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I think 1/r^2 emerges because of the geometry that has emerged. If a pulse of particles is emitted uniformly in n-dimensional space, and each travels at the same speed, then their density will fall off as 1/r^(n-1), since in 3D they cover a spherical surface (2D object of size r^2), and in 2D its a line (1D circular surface of size r). Its the geometry that's important. We should search for why our world is 3D, and not some other space, if we want to know why we have inverse square laws.