The idea of embodied cognition might explain why we struggle to intuitively visualise objects in four-dimensional space. Basically the argument is that our visual imagination is grounded in sensorimotor systems that are optimised for three spatial dimensions. But reasoning is not limited to sensory experience so we can abstractly figure out how spatial systems in higher dimensions would work if they actually existed. Like we do for most mathematical concepts that don't easily map to what our bodies experience.

So by this perspective, it's not arbitrary, but is the result of our physical embodiment and how we interact with the world.