The most efficient message would actually resemble a string of random text: each new symbol would be as informative as possible, and thus as surprising as possible. Not a single symbol would be wasted. Of course, the messages that we want to send one another—whether telegraphs or TV broadcasts—do “waste” symbols all the time. So the speed with which we can communicate over a given channel depends on how we encode our messages: how we package them, as compactly as possible, for shipment. Shannon’s first theorem proves that there is a point of maximum compactness for every message source.
