Submitted July 7, 2002, 2:24 PM
What are your most vivid memories of Claude Shannon?
When asked (newsgroup sci.math 27july02) to vote for :
Re: The best 20th Cent. mathematician (vote here)
I replied without hesitation:
" Claude Shannon, who looked further than mathematics, to 'discover'
(as MSc student MIT '38) Boolean Algebra (then some 90 yrs old;-)
as natural model for digital circuit behaviour.
And 10 years later he founded the discipline of information theory
- by linking discrete and continuous math branches (discrete data
transmission, algorithmic complexity and probability theory / entropy).
His own comment on this: "It just happened that no-one was
familiar with both fields at the same time."
He was a master of interdisciplinary search-and-find, guided by a
fabulous intuition for which theoretical concept is essential *and* practical
(often by specialists dismissed for detailed further development - as being
'trivial' . . . )
-- NB - http://home.iae.nl/users/benschop/search.htm
http://home.iae.nl/users/benschop/links.htm :
re the ECHO project on the history of Science (gmu.edu)
|
How did Claude Shannon affect your own work?
My research (in industry) is in design-automation methods for digital VLSI. And although
an EE by training (TU-Delft .nl, U-Waterloo .ca), my interest shifted through the years
towards disctrete mathematics.
Especially the associative algebra of function composition ('semigroups') applied to
structural analysis and synthesis of FSM's (finite state machines), thus sequential logic.
This includes arithmetic - with associative and commutative operations (+) and (*) -
as well as Boolean logic (set theory, with intersect and union as associative commutative
and idempotent operations) - in a straightforward 3-level hierarchy.
Shannon's first main result in his MSc thesis (1938) as described above, always inspired
me as a prime example of a math-concept that is available but not used in practice, thus not
seen to be essential for engineering purposes. Another hero of mine, of an earlier century, is
Fourier - with his frequency spectrum (1807, 1824) for an equivalent representation of
time-varying signals : an indispensible tool, without which (electrical) engineering as we
know it would not be possible.
Being now in the 'digital age' (of computers) for well over half a century, it is amazing
to me that there is still no formal "digital network theory" - at least not at a practical
level comparable to "linear network theory" (with known five basic components R, L, C,
Trafo, Gyrator) and synthesis tools based on conservation principles such as Kirchoff's
laws, and linear techniques like the Fourier spectrum, convolution, etc.
What Shannon did for combinational logic synthesis (recognizing a math-concept as
indispensible tool for digital circuit engineering) is an inspiration for me regarding
sequential logic synthesis (essentially: FSM synthesis) based on the already some 75 years
old structure theory of finite semigroups (as sequential closure of any FSM) - available in
the PhD thesis of another student : Suschkewitch (Kiev, 1928) [1] regarding the detailed
structure of finite simple semigroups (viz. having no proper ideal). This is, for all practical
purposes, an essential step beyond 'almighty' group theory (re [2] : on the five basic
state machine types, as components of any digital network).
[1] A.Clifford, G.Preston : "The Algebraic Theory of Semigroups", AMS survey #7 (1961),
appendix A, p 207.
[2] N.Benschop : http://arXiv.org/abs/math.GM/0103112
|
Name
Submitted November 11, 2001, 10:45 AM
What are your most vivid memories of Claude Shannon?
We never met, but I have now interviewed many people who knew or worked with him.
|
How did Claude Shannon affect your own work?
I am currently producing a documentary for UC-TV (University of
California)from San Diego on Claude Shannon and his legacy. We staged a
Shannon Symposium in October and interviewed leading scholars in the
field of information theory. We are now looking for video or film clips
or photographs of Shannon at different stages of his career for
inclusion in the documentary (with help from his widow Betty).
If anyone has visuals of Claude Shannon, please give me a call at (858)
822-5825 or email at dramsey@ucsd.edu. Thanks.
|
Name
Submitted September 9, 2001, 10:15 PM
What are your most vivid memories of Claude Shannon?
The following is the text from my website:
http://www2.bc.edu/~lewbel/Shannon.htm
see also my home page http://www2.bc.edu/~lewbel/
In addition to this text, that website includes photo's, illustrations,
& a rare video of claude.
Unlike most other contributors here, I knew Claude primarily through
his work in juggling.
A PERSONAL TRIBUTE TO CLAUDE SHANNON Note: excerpts of this tribute
appeared in the May/June 2001 issue of 'Juggle' magazine. Reprinted by
permission. By Professor Arthur Lewbel March, 2001. 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.
|
Name
Submitted August 8, 2001, 7:17 PM
What are your most vivid memories of Claude Shannon?
Unfortunately I joined Bell Labs from MIT just two weeks after Claude
Shannon migrated in the opposite direction. I never met him until
perhaps six years ago when he toured Bell Laboratories. By then sadly
the onset of Alzheimer's was clear, and the really interesting
technical conversations were with his extremely sharp wife--also an
alumnus of Bell Labs.
Working in the math department at the Labs, I of course heard plenty of
Shannon stories, which you will doubtless pick up from elsewhere: How
Shannon took up the unicycle and when he perfected his technique,
brought it to work and issued forth to ride the 1/4-mile length of the
main corridor, which filled up behind him with a buzz of gawkers. Or
how when Dave Hagelbarger made his "outguessing machine", which with
only 32 bits of state managed over its lifetime to predict 65% of
binary choices of human opponents, Shannon set forth to do better. I
believe Shannon in fact did so, but with a more complex device.
But of course the towering achievements of Shannon were his master's
thesis--one of those brilliant "why didn't I think of that" insights,
that only have to be heard, not studied, to change one's ways of
thinking. And information theory, which I took as an undergraduate at
Cornell only five years after the paper appeared--incredibly quick
adoption. And its application to cryptography, a subject that didn't
really come into its own until the late 1970s, 30 years after Shannon
showed the way. In every case, his is the defining outlook on the
field.
