I have been thinking about the famous Inverse square-laws and how they came out to be that way. Gauss's law elegantly describes the square law for electricity to spherical distribution. Now I am tempted to say that the Inverse square laws for gravity and other forces are merely a consequence of the fact we live in a 3D-world. Going from this, can we say however, abstract it may be, that in a 2-D world such forces will drop linearly $\frac{1}{r}$ and in the same manner for higher dimension?
I don't know much about general relativity, so I maybe hasty in my conclusion.
