A necessary but not sufficient condition for the recognition of extra-terrestrial intelligence is a significant departure from thermodynamic equilibrium. This can be discerned clearly in the inverse problem of the detection of terrestrial intelligence from a distance. Photography of the Earth in reflected sunlight reveals no clear sign of life until 100 m resolution is achieved, at which point the agricultural and urban reworking of the Earth’s surface in rectangular arrays first becomes obvious. This pattern is however detectable only over interplanetary distances. Mars exhibits no such patterns. The departure from radiative equilibrium - represented by radio, television and radar technology - in the microwave spectrum of the Earth is by contrast easily detectable over interstellar distances. Even with a technology no more advanced than our own, a civilization on a planet of a nearby star could easily determine, by auto-correlation techniques, the artificiality of these radio signals. Intentional interstellar radio messages should be detected and decrypted far more readily. Possible message contents for interstellar discourse of a modulated signal at any accessible frequency include (1) m -dimensional imagery represented by the transmission of numbers which are the products of m prime numbers; and (2) the use of a common mathematics, physics or astronomy to convey a range of information on more difficult subjects. The only direct attempts to date to communicate with extra-terrestrial intelligence - the plaques aboard the Pioneer 10 and 11 space-craft - are discussed briefly.