  We consider a massless scalar field propagating on the exterior of the
extreme Reissner-Nordstr\"om black hole. Using a discrete conformal symmetry of
this spacetime, we draw a one-to-one relationship between the behavior of the
field near the future horizon and near future null infinity. In particular, we
show that the polynomial growth of the second and higher transversal
derivatives along the horizon, recently found by Aretakis, reflects well known
facts about the retarded time asymptotics at null infinity.
