# Virtual Reality as an Innovative Tool for Numerosity Perception
## 4 Discussion and Conclusions  
The aim of the current study was to assess the viability of conducting numerosity decisions in a VR setup and to determine whether the key characteristics of numerosity judgments observed in typical laboratory settings can be replicated. The main finding is that the VR platform, powered by Unity and the VIVE Focus 3 headset, proved flexible enough to incorporate the essential features of a psychophysical experiment. In this paradigm, the classical method of adjustment was employed, where the experimenter determines the test trials and their randomization before the experiment begins. This method functioned flawlessly. However, implementing a modern psychophysical experiment in VR presents certain challenges. Numerosity judgments typically require that dots forming a cloud are randomly distributed over a region of interest while adhering to specific constraints (e.g., ensuring objects do not overlap). This real-time computational demand was addressed by pre-calculating a list of coordinates in MATLAB, which was then integrated into the VR pipeline. Although this approach may seem labor-intensive, it is entirely manageable. The Unity application successfully read and interpreted the MATLAB output without issues. At the same time, it is worth noting that over the years several efficient methods have been developed to expedite data collection. To incorporate these, it will certainly be needed to change the work pipeline. Many of these are adaptive methods that analyze stimulus-response histories to suggest efficient stimulus intensities for subsequent data collection. While such algorithms are widely available in various MATLAB toolboxes, they lack proper integration with systems like Unity, which was originally designed for application and game development. In addition, the process of generating real-time stimuli that obey multiple constraints may be challenging and this becomes more complex when the algorithms reside externally. Nonetheless, since these algorithms are based on mathematical and statistical principles, translating them into code compatible with Unity is feasible. This will require additional development and testing to ensure optimal system performance while maintaining a seamless VR experience. From a psychophysical perspective, the experiment was successful. Two distinctive patterns commonly observed in typical 2D displays were successfully replicated, suggesting that the core features of the numerosity estimation system, previously studied only in 2D environments, are preserved in more realistic VR setups, which are inherently three-dimensional [34; 35]. The previous [PERSON] et al. study [35] provided evidence that numerosity and density judgments are governed by separate perceptual mechanisms with different psychophysical characteristics. In particular, for densities up to 0.25 dots/deg\({}^{2}\), Weber fractions remained constant, supporting a direct perception of numerosity; while beyond 0.25 dots/deg\({}^{2}\), Weber fractions decreased, indicating a transition to texture-density mechanisms. The drop in Weber fractions reported here (about a factor of 2) is entirely consistent with these previous findings, which show that, after a breakpoint judgments, the Weber fractions values follow a regime change and obey a square-root law [14; 35]. Interestingly, the quantitative similarity between the current dataset and previous datasets resides not only in the drop of Weber Fractions at higher numerosities but also in the average values. Previous studies have reported Weber fractions ranging from approximately 15% for low and intermediate conditions to approximately 8% in high numerosities conditions [61]. Also, response times exhibited a trend similar to previously published data from the group. In [34], the authors investigated how response times vary across different numerosity perception regimes: subitizing, estimation, and texture. For numerosities greater than four (estimation range) response times are higher due to a higher cognitive demand for estimation tasks.