But these are familiar tales and influences. My personal Shannon story
is that as a kid I used to ski on what was to become his lawn. I had
lived two doors away from the old mansion on Mystic Lake that he bought
when he moved to MIT. The mansion's broad lawn sloping down to the lake
was the local ski and sled hill. I climbed it innumerable times, but
Shannon didn't. Characteristically, this gadgeteer installed a chair
lift, which I saw much later when I visited the intervening neighbor
John Trump, another great MIT professor who founded High Voltage
Engineering.
[Tangential reminiscence: Shannon's approach to switching circuits was
enshrined in the book by Keister, Ritchie, and Washburn, three Bell
Labs authors who impinged on my life in various ways. On my last day at
a summer job in Bell Labs at West Street, NYC, I was introduced to Bill
Keister, who described the subject to me. Having learned Boolean
algebra (from Max Black, the philosopher of religion!) that was all I
needed to go off and do combinatorial circuit design. Ritchie was the
father of Dennis, with whom I long worked on Unix, and of Bill, who
founded a business, Binary Arts, which marketed logic toys that Keister
had invented in his basement. Washburn, a good jazz pianist, used to
play for huge Bell Labs parties held at a bachelor pad where I hung my
hat for a while. I imagine Shannon had attended them before I appeared
on scene--other celebrities like Dick Hamming certainly did.]
|
Name
Submitted August 8, 2001, 10:55 AM
What are your most vivid memories of Claude Shannon?
We never personally met Claude Shannon. We use Shannon’s work in
teaching at Novosibirsk State University in several courses: a) coding
theory (general theorems of coding theory and data compression,
cryptology), b) discrete analysis (complexity theory, constructing of
codes), c) discrete mathematics.
|
How did Claude Shannon affect your own work?
The remarkable scientist C.E. Shannon is no more with us, but his works
will always win the hearts of all people by their originality and some
peculiar novelty.
His works are mostly distinguished by the combination of the deepest
penetration into the essence of various problems with the masterly
statement of a problem and its solution as a true mathematical problem.
Discoveries made by this scientist gave a universal clue to solving
problems in different fields of science starting with mathematics and
technology (communication and computers) up to biology and linguistics.
They originated new fields in mathematics (information theory, coding
theory, complexity theory) as well as stimulated the development of
earlier existing areas (theory of dynamic systems). At one time the
elder mathematicians noticed that there was some special parallelism in
treating obviously and greatly different problems remarked in Shannon’s
works and in descriptive set theory which refers to the highest
sections of mathematics. It won’t be an exaggeration to say that
Shannon’s works have a general mathematical and scientific
significance.
His works are remarkable not only by their results, but also by their
integrity, the logical and natural development of sections into each
other makes an impression that the problem is developing itself. It is
the case when you can speak about the flight of thoughts and the
connection of Reality with its potential of development and Inspiration
that reveals this potential.
Finally, Shannon surprisingly disregarded his outer success –
advertising, prestige or things like that, you can feel his astonishing
reserve even living on another continent. Those who long for success
could object that having such a powerful potential it is easy to be
modest, although lacking that special talent to a great self restraint
might not lead to displaying this powerful potential.
We deeply revere the memory of C.E. Shannon and hope that his
outstanding works will inspire new generations of scientists.
|
Name
Sobolev Institute of Mathematics, Coding and Complexity Theory Groups
(Yuri L. Vasil'ev, Faina I. Solov'eva, Sergey V. Avgustinovich,
Elizaveta A. Okol'nishnikova, Sergey A. Malyugin, Anastasiya Yu.
Vasil'eva, Denis S. Krotov, Vladimir N. Potapov)
|
Submitted July 7, 2001, 12:21 PM
What are your most vivid memories of Claude Shannon?
I am not a researcher in Information Theory and had little contact with
Claude Shannon, but one memory stands out:
I was working on the search for limits on the noise performance of
linear electronic amplifiers in the 50's. I was a fledgling Assistant
Professor at that time. I gave a seminar in which Claude Shannon
honored me with his presence. He treated me "as his equal" in a way I
shall never forget. This was his way with all junior colleagues. He
asked a leading question which resulted in Chapter 4 of the monograph
"Circuit Theory of Linear Noisy Networks," H. A. Haus and R. B. Adler,
John Wiley and Sons, New York (1959). We thanked him in the Preface.
|
Name
Submitted July 7, 2001, 4:40 PM
If you have any other observations or comments, please enter them here.
In the upper part of the 'mitt' of Michigan is a small town alongside
Interstate-75 called Gaylord. It's just a dinky little place in the
sandy soil and piney woods. If it weren't for the Walmart on the edge
of town, it likely would have faded into obscurity. They make a big
thing out of their Bavarian heritage up there.
Back in the 20's a young man, son of the local judge and a school marm,
grew up on a farm on the edge of town. He was a very clever young man.
He used to talk by morse code with his buddy on a farm a few miles away
using the stretch of barbed wire in between the two farms. I imagine he
also liked to pick huckleberries in the summer as so many people up
there do. And, no doubt, he occasionally went along with his parents to
the slightly larger town of Grayling to the south and had a sodee-pop
at Dad's place while they took care of their adult business.
But he was no normal Jackpine Savage. He was going places. He went on
to the University of Michigan and then the Massachusetts Institute of
Technology. After he got out of school, he went to work in the
mathematics department at Bell Labs where he wrote a fascinating book
called "A Mathematical Theory of Communications". It earned him the
title of The Father of Information Theory and set the theoretical basis
for virtually all of today's telecom technology - from bank machines to
wireless data-transfer and much, much more.
Afterwards, he went back to MIT as a professor where he was especially
remembered for two things: (1) travelling around campus on his
unicycle, and (2) his legendary Toy Room at home. He remained an avid
unicyclist as long as he was physically capable of it. His Toy Room was
home to an amazing variety of home-made automated robots. It inspired
among other things, the Toy Maker in the movie "Bladerunner". Much like
that character, he was a very shy and private man who was completely
incapable of self-promotion. Unlike that guy, he had lots of friends.
But speaking before large crowds, which he was often asked to do,
terrified him. His avoidance of such occasions was often mistaken for
arrogance early on until people realized what it was about.
His name was Claude Shannon. He died recently at the age of 84. Truely
an extraordinary man and uniquely playful and gentle American genius.
|
Name
Submitted July 7, 2001, 4:42 PM
What are your most vivid memories of Claude Shannon?
