Is There A Preferred Dimensionality in Nature?

When Newton's laws of motion in 1-D are extended to multiple dimensions, we address these questions. Are Kepler's laws valid? What is the significance of Bertrand's theorem? What role does virial theorem play? How are they applied to the hypothetical 4-D situation? It is the virial theorem that is the most telling about our dimensionality. We find that our 3-D world is indeed privileged.