The Information - James Gleick [83]
Shannon spent a summer working at the Bell Telephone Laboratories in New York City and then, at Vannevar Bush’s suggestion, switched from electrical engineering to mathematics at MIT. Bush also suggested that he look into the possibility of applying an algebra of symbols—his “queer algebra”♦—to the nascent science of genetics, whose basic elements, genes and chromosomes, were just dimly understood. So Shannon began work on an ambitious doctoral dissertation to be called “An Algebra for Theoretical Genetics.”♦ Genes, as he noted, were a theoretical construct. They were thought to be carried in the rodlike bodies known as chromosomes, which could be seen under a microscope, but no one knew exactly how genes were structured or even if they were real. “Still,” as Shannon noted, “it is possible for our purposes to act as though they were.… We shall speak therefore as though the genes actually exist and as though our simple representation of hereditary phenomena were really true, since so far as we are concerned, this might just as well be so.” He devised an arrangement of letters and numbers to represent “genetic formulas” for an individual; for example, two chromosome pairs and four gene positions could be represented thus:
A1B2C3D5 E4F1G6H1
A3B1C4D3 E4F2G6H2
Then, the processes of genetic combination and cross-breeding could be predicted by a calculus of additions and multiplications. It was a sort of road map, far abstracted from the messy biological reality. He explained: “To non-mathematicians we point out that it is a commonplace of modern algebra for symbols to represent concepts other than numbers.” The result was complex, original, and quite detached from anything people in the field were doing.♦♦ He never bothered to publish it.
Meanwhile, late in the winter of 1939, he wrote Bush a long letter about an idea closer to his heart:
Off and on I have been working on an analysis of some of the fundamental properties of general systems for the transmission of intellegence, including telephony, radio, television, telegraphy, etc. Practically all systems of communication may be thrown into the following general form:♦
T and R were a transmitter and a receiver. They mediated three “functions of time,” f(t): the “intelligence to be transmitted,” the signal, and the final output, which, of course, was meant to be as nearly identical to the input as possible. (“In an ideal system it would be an exact replica.”) The problem, as Shannon saw it, was that real systems always suffer distortion—a term for which he proposed to give a rigorous definition in mathematical form. There was also noise (“e.g., static”). Shannon told Bush he was trying to prove some theorems. Also, and not incidentally, he was working on a machine for performing symbolic mathematical operations, to do the work of the Differential Analyzer and more, entirely by means of electric circuits. He had far to go. “Although I have made some progress in various outskirts of the problem I am still pretty much in the woods, as far as actual results are concerned,” he said.
I have a set of circuits drawn up which actually will perform symbolic differentiation and integration on most