Note: excerpts of this tribute appeared in the May/June 2001 issue of 'Juggle' magazine. Reprinted by permission.

By Professor Arthur Lewbel (home page)

March, 2001.

Here are some photos of Claude's juggling machines

Here is a rare movie of Claude demonstrating his two most famous juggling machines (from the 1985 Canadian Broadcasting Company program, "The Nature of Things." quicktime movie

Claude Elwood Shannon 1916-2001. Survived by his wife Mary Elizabeth (Betty) Shannon, a son, Andrew Shannon, and a daughter, Margarita "Peggy" Shannon.

Many Jugglers have heard about the juggling robot invented by Claude Shannon, and jugglers of a mathematical bent will know of Shannon's juggling theorem. However, among mathematicians and computer scientists, Claude Shannon is a legend, widely recognized as one of the most brilliant men of the twentieth century. It is impossible to overstate his importance in the early development of computers and digital communication. In 1990, Scientific American called his paper on information theory, "The Magna Carta of the Information Age."

In the 1980's Claude quietly showed up at a computer science lecture (after having been away from the field for many years). One attendee said, "It was as if Isaac Newton had showed up at a physics conference." When people realized who he was they pushed him on stage. He gave a very short speech, then juggled a bit. Afterwards, attendees lined up to get his autograph.

Any encyclopedia will give you a short biography of Claude's life, and thousands of books, articles, and webpages exist describing his work in math and computer science. I will therefore skip most of that, and instead provide my own recollections and impressions of an extraordinary man.

I first met Claude at the MIT Juggling club. One nice thing about juggling at MIT is that you never know who will show up. For example, one day Doc Edgerton, inventor of the strobe light, stopped by the juggling club and asked if he could photograph some of us juggling under strobe lights. So it wasn't a great surprise when a cheerful, gray haired professor stopped by the club one afternoon and said to me, "Can I measure your juggling?" That was my introduction to Claude Shannon.

Not long after, the MIT juggling club decided to have a video and pizza night, and needed someone with a big TV, in a room large enough to hold dozens of jugglers. We all ended up in Claude's living room, in a stately home (originally owed by Thomas Jefferson's great granddaughter) overlooking a lake in Winchester, Massachusetts. Another time he invited me to dinner at his house, saying only that, "he had another juggler coming over as well." The other guest turned out to be Albert Lucas.

Unlike most brilliant theoretical mathematicians, Claude was also wonderfully adept with tools and machines, and frequently built little gadgets and inventions, usually with the goal of being whimsical rather than practical. "I've always pursued my interests without much regard to financial value or value to the world. I've spent lots of time on totally useless things," Shannon said in 1983. These useless things would include his juggling robot, a mechanical mouse that could navigate a maze, and a computing machine that did all its calculations in roman numerals.

Claude never did care about money. He never even put his paycheck into a bank account that paid interest, until he married and his wife Betty suggested it to him. Still, he became a very wealthy man, partly as a result of early investments with some of his computer scientist pals, including the founders of Teledyne and of Hewlett Packard. When he did think about finance, Claude was as brilliant at that as with anything else he set his mind to. Knowing I was an economist, he once explained to me his thoughts on investing. Some were wonderfully practical, as when he said he'd always buy stocks rather than gold, because companies grow and metals don't. Some were more esoteric, for example, he had ideas regarding mean-variance analysis that jibe well with many aspects of modern portfolio theory.

Some of the juggling artifacts that Claude had in his large 'toy room:' A zoetrope made of a dozen little still figures of juggling clowns. Spin it, and they look like one clown juggling. A sculpture of a juggler, juggling 3 jugglers, each of whom is juggling three jugglers. His famous juggling robot, complete with the head of W. C. Fields stuck on top. A mechanical diorama that shows three clowns, juggling many balls rings and clubs. The props move so realistically that the clubs even rotate and land correctly (triple spins, if I remember right). In the basement was an air hockey table, mounted at an angle, for two dimensional, low gravity juggling. And in the garage, a collection of exotic unicycles.

In addition to his famous juggling theorem, Claude came close to inventing site swaps. In the 1970's, he was asked by Scientific American magazine to write an article about juggling. In addition to including his juggling theorem, the draft of his article contained an attempt to count the number of different possible juggling patterns. Scientific American asked him to revise the article, but by then he was doing other things and never bothered to finish it. (A copy of his draft article can be found in the book, "Claude Elwood Shannon Collected Papers," edited by N.J.A. Sloane and A. D. Wyner, New York, IEEE Press, 1993, pages 850-864). He made an offhand remark that maybe I should write an article for them instead. Years later, I took his advice (see, "The Science of Juggling, Scientific American, Nov. 1995).

Claude told me this story. He may have been kidding, but it illustrates both his sense of humor and his delightfully self deprecating nature, and it certainly could be true. The story is that Claude was in the middle of giving a lecture to mathematicians in Princeton, when the door in the back of the room opens, and in walks Albert Einstein. Einstein stands listening for a few minutes, whispers something in the ear of someone in the back of the room, and leaves. At the end of the lecture, Claude hurries to the back of the room to find the person that Einstein had whispered too, to find out what the great man had to say about his work. The answer: Einstein had asked directions to the men’s room.

