Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges.
Gauss's law implies that a the total flux through a surface completely enclosing a charge is proportional to the total amount of charge.
If we imagine a two-dimensional world of people who knew Gauss's law, they would imagine a surface completely enclosing a charge as a flat circle around the charge. Integrating the flux, they would find that the electrostatic force should be inversely proportional to the distance of the charges, if Gauss's law were true in a two-dimensional world.
However, if they observed a 1/r^2 fall-off, this implies a two-dimensional world is not all there is.
Is this argument correct? Does the 1/r^2 fall-off imply that there are only three spatial dimensions we live in?
I want to make sure this is right before I tell this to my friends and they laugh at me.