Have never met, nor do I know C. Shannon personally.
|
How did Claude Shannon affect your own work?
My area of research is loosely defined as "optimal extraction of
information from physical systems". Thus, the Shannon entropy of the
system comes into play as a metric to insure that any estimates made
are unbiased. Shannon's entropy is actually the same as the
thermodynamic entropy (Jaynes) and can be applied in a rigourous
physical sense. An example of which is described here: If we look at an
"object" the light emission is actually the probability of photon
emission per unit area, per unit solid angle per unit energy. The
response of an imaging system is actually the probability of a photon
entering the telescope at one angle of being diffracted into another
angle and the "image" is the probability of photon collection per
detector area. Thus, given the "image" and the system response we are
trying to estimate the "object" - hence we are estimating a probablity
density and the only unbiased estimate of the probability is that which
has maximal entropy, however, if the source is also in thermodynamic
equilibrium, it is also in a state of maximum thermodynamic entropy.
Thus C. Shannon's work has brought some great insight into physics.
|
Name
Submitted July 7, 2001, 6:31 PM
What are your most vivid memories of Claude Shannon?
In the early Seventies, Claude Shannon gave a seminar at MIT on his
work in investment theory. Many people were aware that in addition to
everything else, Shannon was a very successful investor. Interest
turned out to be so great that the seminar was moved to one of MIT's
largest lecture halls, but even so the audience overflowed the room.
Shannon presented some lovely theoretical results, modeling stock
prices as a random walk, and showing that even if the general trend was
downward, you could still make money from the fluctuations. (I don't
believe that these results have ever been published.)
The first question was: did Shannon use this theory for his own
investments? "Naw," he replied, "the commissions would kill you."
|
How did Claude Shannon affect your own work?
As it happens, my career in information theory is directly due to
Claude Shannon. After I did a master's thesis at MIT on information
theory and quantum mechanics, I was advised that information theory was
dead and that I should look elsewhere for a PhD thesis. (This was
rather poor advice, of course; information theory was not dead, just
getting its second wind.) After six unhappy months of looking
elsewhere, I took Shannon's research seminar in the spring term. His
method of teaching was to talk about problems that he was working on,
partial results, conjectures, etc. Within a month I was working on some
of these problems, within two months I had a thesis topic, within a
year I had a thesis and a doctorate in information theory, and the rest
is history.
|
If you have any other observations or comments, please enter them here.
Information theory is a field that has consistently attracted some of
the brightest engineers who are interested both in elegant theory and
in practical results. It is also a remarkably collegial and supportive
field, with little of the politics and backbiting characteristic of
nearby fields. I believe that these attributes are due directly to the
first generation of information theorists and the tone that they set,
and particularly to Shannon.
Some people have called Shannon as one of the greatest mathematicians
of the twentieth century. I have no problem with that description.
|
Name
Submitted July 7, 2001, 9:09 AM
How did Claude Shannon affect your own work?
I never knew Dr. Shannon personally. However, it was his masters thesis
that influenced me --at the age of nine--to become a mathematician! I
had bought a primitive "computer kit" called "Geniac" by mail. The kit
was basically a bunch of rotary switches and simple experiments.
However, they bundled Shannon's masters thesis: "On the Symbolic
Analysis of Switching Circuits" with it. I read it and decided to
become a mathematician. It was such a clear introduction to Boolean
methods that a nine year girl could understand it. Dr. Shannon changed
my entire life.
|
Name
Submitted July 7, 2001, 3:57 PM
What are your most vivid memories of Claude Shannon?
It was a vicarious meeting, in fact, two of them.
A new employee was installed in my office. He was from Capetown,
S.Africa. I mentioned Shannon in a conversation and I still remember
the electricity. He adored Shannon and it was as if Shannon was in the
room. I was awed by this and felt the Shannon presence, even though I
didn't know much about him since in the 26 years (1967-93) that I had
been in computers he never was mentioned. I came across him in reading
on my own.
Then another new employee was installed in my office. This man was from
Moscow. I again mentioned Shannon. I was floored by what followed. This
man's PhD thesis was proving one of Shannon's unproven theories. To his
own delight and amazement (and to mine too) he discovered that Shannon
was correct. You can't imagine how awed I was that the Great Spirit had
allowed me this personal experience. This young man had never seen a
picture of Shannon and I was able to provide him with one. He also gave
me a copy of his thesis.
|
How did Claude Shannon affect your own work?
Since my "meeting" with Shannon happened in my most mature years, it
gave me confidence in knowing that there is a single source for ideas.
And it works in computers too. It's important to me that the right
himan beings be given credit. It also made me sad as I worked with my
fellow employees to know they had no concept of such things and so
could not revere the computer field the way I did. Above all it gave me
pride in being an American.
|
If you have any other observations or comments, please enter them here.
To think he understood what information really is. What knowledge
really is. And it's mathematical. True spirituality for me.
|
Name
Submitted July 7, 2001, 11:01 AM
How did Claude Shannon affect your own work?
Although I never actually met Claude Shannon, his work greatly
influenced my research -- which has drawn heavily on his concepts of
information theory and redundancy (in some cases constructively added
to achieve error correction and reliable systems out of less reliable
subsystems, and in other cases creatively avoided as in compression
coding), and cryptography. Reading his papers was true intellectual
nourishment, both in graduate school in the 1950s and at Bell Labs in
the 1960s. I always remember his example of the predictive coding of
the text "There is no reverse on a bicycle" in terms of the expected
rank order of the next letter (which began 111511, if I recall
correctly). Even my recent efforts in system security, trustworthiness,
and survivability draw on his original concepts.
|
Name
Submitted July 7, 2001, 10:49 AM
What are your most vivid memories of Claude Shannon?
I met Claude Shannon at the Awards Banquet of the New York Convention
of the Audio Engineering Society (AES) in 1985. I was recognized by the
AES with a Fellowship for my contributions to the Compact Disc. Dr.
