  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. In this letter we
demonstrate an equivalent result about electromagnetic transmissions. We show
that when electromagnetic radiation is used as the transmission medium, the
most information-efficient format for a given message is indistinguishable from
black-body radiation to a receiver who is unfamiliar with that format. 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 its timing, energy or polarization, then the most efficient
format has the form of a one-dimensional black-body spectrum which is easily
distinguished from the three-dimensional case.
