Why 3-D Space? Why 10-D Space? A Possible Simple Geometric Explanation

In physics, the number of observed spatial dimensions (three) is usually taken as an empirical fact, without a deep theoretical explanation. In this paper, we provide a possible simple geometric explanation for the 3-D character of the proper space. We also provide a simple geometric explanation for the number of additional spatial dimensions that some physical theories use. Specifically, it is known that for some physical quantities, the 3-D space model with point-wise particles leads to meaningless infinities. To avoid these infinities, physicists have proposed that particles are more adequately described not as 0-D points, but rather as 1-D strings or, more generally, as multi-D “M-branes”. In the corresponding M-theory, proper space is 10-dimensional. We provide a possible geometric explanation for the 10-D character of the corresponding space.