Shannon was the recipient of the AES Gold medal (the Society's highest
honor). The very concise citation read (I will never forget this
because it is very true): "For contributions that made digital audio
possible". It was an unforgettable evening, where at the end of the
banquet we could discuss various matters of our interest.
|
How did Claude Shannon affect your own work?
Channel coding used in the Compact Disc, DVD, and other digital
recording products is based on the theoretical work of Shannon. The
capacity computations of runlength limited codes such as EFM which is
used in the Compact Disc have first been done by Shannon in his 1948
landmark paper.
|
Name
Submitted June 6, 2001, 6:37 PM
What are your most vivid memories of Claude Shannon?
Shannon once visited Russia. It was in 1960-ies. Shannon arrived for
participation in the Annual Popov Society Conference. About twenty
Russian engineers and scientists arrived to the Moscow airport to meet
Shannon. We did not see Shannon before and were afraid not to recognize
him in flow of incoming passengers. However, when Shannon appeared, it
was impossible not to recognize him. Shannon radiated, as it seemed to
us, a powerful inherent intellectual light.
At the conference, Shannon presented the last results on the bounds to
error probability for optimal coding in discrete memoryless channel.
The talk was great and raised a long stream of questions and comments.
One of the main Russian newspapers "Literaturnaia Gazeta" published an
article about Shannon with short interview.
When Shannon visited Moscow, he had a meeting with A. N. Kolmogorov in
Moscow State University. I was present at that meeting. Shannon told
Kolmogorov about some open Information Theory problems. That were the
problems on multiuser channels and sources. The problems were new and
very interesting. Shannon presented also his intuition on in which
Information Theory terms he saw the solutions of these problems. (As we
know now, some years after that meeting and independently, T. Cover
published his famous paper on one of the multiuser problems. The
outstanding results of D. Slepian, J. Wolf, and R. Ahlswede should be
mentioned also in this context.) Kolmogorov expressed his extremely
high appreciation of Shannon's work and pointed out the significance of
the concepts of entropy and epsilon-entropy not only for the
communications science.
I had two long-lasting personal conversations with Shannon. The first
of them was in Moscow. I accompanied him to the Publishing House Mir,
which published the book of Shannon's papers in Russian. Shannon, his
wife Mary (as she asked to call her at that time) , and me were on that
trip to and from the Publishing House Mir for about one hour. It was
interesting for me to learn the Shannon opinion on some unsolved
Information Theory problems and some papers, which appeared at that
time.
My second conversation with Shannon was at MIT (Massachusetts Institute
of Technology). Professors P. Elias and R. Gallager invited me in 1969
to work with them for three months at MIT. When I arrived at MIT, I saw
an office door with the name "Prof. Claude Shannon". However soon I
noticed that Shannon did not come to work at MIT. Professors R. S.
Kennedy, H. L. Van Trees, and M. Hellmann told me that Shannon did not
appear at MIT at least for a year. I asked to call Shannon and ask him
whether he wants to meet me and talk. In spite of a priori skepticism
on getting a positive reply such call was done. As a result, Shannon
appointed a meeting with me in the MIT Faculty Club Restaurant on
lunchtime. One of famous MIT professors suggested accompanying me to
the Club. I replied that I could come to the Club without help. I asked
that might be the professor had his own interest in accompanying. He
answered yes and told me that he wanted to meet Shannon, lift with us
in an elevator up to the top floor where the Club was located, and then
leave us. During the time in the elevator, he said that he wanted to
speak to Shannon about a new problem, which he (the professor) solved
recently, and to ask for Shannon's opinion on the problem and the
results. The professor said (R. Fano told me the same earlier) that
usually, with rare exceptions, the Shannon opinion was that he
(Shannon) knew the problem and knew its solution.
As it was preplanned, our lifting in the elevator began with the
professor talk about his new problem. Just before the stop at the top
floor, the professor asked the Shannon opinion. At this time, Shannon
said just the same that he was usually saying.
During the lunch Shannon writing on the ordinary napkins explained his
view on the application of Information Theory to the analysis and
prediction of share prices and stock exchange indices. I was very
impressed by this presentation. Shannon told me that in the US there
was a possibility to get money by playing with shares, whereas in the
USSR there was no such possibility.
I should say that one month after this meeting with Shannon and after
my lecture at IBM, I told B. B. Mandelbrot about Shannon's applications
of the information concept and channel capacity to stock exchange
processes. B. B. Mandelbrot did not agree with Shannon's approach and
said that the stock exchange processes had to be modeled with the help
of self-similar processes. Frankly speaking, I do not know up to now
which approach is more productive in practice.
Also, I remember my brief conversations with Shannon, one on a party
given by P. Elias in 1969 and another one on the Information Theory
Symposium in June 1985.
I am very lucky to be influenced by Shannon who, in my opinion, was a
real genius of science.
|
How did Claude Shannon affect your own work?
Shannon became famous in Russia after his paper "A mathematical theory
of communication." In the time of its publication, the Russian
authority raised a war against cybernetics naming it as "a false
science of obscurantists" (in Russian "lzhenauka mrakobesov"). The
paper of Shannon was considered as a part of cybernetics. A nontrivial
adroitness was needed to publish its translation in Russian. It was a
merit of Professor Zheleznov from Leningrad.
The Shannon paper opened a door for numerous research works in
Information Theory. The paper itself and the shown-by-it directions for
future work became very popular in Russia. They attracted attention not
only of communication engineers but also of mathematicians. I think
that it was the first time in the history of communication engineering
that a remarkable number of mathematicians became involved in the
solution of its problems.
The outstanding communication engineers A. A. Kharkevich and V. I.
Siforov, famous mathematicians A. H. Kolmogorov, I. M. Gelfand, A. M.
Yaglom, young scientists M. S. Pinsker, R. R. Varshamov, R. L.
Dobrushin, students V. I. Levenshtein, Y. G. Sinai and many others were
among the first Shannon followers in Russia at that time. A. A.
Kharkevich proposed to elect Shannon to the USSR Academy of Sciences as
a foreign member. Unfortunately, the proposal did not find enough
support in the Academy.
