I hear what you say, and what you say is true. Having said that, for me, I don't think your observations really help to develop an intuition that helps when wo

I hear what you say, and what you say is true. Having said that, for me, I don't think your observations really help to develop an intuition that helps when working in a higher dimensional space. My experience is that people know it's roomy, but don't appreciate the consequences. The early comment about there being 10^5400 "places to be" if you have 1000 in each direction for a 1800 dimensional space immediately conveys the idea that space is big, but it's the implications that tend to go missing. People still think of spheres are round, and that "smooth" means "like a landscape in 3D." So while your comments are true, and add usefully to the discussion, to me they don't really convey a helpful visualization.