The Information - James Gleick [97]
Telephones, meanwhile, were sending their human voices across the network in happy, curvaceous analog waves. Where were the symbols in those? How could they be counted?
Hartley followed Nyquist in arguing that the continuous curve should be thought of as the limit approached by a succession of discrete steps, and that the steps could be recovered, in effect, by sampling the waveform at intervals. That way telephony could be made subject to the same mathematical treatment as telegraphy. By a crude but convincing analysis, he showed that in both cases the total amount of information would depend on two factors: the time available for transmission and the bandwidth of the channel. Phonograph records and motion pictures could be analyzed the same way.
These odd papers by Nyquist and Hartley attracted little immediate attention. They were hardly suitable for any prestigious journal of mathematics or physics, but Bell Labs had its own, The Bell System Technical Journal, and Claude Shannon read them there. He absorbed the mathematical insights, sketchy though they were—first awkward steps toward a shadowy goal. He noted also the difficulties both men had in defining their terms. “By the speed of transmission of intelligence is meant the number of characters, representing different letters, figures, etc., which can be transmitted in a given length of time.”♦ Characters, letters, figures: hard to count. There were concepts, too, for which terms had yet to be invented: “the capacity of a system to transmit a particular sequence of symbols …”♦
THE BAUDOT CODE
Shannon felt the promise of unification. The communications engineers were talking not just about wires but also the air, the “ether,” and even punched tape. They were contemplating not just words but also sounds and images. They were representing the whole world as symbols, in electricity.
* * *
♦ In an evaluation forty years later the geneticist James F. Crow wrote: “It seems to have been written in complete isolation from the population genetics community.…[Shannon] discovered principles that were rediscovered later.… My regret is that [it] did not become widely known in 1940. It would have changed the history of the subject substantially, I think.”
♦ In standard English, as Russell noted, it is one hundred and eleven thousand seven hundred and seventy-seven.
7 | INFORMATION THEORY
(All I’m After Is Just a Mundane Brain)
Perhaps coming up with a theory of information and its processing is a bit like building a transcontinental railway. You can start in the east, trying to understand how agents can process anything, and head west. Or you can start in the west, with trying to understand what information is, and then head east. One hopes that these tracks will meet.
—Jon Barwise (1986)♦
AT THE HEIGHT OF THE WAR, in early 1943, two like-minded thinkers, Claude Shannon and Alan Turing, met daily at teatime in the Bell Labs cafeteria and said nothing to each other about their work, because it was secret.♦ Both men had become cryptanalysts. Even Turing’s presence at Bell Labs was a sort of secret. He had come over on the Queen Elizabeth, zigzagging to elude U-boats, after a clandestine triumph at Bletchley Park in deciphering Enigma, the code used by the German military for its critical communication (including signals to the U-boats). Shannon was working on the X System, used for encrypting voice conversations between Franklin D. Roosevelt at the Pentagon and Winston Churchill in his War Rooms. It operated by sampling the analog voice signal fifty times a second—“quantizing” or “digitizing” it—and masking it by applying a random key, which happened to bear a strong resemblance to the circuit