When I finished my first research work and intended to write a paper on
it, I had the questions how to construct the paper, how to begin it,
how to present the results, and other similar questions. I looked at
several papers of the authors famous at that time in order to find a
pattern suitable for me. As a result, I chose the paper of Shannon. It
had no extra words and sentences. The problem was clearly stated from
the beginning. All the concepts and statements were presented without
superfluous mathematical symbolic. The relation with other papers was
pointed out concretely and essentially. Up to now I keep admiring
Shannon's ability to write his papers.
|
Name
Submitted May 5, 2001, 3:20 PM
What are your most vivid memories of Claude Shannon?
I never met Shannon. However, some years ago I had decided that he
would be intrigued by the progress I had made and sent him some of my
papers. I got no response for a while until one day I got a phone call.
It was from Betty Shannon, who said that unfortunately Shannon had
Altzheimer's and could not respond. At that sad point it was clear that
I was on my own...
|
How did Claude Shannon affect your own work?
Shannon's information theory dramatically affected my work. I entered
graduate school looking for a mathematics to describe how living things
work. I found out that I could use information theory to dissect what
the molecules are doing in living things. Lots more information about
this work is given at my web site, http://www.lecb.ncifcrf.gov/~toms/.
|
If you have any other observations or comments, please enter them here.
My contact info:
Dr. Thomas D. Schneider
National Cancer Institute
Laboratory of Experimental and Computational Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
permanent email: toms@alum.mit.edu
http://www.lecb.ncifcrf.gov/~toms/
|
Name
Submitted April 4, 2001, 2:59 PM
How did Claude Shannon affect your own work?
Claude Shannon and his theory of communication opened up to me an
entirely new approach to describing the dynamics of ecosystem behavior.
Not that ecosystems fit the scheme of sender- receiver- interpreter
that Shannon sketched out, but rather that his formalisms could be so
nicely adapted to quantifying the amount of constraint inherent in a
network of ecosystem exchanges.
I have spent the last 23 years applying Shannon's information theory to
ecosystems, and I am still discovering new applications and insights.
His work stands for me as a necessary foundation on which I have built
my whole career.
|
Name
Submitted April 4, 2001, 5:38 PM
What are your most vivid memories of Claude Shannon?
Although I was a student at MIT, I never met Claude Shannon.
Nonetheless, his work started my interest in Information Theory that
continues to this day.
|
How did Claude Shannon affect your own work?
Much of my early publications on information theory (1971-1988) relied
on Shannon thepory. I shifted to algorithmiccomplexity theory betwen
1988 and 1990,
however, because of its conncetions to logic. I now found information
theory on
logic, and I am developing propositional and predicate calculus within
a generalised theory. I consider Shannon's work both brilliant and
seminal. Without it, I would not have set off on my own path. On the
other, I now consider his work to be a very special (but important)
aspect of information
theory. Much of my recent work with the Newcastle Complex Organised
Adaptive Systems Group is based on information theory.
|
If you have any other observations or comments, please enter them here.
Readers may be interested in an article of mine on general information
theory at http://www.newcastle.edu.au/department/pl/Staff/JohnCollier/information/information.html
|
Name
Submitted March 3, 2001, 12:44 PM
How did Claude Shannon affect your own work?
To pin down a vague but important idea, like energy or infinity or
chance, with sufficient precision to make it quantifiable and thus
available for rigorous study constitutes a major contribution to
civilization. This is what Claude Shannon accomplished with the idea
of information. In my own field of ergodic theory, Shannon's
information-theoretic entropy has been central since the 1950's. The
study of Shannon's channels, sources, automata, and measures of
maximal entropy has inspired much work in symbolic dynamics (besides
of course information and coding theory and probability). I worked on
these matters some time ago with Brian Marcus and Susan Williams, and
one of my current research projects (joint with Sujin Shin) is the
identification of relatively maximal (Shannon-Parry) measures for
factor maps betwen subshifts of finite type (information-compressing
channels with restrictions). I find the questions in this area
fascinating, because of their approachability, mathematical depth and
interest, and potential for applications; I do not expect to run out
of them.
|
Name
Submitted March 3, 2001, 11:44 AM
What are your most vivid memories of Claude Shannon?
I believe the year was 1958. Shannon had just returned to MIT from
spending a year at Stanford's Institute For Advanced Study in the
Behavorial Sciences. He was teaching an advanced seminar on research
topics on information theory. I was doing research on the theory of
quantization noise. I got to know him, and we had several conversations
about research. I was an Assistant Prof of EE at MIT at that time. I
had been in contact with John Linvill at Stanford about my joining the
faculty there. The decision was made to do this. I told Dr. Shannon
that I was going to Stanford to join the faculty in 1959. And he said,"
Bernie, you are going to God's country. All you need is a great white
apron, a chef's hat, and a barbecue, and you'll be all set." (Note:
Stanford was pretty quiet then.)
At about that time, Dr. Shannon was riding a unicycle. His construction
projects were the following, as he described them to me. He had a
Volkswagen microbus and he was devising a way to install a shower in
it. Thus he was inventing the motorhome. His second project takes some
explanation. He described his house as being on a hill overlooking a
lake that was good for swimming during summertime. The problem was to
devise a way to get from the house into the lake as fast as possible.
He set up pulleys and ropes that he could grab onto and zoom down the
hill into the lake. GERONIMO! Can you picture this? I can. I could
never forget him.
|
Name
Submitted March 3, 2001, 5:12 AM
What are your most vivid memories of Claude Shannon?
How did Claude Shannon affect your own work?
Shannons contribution to the field of computational physics not only
advanced modern computer technology but also provided tools for
handling physical problems in many other directions, for instance, in
statistical physics, most famous his definition of entropy. This notion
of entropy has been used to describe level statistics and localization
phenomena in mesoscopics and in quantum chaology. For analogies between
mesoscopic physics and quantum chaos see e.g.
http://www.mpipks-dresden.mpg.de/mpi-doc/buchleitnergruppe/start.html
&
http://www.mpipks-dresden.mpg.de/~saw
|
If you have any other observations or comments, please enter them here.
I really like his book on communication theory.
|
Name
Submitted March 3, 2001, 5:57 PM
What are your most vivid memories of Claude Shannon?
