation, may choose to adjust their numerosity estimation strategy to adapt to changes in the perceptual system. This adjustment may involve balancing information from different sources to achieve optimal performance in numerosity perception tasks ( Wolfe, 2014 ; Summerfield & Egner, 2009 ). To further unveil the neural basis of motor adaptation and grouping effects on numerosity perception, future research could employ neuroimaging techniques such as functional magnetic resonance imaging (fMRI) or electroencephalography (EEG). These techniques can provide more detailed insights into neural activity and connectivity patterns, allowing a deeper understanding of the neural mechanisms involved.

Experiment 2, focusing on visual motion adaptation, aimed to investigate whether adaptation to visual motion induces effects similar to proprioceptive motor adaptation and to examine the relationship between visual motion adaptation and groupitizing. The results closely mirrored those of Experiment 1, revealing a consistent pattern where fast visual motion adaptation led to underestimation, and slow visual motion adaptation led to overestimation. However, in Experiment 2, adaptation effects under the grouping condition were observed to be weaker compared to the no-grouping conditions. This difference suggests that the impact of visual motion adaptation on grouping effects might not be as pronounced as that of proprioceptive motion adaptation, providing room for participants to employ grouping strategies effectively and mitigate estimation biases. A plausible explanation for this observation is that participants may dynamically adjust their cognitive strategies under different adaptation conditions. In Experiment 1, the pronounced adaptation effects induced by proprioceptive motion adaptation may have inclined participants to preferentially adopt a singular adaptation strategy. Conversely, in Experiment 2, where visual motion adaptation was relatively weaker, participants seemed more inclined to flexibly adjust their cognitive strategies to adapt to grouping conditions.

Our results also suggest that the range of numerosity values used in the estimation task may influence the relationship between adaptation and grouping strategies. In Experiment 2, the borderline significant main effect of the grouping condition on sensory precision may be attributed to the limited range of numerosity values used (9–14). Future research could explore the relationship between adaptation and grouping strategies by manipulating the range of numerosity values under the adaptation to visual motion condition to further investigate the effects of grouping on sensory precision.

In conclusion, our research findings contribute to the understanding of the interaction between motion adaptation, groupitizing, and numerosity perception. The findings from Experiment 1 and Experiment 2 consistently showed that proprioceptive motor adaptation involving high or low-frequency tapping of the fingers, as well as visual motion adaptation from observing rapid or slow-motion dot arrays, leads to subsequent underestimation or overestimation of presented numerosity. The use of a grouping strategy, known as “groupitizing”, appeared to have a differential effect on motor adaptation depending on the context. In Experiment 1, the grouping strategy influenced proprioceptive motor adaptation, while in Experiment 2, it had limited effects on visual motion adaptation. Additionally, more research is needed to investigate the mechanisms of visual motion adaptation as it has received limited attention compared to proprioceptive motor adaptation in the field of motion perception. Overall, our study highlights the complex relationship between motor adaptation, grouping strategies, and numerosity perception and provides important insights for future research in this area.