Abstract: Numerosity perception involves humans' cognitive ability to extract numerical information from various stimuli, forming a crucial foundation for understanding the world and processing information. Grouping strategies, known as “groupitizing,” encompass the organization of objects into sets or categories during the numerosity perception process. This facilitates rapid and effective numerosity estimation, particularly in situations with short presentation times and numerous quantities. Groupitizing combines the advantages of subitizing and counting, influencing individual arithmetic abilities. However, previous studies have often overlooked the influence of perceptual grouping cues-both intrinsic and extrinsic-on groupitizing strategies in numerosity perception. Additionally, they have failed to comprehensively explore the cognitive and neural mechanisms underlying groupitizing strategies across multiple dimensions.
To deepen our understanding of this cognitive phenomenon, this study adopts the “A theory of magnitude” (ATOM) as its theoretical framework to systematically investigate groupitizing strategies in visual numerosity perception. The ATOM posits a shared neural basis among time, space, and quantity, linked through the concept of motion. This linkage relies on the brain's shared neural systems involved in encoding temporal, spatial, and numerical information, all of which involve motion, such as objects moving in space, the passage of time, and changes in quantity. By converting different types of motion information into shared neural representations, the brain can establish connections between quantity, time, and space. Therefore, this study integrates the ATOM and comprehensively utilizes behavioral and fMRI techniques to explore the influences of different dimensions of magnitude systems on groupitizing strategies in numerosity perception and investigate their characteristics in individual developmental processes. The research comprises three studies, totaling six experiments, conducted from the dimensions of space, time, and motion.
Study 1 investigates the influence of intrinsic and extrinsic spatial grouping cues on the cognitive and neural mechanisms underlying numerosity perception in groupitizing, using spatial dot array stimuli. Combining behavioral experiments and fMRI, the study examines how participants process grouping cues at both cognitive and neural levels. The behavioral task involves numerosity estimation, while fMRI reveals the neural basis of processing different types of grouping cues. Study 2 explores the impact of temporal grouping cues on numerosity perception, using sequentially presented stimuli. Participants completed a numerosity estimation task under different stimulus onset asynchrony (SOA) conditions to compare intrinsic and extrinsic grouping cues. The study also employed fMRI to examine brain regions activated during grouping and no-grouping conditions, providing insights into the cognitive and neural mechanisms of temporal grouping and the role of attentional processes in numerosity perception. Study 3, grounded in the sensorimotor numerosity system (SNS), employs a motion adaptation paradigm along with event-related potential (ERP) technology to investigate numerosity perception in the motion dimension. The study includes two adaptation experiments: one involving proprioceptive adaptation through high or low frequency finger tapping and another involving visual adaptation to high or low speed motion point arrays. It explores how both proprioceptive and visual motion adaptation affect numerosity perception and how grouping conditions modulate these adaptation effects.
This study highlights several significant innovations:
Firstly, this study explores numerosity perception and groupitizing strategies across multiple dimensions—spatial, temporal, and motion. Compared to previous research that focused on a single dimension, this study provides a more comprehensive examination of how different dimensions affect numerosity perception, offering a new perspective for understanding groupitizing strategies.
Secondly, by employing fMRI and ERP technology, this study investigates the neural basis of groupitizing strategies in numerosity perception, revealing specific brain regions involved in the process. The validation of these neural mechanisms not only enhances our understanding of groupitizing strategies in numerosity perception but also provides valuable empirical support for the field of cognitive neuroscience.
Lastly, the study emphasizes the importance of extrinsic grouping cues in numerosity perception, demonstrating that, compared to intrinsic cues, extrinsic cues have a more significant impact on groupitizing strategies. This finding contributes to a better understanding of how groupitizing strategies are formed and operate in numerosity perception.
In summary, this study enhances the understanding of numerosity perception and groupitizing strategies by examining spatial, temporal, and motion dimensions within the framework of “A theory of magnitude” (ATOM). Utilizing behavioral, ERP and fMRI techniques, it reveals the cognitive and neural mechanisms involved in groupitizing, highlighting the significant roles of intrinsic and extrinsic grouping cues. These findings emphasize the complexity of numerosity perception and the importance of external cues in shaping groupitizing strategies, offering valuable insights for future research.

Key words: numerosity perception, groupitizing, grouping cues, ATOM, fMRI