# Virtual Reality as an Innovative Tool for Numerosity Perception
## 1 Introduction
This can be useful for exploring how environmental and contextual factors influence numerosity estimation. This approach allows for a more natural interaction with numerical stimuli, where arrays of objects can be distributed in three-dimensional space rather than being constrained to a two-dimensional screen. This can be particularly useful for simulating real-world environments where participants estimate numerosities in dynamic and spatially complex scenes, such as evaluating the number of objects in a cluttered room or assessing the density of elements in a natural setting. VR-based studies could significantly improve the ecological validity of numerosity perception experiments compared to traditional 2D methods based on monitors. Moreover, there is recent evidence linking actions to numerosity perception, suggesting the existence of a \"sensorimotor numerosity mechanism\" integrating sensory numerical information coming from the environment with that internally generated by actions [42; 43; 44; 45]. Even if the link between this newly discovered system and math skills is still to be tested, VR stands as a potentially excellent tool for the implementation of setups aimed at promoting the interaction between action and numerical perception. Unlike traditional methods, VR enables direct sensorimotor engagement through embodied interactions such as reaching, grasping, or manipulating numerical stimuli in an immersive space. This could be particularly relevant for studying how proprioceptive and haptic feedback influence numerical estimation [44] and for developing novel training paradigms that leverage multimodal learning. Furthermore, VR allows for greater experimental control and flexibility in the presentation of numerical stimuli [46]. In the case of numerosity judgments, variables such as object size, spatial arrangement, motion, and environmental lighting conditions can be dynamically isolated or adjusted to investigate their influence on numerosity perception. For example, researchers can test whether numerical estimation differs when elements are presented in peripersonal space versus extrapersonal space or how different levels of visual complexity affect estimation accuracy. The ability to manipulate such parameters in real-time and in an ecologically valid manner makes VR a valuable tool for uncovering underlying cognitive mechanisms that might not be evident with traditional screen-based tasks. Additionally, VR offers the possibility of incorporating adaptive learning mechanisms, where task difficulty dynamically adjusts based on user performance. This can increase engagement, prevent fatigue, and provide personalized training experiences tailored to individual needs. In general, VR experiences delivered to young populations yield high engagement [47; 48; 49], and it is likely that the immersive nature of VR can also enhance motivation by transforming traditionally repetitive numerical estimation tasks into more interactive and gamified experiences, potentially improving long-term learning outcomes. Taken together, these advantages highlight the potential of VR not only as an alternative to traditional numerosity tasks but as a powerful platform for advancing the understanding of numerical cognition. At the same time, transposing typical experimental paradigms into a VR system does not come without its challenges. Inconsistent signals from our visual and vestibular systems during space exploration can cause motion sickness [50], which may hamper the participant compliance to long experimental sessions. In addition, the sense of agency--the subjective experience of controlling one's actions and their outcomes--and presence --the perceptual illusion of being physically immersed in the virtual environment-- need to be satisfied, otherwise one risks delivering to the user an immersive but unrealistic environment [51; 52]. Further, some VR systems, in particular head mounted displays (HMDs), could provide inconsistent accommodation and vergence signals, which bring about erroneous spatial estimates [53].