  In this paper, we give a new, short, simple and geometric proof of the
optimal er-godization time for linear flows on tori. This result was first
obtained by Bourgain, Golse and Wennberg in [BGW98] using Fourier analysis. Our
proof uses geometry of numbers: it follows trivially from a Diophantine duality
that was established by the author and Fischler in [BF13].