Shannon effectively retired around 1965, and so young researchers who
entered the field of information theory after that time (including me)
never got a chance to meet him until June 1985, when he unexpectedly
showed up in Brighton, England, at an International Information theory
Symposium. Everyone at the symposium was thrilled to see him, and
cameras were clicking all week. At the closing banquet, Shannon was, of
course, seated at the head table. About halfway through the banquet Lee
Davisson, who was at that time head of the electrical engineering
department at the University of Maryland, did what we the rest of us
had secretly wanted to do all week: he asked Shannon for his autograph.
That opened the floodgates. For the rest of the meal, there was a long
line of autograph hounds (including me) waiting for Shannon's
autograph. If you know how large scientific egos tens to be, you'll
understand how really astonishing this scene was. It was as if Newton
had showed up at a physics conference.
|
How did Claude Shannon affect your own work?
Since I am an information theorist, Shannon gave me my life's work. I
first read (parts of) his 1948 paper in 1966, and I reread it every
year, with undiminished wonder. I'm sure I get an IQ boost every time.
It is no exaggeration to say that Shannon was one of the finest
scientific minds of this or any other century, and as a professor I am
fortunate in being able to teach Shannon's ideas to new generations of
students. The Shannon limits for communication systems will remain as
the ultimate goals for communications engineers forever.
|
Name
Submitted March 3, 2001, 4:24 PM
How did Claude Shannon affect your own work?
I never met Claude Shannon, but as a person on the boundary between
physics and computer science I can say that his work changed both
fields fundamentally. The connection between information and
thermodynamic entropy was the first bridge built between computer
science and physics --- and contributed historically to others, such as
quantum computation and phase transitions in NP-complete problems,
which are areas of intense research today. It inspired physicists to
see the evolution of physical systems as a form of computation, and
gave a mathematical foundation to a seemingly mystical relationship ---
the instantiation of information and meaning in a physical form. Manuel
Campagnolo, Jose Felix Costa and I have extended Shannon's work on
analog computation. He set the stage by showing that his General
Purpose Analog Computer (GPAC) is capable of computing exactly the
differentially algebraic functions, a beautiful class which is closed
under composition and under the process of solving differential
equations. By adding various operators to the GPAC, we have obtained
analog computation classes closely related to various digital classes
from the theory of computational complexity and recursive functions.
|
If you have any other observations or comments, please enter them here.
Another wonderful contribution of Shannon's was an analog machine for
playing the game of Hex, invented by Piet Hein --- in which the board
was represented as an electrical network, and the machine places stones
at the saddle points of the potential. It performed poorly in the
endgame, but did well at the early stages where exhaustive search is
impractial.
|
Name
Submitted March 3, 2001, 11:57 PM
What are your most vivid memories of Claude Shannon?
Unfortunately, I never had the chance to meet him.
|
How did Claude Shannon affect your own work?
I first encountered Shannon's great 1948 paper in an undergraduate
course taught at Cornell by an astronomer, Martin O. Harwit, and was
immediately captivated. Indeed, at that time I was not a math major and
I credit this encounter with one of the great scientific works of all
time as being one of the two major influences which impelled me to
change my major and eventually to earn a Ph.D. in mathematics.
Even today, after fifty years of tremendous and intensive development,
Shannon's paper remains as fresh and intellectually exciting as the day
it was written--- in fact, it is so clearly written, so imaginative,
and so lively, that even today it remains probably the best short
introduction the subject of information theory. This alone is a
phenomenon almost without precedent in science (Einstein's papers
founding special and general relativity, for example, by 1960 could be
clearly seen to have aged not nearly so well).
It would be impossible to overestimate the beneficial influence this
particular paper has had on my life. I'll briefly describe just one
place where it played a truly critical role in my own professional
development. In my thesis work on generalized Penrose tilings, I was
stuck trying to understand the simplest case, a type of dynamical
system called a Sturmian shift. One day I thought of applying Shannon's
simple but profound notion of finite type approximations to an
information source. This immediately got me "unstuck" and within a few
days led almost without effort to my first independent results
concerning Sturmian shifts, which later turned out to be among the main
theorems in my dissertation (although for lack of time and energy they
were only announced there, not really proven). So without Shannon, not
only do I doubt I would have -attempted- to earn a Ph.D. in math, but I
doubt that would (after a fashion) have succeeded! I truly cannot begin
to imagine the course my life would have taken if I had never read (and
reread, often) Shannon 1948.
This particular notion of Shannon (finite type approximations), which
occurs more or less as a motivational remark in his 1948 paper, has
continued to greatly influence my subsequent thinking in the field of
dynamical systems, and I try to underline its fundamental nature to my
colleagues whenever I have the opportunity.
|
If you have any other observations or comments, please enter them here.
I think his stature, which is already tremendous, can only increase
with the passage of time. Even now would not be inappropriate to
compare him with such figures as Plato, Aristotle, Newton, Einstein,
and Darwin, in terms of his influence on the way we think and live.
To briefly recall just three highlights of his career:
I doubt whether anyone would dispute the assertion that Shannon's
master's thesis was the most important master's thesis ever written. In
it, he showed how to perform computations in Boolean propositional
logic using electronic switching circuits; I hardly need point out that
this development was every bit as fundamental to the development of the
digital computer as the more theoretical work of Turing and von
Neumann. And it is not at all clear how long this crucial development
would have taken if Shannon had not figured it out so early in his
career. Without Shannon, it is not clear that the reader would be
reading these words, for presumably he or she is doing so using a
computer connected to the InterNet--- neither computers nor the
InterNet would be possible without the ideas developed in Shannon's
remarkable thesis.
It is ironic that Shannon's Ph.D. dissertation is less well known today
than his master's thesis. In it, he used ideas from what is now called
"abstract algebra" (ideas which where then still rather new--- there
were hardly any textbooks in any language on this subject yet, despite
the fact that the best mathematicians were using these ideas
extensively) in a highly original study of genetics. I understand that
many years later someone independently rediscovered a similar algebraic
model.
