The representation of space, time and number is believed to rely on a common encoding system developed to support action guidance. While the ecological advantage of such a shared system is evident when objects are located within the region of space we can act on (known as peri-personal space), it is less obvious in the case of objects located beyond our arms' reach. In the current study we investigated whether and to what extent the distance of the stimuli from the observer affects the perception of duration and numerosity. We first replicated Anelli et al.'s (2015) experiment by asking adult participants to perform a duration reproduction task with stimuli of different sizes displayed in the peri- or extra-personal space, and then applied the same paradigm to a non-symbolic numerosity estimation task. Results show that, independently of size, duration estimates were overestimated when visual stimuli were presented in the extra-personal space, replicating previous findings. A similar effect was also found for numerosity perception, however overestimation for far stimuli was much smaller in magnitude and was accounted by the difference in perceived size between stimuli presented in peripersonal or extrapersonal space. Overall, these results suggest that, while the processing of temporal information is robustly affected by the position of the stimuli in either the peri- or extra-personal space, numerosity perception is independent from stimulus distance. We speculate that, while time and numerosity may be encoded by a shared system in the peri-personal space (to optimize action execution), different and partially independent mechanisms may underlie the representation of time and numerosity in extra-personal space. Furthermore, these results suggest that investigating magnitude perception across spatial planes (where it is or is not possible to act) may unveil processing differences that would otherwise pass unnoticed.

相信空间，时间和数字的表示依赖于开发用于支持动作指导的通用编码系统。当物体位于我们可以作用的空间区域（称为人身空间）中时，这种共享系统的生态优势是显而易见的，但是当物体位于我们的手臂无法触及的范围时，这种优势就不那么明显了。在当前的研究中，我们调查了刺激与观察者的距离是否以及在多大程度上影响了持续时间和数字的感知。我们首先复制了Anelli等人（2015）的实验，方法是让成年参与者通过在个人或个人外空间中显示不同大小的刺激来执行持续时间的再现任务，然后将相同的范例应用于非符号系统数量估计任务。结果表明，与大小无关，当在人际空间中呈现视觉刺激时，会持续时间估计过高，从而重复了先前的发现。在数字感知方面也发现了类似的效果，但是远距离刺激的高估幅度要小得多，这是由在个人或人外空间中呈现的刺激之间感知大小的差异引起的。总体而言，这些结果表明，虽然时间信息的处理受到周围或人外空间中刺激位置的强烈影响，但数字知觉与刺激距离无关。我们推测，虽然时间和数字可能是由个人系统中的共享系统编码的（以优化动作执行），不同的和部分独立的机制可能是个人外空间中时间和数字表示的基础。此外，这些结果表明，研究跨空间平面（可能或不可能采取行动）的震级感知可能会揭示出处理差异，而这些差异本来是不会引起注意的。