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Perfect Information

With the encouragement of Vannevar Bush, Shannon decided to follow up his master’s degree with a doctorate in mathematics-a task that he completed in a mere year and a half. Not long after receiving this degree in the spring of 1940, he joined Bell Labs. Since U.S. entry into World War II was clearly just a matter of time, Shannon immediately went to work on military projects such as antiaircraft fire control and cryptography (code making and breaking).

Nonetheless, Shannon always found time to work on the fundamental theory of communications, a topic that had piqued his interest several years earlier. “Off and on,” Shannon had written to Bush in February 1939, in a letter now preserved in the Library of Congress archives, “I have been working on an analysis of some of the fundamental properties of general systems for the transmission of intelligence, including telephony, radio, television, telegraphy, etc.” To make progress toward that goal, he needed a way to specify what was being transmitted during the act of communication.

Building on the work of Bell Labs engineer Ralph Hartley, Shannon formulated a rigorous mathematical expression for the concept of information. At least in the simplest cases, Shannon said, the information content of a message was the number of binary ones and zeroes required to encode it. If you knew in advance that a message would convey a simple choice-yes or no, true or false-then one binary digit would suffice: a single one or a single zero told you all you needed to know. The message would thus be defined to have one unit of information. A more complicated message, on the other hand, would require more digits to encode, and would contain that much more information; think of the thousands or millions of ones and zeroes that make up a word-processing file.

As Shannon realized, this definition did have its perverse aspects. A message might carry only one binary unit of information-“Yes”-but a world of meaning-as in, “Yes, I will marry you.” But the engineers’ job was to get the data from here to there with a minimum of distortion, regardless of its content. And for that purpose, the digital definition of information was ideal, because it allowed for a precise mathematical analysis. What are the limits to a communication channel’s capacity? How much of that capacity can you use in practice? What are the most efficient ways to encode information for transmission in the inevitable presence of noise?

Judging by his comments many years later, Shannon had outlined his answers to such questions by 1943. Oddly, however, he seems to have felt no urgency about sharing those insights; some of his closest associates at the time swear they had no clue that he was working on information theory. Nor was he in any hurry to publish and thus secure credit for the work. “I was more motivated by curiosity,” he explained in his 1987 interview, adding that the process of writing for publication was “painful.” Ultimately, however, Shannon overcame his reluctance. The result: the groundbreaking paper “A Mathematical Theory of Communication,” which appeared in the July and October 1948 issues of the Bell System Technical Journal.

Shannon’s ideas exploded with the force of a bomb. “It was like a bolt out of the blue,” recalls John Pierce, who was one of Shannon’s best friends at Bell Labs, and yet as surprised by Shannon’s paper as anyone. “I don’t know of any other theory that came in a complete form like that, with very few antecedents or history.” Indeed, there was something about this notion of quantifying information that fired peoples’ imaginations. “It was a revelation,” says Oliver Selfridge, who was then a graduate student at MIT. “Around MIT the reaction was, Brilliant! Why didn’t I think of that?’”

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