During the Summer of 1949 on BBC radio a young couple from Australia started broadcasting in London what seemed to be genuine feats of mindreading and telepathy. The whole of Britain was stunned as messages were transmitted from BBC headquarters to places such as the Tower of London or an underwater diving bell.

Despite the long range, Sydney and Lesley Piddington were apparently able to communicate with each other in a way that defied explanation. The exact methods used have never been revealed and although many magicians claim to know exactly how they worked their act an explanation is...