Introduction
Numerosity perception is a fundamental perceptual property, akin to color, brightness, size, and motion ( He et al., 2015 ; Grasso et al., 2022 ; Leslie, Gelman & Gallistel, 2008 ). This cognitive ability enables the extraction of numerical information from stimuli by human adults, infants, and even animals, facilitating quick estimation, manipulation, and processing of numerosities, and comprehension of their relationships ( Deheane, 1998 ; Clarke & Beck, 2021 ; Crollen & Collignon, 2020 ; Grasso et al., 2022 ). Recent studies exploring animal numerosity perception delve into the quantitative assessments made by animals during environmental negotiations. These investigations reveal the engagement of both cortical and subcortical brain regions in magnitude estimation, suggesting a more extensive neural network at play ( Vallortigara et al., 2022 ). Another line of research provides a comprehensive review of numerosity perception across various animal species, underscoring the necessity of comprehending the neural mechanisms underpinning observed behavioral patterns ( Lorenzi, Perrino & Vallortigara, 2021 ). Furthermore, a study focusing on vertebrates, particularly fish, showcases their adeptness at estimating quantities, shedding light on the neurobiological foundations that support this cognitive capacity ( Messina et al., 2022 ). These studies indicate that both humans and other species are capable of perceiving and processing numerical information in their environment. Some researchers have suggested that individuals, both human and animal, draw inferences based on life experiences in numerosity judgment, incorporating non-numerical characteristics of stimuli such as color, size, and orientation ( Grasso et al., 2022 ; Dehaene, Bossini & Giraux, 1993 ; Zorzi, Stoianov & Umiltà, 2005 ). Hence, the investigation of numerosity perception necessitates a multidimensional approach, linking numerical quantity or numerosity with diverse perceptual features.

One of the prominent theories of the interaction of numerosity and other perceptual features is “A Theory of Magnitude” (ATOM). ATOM suggests that, space, time, and number are processed through a common magnitude system and are linked by the action. The parietal cortex is an important brain area for magnitude system processing, to optimize action programming and execution ( Walsh, 2003 ). ATOM exhibits species generality, as it observed not only in humans but also prevalent across various animal species. Initially discovered in mammals, it was linked to the mediation by the parietal cortex. However, recent research indicates that this theory extends beyond mammals to encompass a broader range of animals. For instance, studies in birds, despite lacking a cortex akin to mammals, reveal reliable space–time interactions, supporting the cross-species applicability of ATOM ( De Corte, Navarro & Wasserman, 2017 ). Insects, such as bees, demonstrate numerical discrimination, and training experiments illustrate a cross-dimensional transfer between numerical and spatial dimensions. This provides compelling evidence for the universal coding of general magnitude ( Bortot, Stancher & Vallortigara, 2020 ). Therefore, the omnipresence of magnitude theory in animals establishes a unified cognitive framework for comprehending their perception of time, space, and quantity. The widespread applicability of the theory underscores a common neural basis that transcends species differences. Research on ATOM mostly focused on the shared mechanism of number and other perceptual features, but little attention has been paid to how quantity information combines with action planning and execution. Anobile et al. (2021a) and Anobile et al. (2021b) proposed a “sensorimotor numerosity system” that can simultaneously process perception and action planning or execution. The sensorimotor numerosity system possesses the ability to estimate the numerical value of externally induced events as well as the magnitude of internally initiated actions. Additionally, this system is capable of processing quantitative information pertaining to non-numerical attributes such as spatial and temporal dimensions ( Anobile et al., 2021a ; Anobile et al., 2021b ). In recent years, more and more research has proposed numerosity perception is intrinsically linked with action, as evidenced by adaptation techniques ( Burr et al., 2021 ).

Perceptual adaptation, known as “psychologist’s micro-electrode”, is one of the most effective methods to investigate perceptual mechanisms. The efficacy of this tool as a fundamental psychophysical instrument for investigating numerous perceptual properties has been empirically established ( Thompson & Burr, 2009 ), numerosity, as a primary perceptual property, can also be adapted ( Burr & Ross, 2008 ). Recent empirical investigations employing motor adaptation techniques have successfully unveiled a robust association between motion and the numerosity estimation ( Burr et al., 2021 ; Anobile et al., 2021a ; Anobile et al., 2021b ; Anobile et al., 2016 ; Togoli et al., 2020 ). Participants were asked to tap in midair with their dominant hand, either very fast or slow. It was found that fast tapping caused participants underestimate of the numerosity perception, while slow tapping caused overestimation. The motor adaptation has a strong effect, causing a deviation of about 20% to 25% in the numerosity perception. This effect is cross-modal and exists in both the temporal sequences and spatial arrays ( Arrighi, Togoli & Burr, 2014 ; Anobile et al., 2016 ; Maldonado Moscoso et al., 2020a ; Maldonado Moscoso et al., 2020b ). The motor adaptation effect on numerosity perception is not limited to vision; it is also present in sequences of auditory tones. Even more intriguingly, motor adaptation similarly affects auditory numerosity in congenitally blind adults, indicating that the interaction between action and numerosity perception remains intact irrespective of visual input or even prior visual experience ( Togoli et al., 2020 ). Additionally, there is also brain imaging evidence that reveals a link between numerosity perception and motion. The activated regions involved in the process of numerosity perception are located near the parietal cortex and partially overlap with the action-related brain regions ( Hubbard et al., 2005 ; Simon et al., 2002 ).

