A natural definition of the rate of transmission of information is given, arising out of the usual theory. We call it the “Riemannian” rate of transmission. It is shown that the definition leads to a paradox if taken in conjunction with the notion of (time-unlimited) band-limited white noise. A mathematical model can hardly contain both these notions at the same time. The Riemannian rate of transmission does however lead to sensible results if used in conjunction with periodic band-limited white noise. In particular it leads to the Hartley-Wiener-Tuller-Sullivan-Shannon formula without the necessity of introducing Shannon's notion of “dimension rate.” The discussion refers to matrix signal-to-noise ratios and to the entropy of singular multivariate normal distributions.
