Claude Shannon, Mathematician,  Dies at 84

        By GEORGE JOHNSON

           Dr. Claude Elwood Shannon, the American
            mathematician and computer scientist whose
        theories laid the groundwork for the electronic
        communications networks that now lace the earth, died
        on Saturday in Medford, Mass., after a long fight with
        Alzheimer's disease. He was 84.

        Understanding, before almost anyone, the power that
        springs from encoding information in a simple language
        of 1's and 0's, Dr. Shannon as a young man wrote two
        papers that remain monuments in the fields of computer
        science and information theory.

        "Shannon was the person who saw that the binary digit
        was the fundamental element in all of communication,"
        said Dr. Robert G. Gallager, a professor of electrical
        engineering who worked with Dr. Shannon at the
        Massachusetts Institute of Technology. "That was really
        his discovery, and from it the whole communications
        revolution has sprung."

        Dr. Shannon's later work on chess- playing machines
        and an electronic mouse that could run a maze helped
        create the field of artificial intelligence, the effort to
        make machines that think. And his ability to combine
        abstract thinking with a practical approach — he had a
        penchant for building machines — inspired a
        generation of computer scientists.

        Dr. Marvin Minsky of M.I.T., who as a young theorist
        worked closely with Dr. Shannon, was struck by his
        enthusiasm and enterprise. "Whatever came up, he
        engaged it with joy, and he attacked it with some
        surprising resource — which might be some new kind
        of technical concept or a hammer and saw with some
        scraps of wood," Dr. Minsky said. "For him, the harder
        a problem might seem, the better the chance to find
        something new."

        Born in Petoskey, Mich., on April 30, 1916, Claude
        Elwood Shannon got a bachelor's degree in
        mathematics and electrical engineering from the
        University of Michigan in 1936. He got both a master's
        degree in electrical engineering and his Ph.D. in
        mathematics from M.I.T. in 1940.

        While at M.I.T., he worked with Dr. Vannevar Bush on
        one of the early calculating machines, the "differential
        analyzer," which used a precisely honed system of
        shafts, gears, wheels and disks to solve equations in
        calculus.

        Though analog computers like this turned out to be little
        more than footnotes in the history of the computer, Dr.
        Shannon quickly made his mark with digital
        electronics, a considerably more influential idea.

        In what has been described as one of the most important
        master's theses ever written, he showed how Boolean
        logic, in which problems can be solved by
        manipulating just two symbols, 1 and 0, could be
        carried out automatically with electrical switching
        circuits. The symbol 1 could be represented by a
        switch that was turned on; 0 would be a switch that was
        turned off.

        The thesis, "A Symbolic Analysis of Relay and
        Switching Circuits," was largely motivated by the
        telephone industry's need to find a mathematical
        language to describe the behavior of the increasingly
        complex switching circuits that were replacing human
        operators. But the implications of the paper were far
        more broad, laying out a basic idea on which all
        modern computers are built.

        George Boole, the 19th-century British mathematician
        who invented the two-symbol logic, grandiosely called
        his system "The Laws of Thought." The idea was not
        lost on Dr. Shannon, who realized early on that, as he
        once put it, a computer is "a lot more than an adding
        machine." The binary digits could be used to represent
        words, sounds, images — perhaps even ideas.

        The year after graduating from M.I.T., Dr. Shannon took
        a job at AT&T Bell Laboratories in New Jersey, where
        he became known for keeping to himself by day and
        riding his unicycle down the halls at night.

        "Many of us brought our lunches to work and played
        mathematical blackboard games," said a former
        colleague, Dr. David Slepian. "Claude rarely came. He
        worked with his door closed, mostly. But if you went
        in, he would be very patient and help you along. He
        could grasp a problem in zero time. He really was quite
        a genius. He's the only person I know whom I'd apply
        that word to."

        In 1948, Dr. Shannon published his masterpiece, "A
        Mathematical Theory of Communication," giving birth
        to the science called information theory. The motivation
        again was practical: how to transmit messages while
        keeping them from becoming garbled by noise.

        To analyze this problem properly, he realized, he had
        to come up with a precise definition of information, a
        dauntingly slippery concept. The information content of
        a message, he proposed, has nothing to do with its
        content but simply with the number of 1's and 0's that it
        takes to transmit it.

        This was a jarring notion to a generation of engineers
        who were accustomed to thinking of communication in
        terms of sending electromagnetic waveforms down a
        wire. "Nobody had come close to this idea before," Dr.
        Gallager said. "This was not something somebody else
        would have done for a very long time."

        The overarching lesson was that the nature of the
        message did not matter — it could be numbers, words,
        music, video. Ultimately it was all just 1's and 0's.

        Today, when gigabytes of movie trailers, Napster files
        and e-mail messages course through the same wires as
        telephone calls, the idea seems almost elemental. But it
        has its roots in Dr. Shannon's paper, which may contain
        the first published occurrence of the word "bit."

        Dr. Shannon also showed that if enough extra bits were
        added to a message, to help correct for errors, it could
        tunnel through the noisiest channel, arriving unscathed
        at the end. This insight has been developed over the
        decades into sophisticated error-correction codes that
        ensure the integrity of the data on which society
        interacts.

        In later years, his ideas spread beyond the fields of
        communications engineering and computer science,
        taking root in cryptography, the mathematics of
        probability and even investment theory. In biology, it
        has become second nature to think of DNA replication
        and hormonal signaling in terms of information.

        And more than one English graduate student has written
        papers trying to apply information theory to literature
        — the kind of phenomenon that later caused Dr.
        Shannon to complain of what he called a "bandwagon
        effect."

        "Information theory has perhaps ballooned to an
        importance beyond its actual accomplishments," he
        lamented.

        After he moved to M.I.T. in 1958, and beyond his
        retirement two decades later, he pursued a diversity of
        interests — a mathematical theory of juggling, an
        analog computer programmed to beat roulette, a system
        for playing the stock market using probability theory.

        He is survived by his wife, Mary Elizabeth Moore
        Shannon; a son, Andrew Moore Shannon; a daughter,
        Margarita Shannon; a sister, Catherine S. Kay; and two
        granddaughters.

        In the last years of his life, Alzheimer's disease began
        to set in. "Something inside him was getting lost," Dr.
        Minsky said. "Yet none of us miss him the way you'd
        expect — for the image of that great stream of ideas
        still persists in everyone his mind ever touched."