A conventional explanation of the dipole anisotropy of the cosmic microwave background radiation is in terms of the Doppler effect: our Galaxy is moving with respect to the cosmic microwave background frame with ∼600 km s-1. However, as the deep redshift surveys fail to reveal a convergence of the large-scale flow to zero at distances as large as d ∼ H-115,000 km s-1 (Lauer & Postman 1994), the uniqueness of the conventional interpretation has to be investigated. A possible alternative might be a cosmological entropy gradient, as suggested by Paczynski & Piran (1990). We find that contrary to that suggestion a quadrupole anisotropy is generically of the same order of magnitude as the dipole anisotropy (or larger) not only for adiabatic but also for isocurvature initial perturbations. Hence, the observed dipole cannot be explained with a very large scale perturbation which was initially isocurvature.