People will use multiple strategies according to their needs when processing numerosity, such as fast and accurate processing of small numerosities within the subitizing range ( Mandler & Shebo, 1982 ); fast but rough approximate estimation ( Zhou et al., 2016 ); accurate but time-consuming counting ( Simon & Vaishnavi, 1996 ); and the groupitizing strategy, which has attracted more and more attention in recent studies. “Groupitizing” means that when estimating the number of an array, dividing the array into several subgroups, the estimated result is faster and more accurate than the ungrouped one ( Pan et al., 2021 ; Anobile et al., 2020a ; Anobile et al., 2020b ; Maldonado Moscoso et al., 2020a ; Maldonado Moscoso et al., 2020 ; Starkey & McCandliss, 2014 ). Groupitizing combines the advantages of subitizing and estimation. When the grouped subgroups and the number of items in each subgroup are within the subitizing range, the subgroups and the number of items in each subgroup can be processed simultaneously. Groupitizing is like processing several arrays within the subitizing range at the same time. Therefore, the processing is faster and more accurate than that of non-grouped arrays ( Wege, Trezise & Inglis, 2021 ). In addition, using the grouping strategy involves advanced cognitive processing, such as mental arithmetic ( Maldonado et al., 2021 ; Anobile et al., 2020a ; Anobile et al., 2020b ; Ciccione & Dehaene, 2020 ; Maldonado Moscoso et al., 2020a ; Maldonado Moscoso et al., 2020 ), making the result of numerosity perception more accurate. The grouping effect is also cross-modal and cross-format. Groupitizing is found in both time and space dimensions ( Anobile et al., 2021a ; Anobile et al., 2021b ), and not only visually grouped array have the grouping advantage, but also the auditory tones sequence ( Anobile et al., 2021a ; Anobile et al., 2021b ).

Perceptual adaptation typically elicits erroneous perception of specific aspects of stimuli, such as motion aftereffect, exhibiting a bias in the direction opposite to that of the adaptation. One of the most prototypical examples is the waterfall illusion: after observing the downward motion of a waterfall for several seconds, redirecting one’s gaze to the adjacent region induces an illusory perception of upward motion ( Thompson & Burr, 2009 ; Anobile et al., 2021a ; Anobile et al., 2021b ; Barlow & Hill, 1964 ; Addams, 1833 ). This phenomenon can be ascribed to the disparity in relative neuronal activities resulting from the continuous stimulation of neurons specialized for vertical motion, leading to adaptation and subsequent imbalance with neurons specialized for downward motion. As a result, when a test stimulus is presented, it makes use of an unbalanced system, which produces measurable illusion perception aftereffects ( Solomon & Kohn, 2014 ). Adaptation is a pervasive phenomenon observed across various sensory systems and serves as a transient form of plasticity that can be leveraged as a valuable mechanism for recalibrating the perception of environmental statistics ( Webster, 2015 ; Anobile et al., 2021a ; Anobile et al., 2021b ). Therefore, visual motion adaptation also induces perceptual adaptation. Previous research has demonstrated that adapting to fast or slow proprioceptive hand movements leads to subsequent deviations in numerosity estimation, thus resulting in an adaptation effect. Regarding visual motion adaptation, only a few studies have explored it ( Fornaciai, Togoli & Arrighi, 2018 ). Previous research has laid the groundwork for our understanding of visual motion adaptation. Building upon this foundation, our study aims to further investigate whether motion adaptation effects occur when observing objects with different speeds. Additionally, we will introduce grouping strategies to explore the interplay between these two factors. This endeavor contributes to constructing a more comprehensive theoretical model in the field of numerosity perception. Consequently, this study expands upon the proprioceptive motion adaptation paradigm utilized by prior researchers and incorporates a visual motion adaptation paradigm. Its objective is to examine whether participants, after being exposed to arrays of rapidly or slowly moving stimuli, demonstrate a adaptation effect in numerosity estimation.

The investigation of the interplay between numerosity perception and motor adaptation constitutes a significant domain deserving of scholarly attention, however, the cognitive mechanism of numerosity perception under visual motion adaptation has not been studied in-depth. “Groupitizing” can improve the sensory precision of numerosity perception, while motor adaptation can bias the results: fast or high-frequency motor adaptation leads to underestimation, while slow or low-frequency motor adaptation leads to overestimation. So, an intriguing question is, after the motor adaptation, the next numerosities is presented in groups, then what will be the result of numerosity perception? Therefore, the purpose of this study is to explore whether motor adaptation affects the groupitizing under two motor adaptation conditions or whether there is still an adaptation effect if the groupitizing strategy is used. Based on this, we designed two experiments: Experiment 1 adopts proprioceptive motor adaptation (hand tapping) similar to previous studies, and Experiment 2 adopts adaptation to visual motion (viewing moving dots) to explore the relationship between motor adaptation and grouping effect. Since many previous studies have proven that the groupitizing strategy has a robust advantage in the numerosity perception, here, we assume that even with motor adaptation before numerosity estimation, the grouping effect still exists. In other words, grouping can reduce the perception deviation after motor adaptation, making the result of numerosity perception more accurate.