Claude wrote the first paper describing how one might program a computer to play chess. He wrote, "Communication Theory of Secrecy Systems, " which the Boston Globe newspaper said "transformed cryptography from an art to a science." Yet neither one of these were his greatest works.

Here's my own interpretation of Claude's two most famous and important papers. His 1937 thesis basically said, "if we could someday invent a computing machine, the way to make it think would be to use binary code, by stringing together switches and applying Boole's logic system to the result." This work, done while he was still a student at MIT, has been called the most important master's thesis of the twentieth century. The idea was immediately put to use in the design of telephone switching systems, and is indeed how all modern computers think.

But that was only Claude's second most important idea. His most famous paper, written in 1948 at Bell Labs, created what is now known as information theory. In "A Mathematical Theory of Communication," Shannon proposed the idea of converting any kind of data, (such as pictures, sounds, or text) to zeroes and ones, which could then be communicated without errors. Data are reduced to bits of information, and information transmission is then measured in terms of the amount of disorder or randomness the data contains (entropy). Optimal communication of data is achieved by removing all randomness and redundancy (now known as the Shannon limit). In short, Claude basically invented digital communication, as is now used by computers, CD's, and cell phones. In addition to communications, fields as diverse as computer science, neurobiology, code breaking, and genetics have all been revolutionized by the application of Shannon's information theory. Without Claude’s work, the internet as we know it could not have been created.

Some of Claude’s honors include the National Medal of Science, Japan's Kyoto Prize, the IEEE Medal of Honor, and about a dozen honorary degrees. In 1998, the two building AT&T labs complex in Florham Park, N.J., was named the Shannon Laboratory.

One day, almost immediately after I'd arrived at his house, Claude said to me, "Do you mind if hang you upside down by your legs?" He had realized that while bounce juggling is much easier than toss juggling in terms of energy requirements, throwing upward as in toss juggling is physiologically easier, and so he wanted to try combining the two, which meant bounce juggling while hanging upside down.

For every one invention he built or theorem he proved, he had a hundred other ideas that he just never got around to finishing. One juggling example: He showed me a vacuum cleaner strapped to a pole, pointing straight up, with the motor reversed to blow instead of suck. He turned it on, and placed a styrofoam ball in the wind current. It hovered about a foot above the vacuum. He then varied the speed of the motor, and the ball drifted up and down as the speed changed. "Now," he said, "Imagine three balls and two blowers, with the blowers angled a bit towards each other, and the motors timed to alternate speeds."

The last time I saw Claude, Alzheimer's disease had gotten the upper
hand. As sad as it is to see anyone's light slowly fade, it is an especially
cruel fate to be suffered by a genius. He vaguely remembered I juggled,
and cheerfully showed me the juggling displays in his toy room, as if for
the first time. And, despite the loss of memory and reason, he was every
bit as warm, friendly, and cheerful as the first time I met him. Billions
of people may have benefited from his work, but I, and thousands of others
who knew him a little bit, are eternally grateful to have known him as
a person.

"Shannon's juggling theorem" and "Shannon's juggling robot" below
reprinted with permission from The Science of Juggling, By Peter J. Beek
and Arthur Lewbel, Scientific American, November, 1995, Volume 273, Number
5, pages 92-97. Copyright © 1995 by Scientific American, Inc. All
rights reserved. The entire Science of Juggling article (except for some
copyrighted photos) may be found here: The
Science of Juggling.

**Shannon's juggling robot**.

Shannon pioneered juggling robotics, constructing a bounce-juggling machine in the 1970s from an Erector set. In it, small steel balls are bounced off a tightly stretched drum, making a satisfying "thunk" with each hit. Bounce juggling is easier to accomplish than is toss juggling because the balls are grabbed at the top of their trajectories, when they are moving the slowest.

In Shannon's machine, the arms are fixed relative to each other. The unit moves in a simple rocking motion, each side making a catch when it rocks down and a toss when it rocks up. Throwing errors are corrected by having short, grooved tracks in place of hands. Caught near the zenith of their flight, balls land in the track; the downswing of the arm rolls the ball to the back of the track, thus imparting suffcient energy to the ball for making a throw. Shannon's original construction handled three balls, although Christopher G. Atkeson and Stefan K. Schaal of the Georgia Institute of Technology have since constructed a five-ball machine along the same lines.

**Shannon's juggling therorem**

JUGGLING THEOREM proposed by Claude E. Shannon of the Massachusetts
Institute of Technology is schematically represented for the three-ball
cascade. The exact equation is (F+D)H=(V+D)N, where F is the time a ball
spends in the air, D is the time a ball spends in a hand, V is the time
a hand is vacant, N is the number of balls juggled, and H is the number
of

hands. The theorem is proved by following one complete cycle of the
juggle from the point of view of the hand and of the ball and then equating
the two.