And of course in his 1948 paper, "A Mathematical Theory of
Communication", Shannon founded at one stroke not one but two of the
most important, powerful, successful, and still flourishing fields in
all of applied mathematics, namely what the subject now called
"information theory" (which has elaborated in literally thousands of
directions the probabilistic/ergodic theoretic aspects of Shannon's
papers) and the subject now called "algebraic coding theory" (which has
developed the early ideas of Shannon and Fano on constructing efficient
codes which approach the optimal performance which Shannon's great
coding theorems guarantee--- after fifty years of continuous
development, this goal has finally come significantly closer to being
achieved).
Information theory in particular is, to my mind, along with linear
algebra, the very model of what an ideal mathematical theory is and
does. This theory has everything one could possibly ask for:
1. The intuitive meaning of the fundamental quantity of study (entropy)
is as clear as such things ever get in mathematics, and this meaning is
extremely well motivated (due to Shannon 1948 as well as later work).
2. These entropies are readily -computable- for a huge variety of
"information sources" of theoretical or practical interest, and it is
always clear what these numbers are telling you when you can compute
(or estimate) them.
3. The theory contains a plethora of amazing and beautiful general
theorems: Shannon's coding theorems stand out here, but many more have
been proven in the fifty years since Shannon founded the field.
4. This theory has been extremely successful at -solving- a variety of
tremendously important practical problems, or at least in motivating
people to try to do very hard things (find really good codes) which
no-one knew, before Shannon, were even -possible-.
5. The theory has been tremendously fruitful--- hundreds if not
thousands of individuals, including many of the best mathematicians of
the last fifty years, have contributed their own unique insights to
provide important new theorems or constructions, and ideas from this
theory have been incorporated into a great many other fields in modern
mathematics, such as dynamical systems (where various kinds of entropy,
including "topological entropy", a notion introduced by Shannon in his
1948 paper under the name of "channel capacity", and closely related
quantities such as Lyapounov exponents, are so pervasive they might
even be said to dominate the field).
In my own work, I have always tried to keep before me the example of
Shannon's greatest accomplishment, the theory of information, as
something to try, as far as possible, to emulate, in its generality,
clarity, focus, power, and intellectual beauty.
|
Name
Submitted March 3, 2001, 11:01 AM
What are your most vivid memories of Claude Shannon?
When I met him and his lovely wife during the Brighton ISIT Symoposium
in 1985. He was very timid and enjoyed our admiration. He was juggling
with 3 balls during the banquet in order to entertain us. His wife
escorted him around and looked after him with love.
|
How did Claude Shannon affect your own work?
Not very much until the Turbo codes were discovered. Not because his
work was not good, but because the practical codes were very far from
those which could be implemented.
Then after the discovery of the turbo codes, the performance her
predicted all by a suddent became practical bounds, only a few tenth of
a dB from practical implemented codes.
|
If you have any other observations or comments, please enter them here.
I attach a picture of Claude, Tor Aulin and myself taken in Brighton 1985, by email.
|
Name
Submitted March 3, 2001, 8:33 AM
What are your most vivid memories of Claude Shannon?
Shannon will be remembered for his profound insight; for his ability to
strike at the very heart of a complicated problem in a clear and
uncomplicated way. Although I never met him, I, along with all
researchers in coding and information theory, have been affected
greatly by his work. I have always been attracted to Shannon's work,
both because of the clean elegance of the central ideas, and by the
fact that these ideas have so much to say about actual practice. In my
experience, designers of communication systems who ignore the wisdom of
Shannon do so at their peril, for those well-versed in Shannon's work
will often be able to design communication systems that work better.
|
Name
Submitted March 3, 2001, 8:48 PM
What are your most vivid memories of Claude Shannon?
The only time I met Claude was at the IEEE International Symposium on
Information Theory at Ann Arbor, Michigan, in October 1986. After an
absence of many years (since 1973, in fact, when he delivered the first
Shannon Lecture in Ashkelon, Israel) from attending our Symposia,
Claude showed up unannounced at our 1985 Symposium in Brighton,
England. Most of us, including myself, didn't even know who he was. But
there was a buzz going the Symposium: "Shannon's here. Where, where?
Well, I saw him on the elevator about an hour ago." Anyway, I never met
him at Brighton, but as President of the Society in 1986, we decided to
invite him to formally participate. He and Betty both came and enjoyed
themselves immensely. His Alzheimer's had already begun by that time,
and we asked Betty if it was okay for Claude to make a few remarks at
our banquet. She said she thought he would be fine. As things turned
out, he was more than fine, wowing the audience with a roughly 15
minute talk laced with interesting anecdotes and delightful humor. It
was a joy to behold.
|
How did Claude Shannon affect your own work?
I work in the area of channel coding. I always tell my students that
Shannon had the foresight to prove the EXISTENCE of good codes in his
1948 paper, but not to tell us how to find them. Thus he provided
myself and many other researchers around the world with gainful
employment over the last 50+ years searching for good codes and
efficient methods of decoding them! What more could we ask from a
mentor?
|
Name
Daniel Joseph Costello Jr.
|
Submitted March 3, 2001, 8:52 PM
What are your most vivid memories of Claude Shannon?
I had no direct exposure to Shannon.
|
How did Claude Shannon affect your own work?
I was very much impacted by his work in that he set the bounds and the
basic methods that we eventually used to reach near-capacity
transmission levels in DSL. Being fascinated by the work as a young
graduate student, I actually named my dog, a golden retriever who was
my companion and best friend for 16 years, Shannon. I have pursued the
achievement of Shannon's bounds in all my work for the past 20 years.
Shannon's work was indeed the most influential in the area of DSL, and
indeed some kind of concept of DSL is what probably what his original
motivating application for the theory of mathematical communication,
making phone lines play at the maximum possible data rates. It was an
ironic shame that his company Bell Laboratories opposed the use of
those techniques right up to the end (and actually Intel's Chairman
made a personal request to Bell Labs Chairman to stop blocking
international standardization of DSL using methods basically outlined
by Shannon in the original paper), and even today Lucent Bell Labs
oppose his methods' use in a few areas (although AT&T's Research
Lab -- sometimes called Shannon labs -- and Bell Communications
Research have supported their use for many years).
|
Name
Submitted March 3, 2001, 4:05 PM
What are your most vivid memories of Claude Shannon?
