It has been well known since the pioneering work of Claude Shannon in the 1940s that a message transmitted with optimal efficiency over a channel of limited bandwidth is indistinguishable from random noise to a receiver who is unfamiliar with the language in which the message is written. We derive some similar results about electromagnetic transmissions. In particular, we show that if electromagnetic radiation is used as a transmission medium, the most information-efficient format for a given message is indistinguishable from black-body radiation. The characteristic temperature of the radiation is set by the amount of energy used to make the transmission. If information is not encoded in the direction of the radiation, but only in its timing, energy, and polarization, then the most efficient format has the form of a one-dimensional black-body spectrum.