I got in touch with information theory in my PhD, in 1983 and I
immediately loved this area, especially channel coding. My doctor
father often told about Claude Shannon when he met him at conferences.
I remember the conference where Shannon was juggling.
|
How did Claude Shannon affect your own work?
Since I am working in information theory I know and like all the work
of Shannon. It is amazing how clear and beautiful his papers are.
|
If you have any other observations or comments, please enter them here.
Unfortunately more people know Einstein than Shannon even if the work
of Einstein did not influence the ''every day life'' of people so
sustainably than Shannons work.
|
Name
Submitted August 8, 2001, 10:45 AM
How did Claude Shannon affect your own work?
My professors at Berkeley were both students of Claude Shannon. David
Sakrison and George Turin were responsible for the graduate program in
communications theory. As a Masters student, I went though the program,
and was able to successfully navigate the courses, and perform much
better than I had originally expected.
I had one problem: I just didn't really grasp the basics. Everyone was
so busy instructing, teaching, writing new books, and I had somehow
missed something important.
One day in George Turin's office, I mentioned that I just didn't get
it. He was obviously hurt, but then asked if I had read the original
papers by Shannon. I had not. He handed me his personal copy of the
orginal three papers that he had used while a student at MIT.
In 15 minutes, there in his office, I read, and finally understood what
it was all about. The elegance, and beauty of the field of
communications theory was suddenly clear. When finished, I was shaking.
I never met the man, but I have the utmost respect and admiration for
anyone who can communicate so clearly in a technical paper. As a
standard, I hope all professors strive to achieve what Claude Shannon
was able to achieve.
I refer to myself as "third generation Shannon" as I now take the
legacy on, and pass out copies of the three papers, rather that attempt
to place my own academic mark on them.
|
Name
Submitted August 8, 2001, 9:30 AM
How did Claude Shannon affect your own work?
He inspired my web site:
http://www.jtan.com/guess/
|
Name
Submitted March 3, 2001, 6:29 PM
What are your most vivid memories of Claude Shannon?
Shannon's foundational work on information theory is one of the
greatest scientific accomplishments of the last century. In addition to
this work, Shannon made pioneering contributions to computer
architecture, cryptography, and artificial intelligence. His Master's
thesis demonstrates that it is possible to build circuits that perform
Boolean algebra in order to carry out calculations. This computing
calculus is fundamental to the operation of modern computers. Shannon's
1949 paper on cryptography transformed the field from an art to a
science. Shannon also built the first chess-playing machine and the
first maze-solving mechanical mouse, thus helping to create the
discipline of artificial intelligence.
I never knew Shannon personally, but my thesis advisor in graduate
school was one of the few people to collaborate with Shannon. Shannon
had a tremendous influence on the way my advisor and his peers looked
at science and engineering problems. This influence has now propagated
to another generation of students. Thousands of people have been
inspired by Shannon's writings and his fame was of legendary
proportions.
|
How did Claude Shannon affect your own work?
I am a Member of Technical Staff in the Computing Principles Research
department, which is a part of the Computing Sciences Research center
at Bell Labs.
The first problem that Shannon addressed in his landmark 1948 paper on
information theory was the ultimate compression achievable on discrete
data. My own research has primarily focused on the design and analysis
of data compression algorithms. Though people have been studying and
creating compression algorithms for over fifty years, compression is
continually gaining importance because the information revolution has
produced a society that creates, transmits, and stores vast amounts of
data. Compression is so significant a research area that since 1991,
the Institute for Electrical and Electronics Engineers (IEEE) has
sponsored an annual conference devoted exclusively to data compression.
|
If you have any other observations or comments, please enter them here.
Claude Elwood Shannon
American Mathematician and Electrical Engineer
----------------------------------------------
Shannon was born in Petoskey, Michigan, on April 30, 1916.He graduated
from the University of Michigan in 1936 with bachelor's degrees in
mathematics and electrical engineering. In 1940 he earned both a
master's degree in electrical engineering and a Ph.D. in mathematics
from the Massachusetts Institute of Technology (MIT). Shannon joined
the mathematics department at Bell Labs in 1941 and remained affiliated
with the Labs until 1972. He became a visiting professor at MIT in
1956, a permanent member of the faculty in 1958, and a professor
emeritus in 1978.
In 1948 Shannon published his landmark "A Mathematical Theory of
Communication." He begins this pioneering paper on information theory
by observing that "the fundamental problem of communication is that of
reproducing at one point either exactly or approximately a message
selected at another point." He then proceeds to so thoroughly establish
the foundations of information theory that his framework and
terminology remain standard. Shannon's theory was an immediate success
with communications engineers and stimulated the technology which led
to today's Information Age.
Shannon published many more provocative and influential articles in a
variety of disciplines. His master's thesis, "A Symbolic Analysis of
Relay and Switching Circuits," used Boolean algebra to establish the
theoretical underpinnings of digital circuits. This work has broad
significance because digital circuits are fundamental to the operation
of modern computers and telecommunications systems. Another example is
Shannon's 1949 paper entitled "Communication Theory of Secrecy
Systems." This work is now generally credited with transforming
cryptography from an art to a science.
Shannon was renowned for his eclectic interests and capabilities. A
favorite story describes him juggling while riding a unicycle down the
halls of Bell Labs. He designed and built chess-playing, maze-solving,
juggling and mind-reading machines. These activities bear out Shannon's
claim that he was more motivated by curiosity than usefulness. In his
words "I just wondered how things were put together."
|
Name
Submitted March 3, 2001, 5:14 PM
What are your most vivid memories of Claude Shannon?
His 1948 paper. In one stroke, this paper laid down the foundations of
digital communication. Seldom a field is started by one paper. This one
did.
|
How did Claude Shannon affect your own work?
I am most influenced by his "simple model" approach to solving
difficult engineering problems: take a complex problem, strip it down
to its essentials, formulate a simple model to capture the essence, and
ask the right questions. The answers in turn provide deep insights for
the original problem. Communication researchers are still following the
path he showed us.
|
Name
|
|
