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An Introduction to Information Theory: Symbols, Signals and Noise (Dover Books on Mathematics), by John R. Pierce
Ebook An Introduction to Information Theory: Symbols, Signals and Noise (Dover Books on Mathematics), by John R. Pierce
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"Uncommonly good...the most satisfying discussion to be found." — Scientific American.
Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter. Even more revolutionary progress is expected in the future.
To give a solid introduction to this burgeoning field, J. R. Pierce has revised his well-received 1961 study of information theory for a second edition. Beginning with the origins of the field, Dr. Pierce follows the brilliant formulations of Claude Shannon and describes such aspects of the subject as encoding and binary digits, entropy, language and meaning, efficient encoding, and the noisy channel. He then goes beyond the strict confines of the topic to explore the ways in which information theory relates to physics, cybernetics, psychology, and art. Mathematical formulas are introduced at the appropriate points for the benefit of serious students. A glossary of terms and an appendix on mathematical notation are proved to help the less mathematically sophisticated.
J. R. Pierce worked for many years at the Bell Telephone Laboratories, where he became Director of Research in Communications Principles. His Introduction to Information Theory continues to be the most impressive nontechnical account available and a fascinating introduction to the subject for lay readers.
- Sales Rank: #20076 in Books
- Published on: 1980-11
- Released on: 1980-11-01
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .68" w x 5.39" l, .77 pounds
- Binding: Paperback
- 336 pages
Most helpful customer reviews
106 of 112 people found the following review helpful.
An Absolute Gem
By Clark M. Neily
Claude Shannon died last year, and it's really disgraceful that his name is not a household word in the manner of Einstein and Newton. He really WAS the Isaac Newton of communications theory, and his master's thesis on Boolean logic applied to circuits is probably the most cited ever.
This is the ONLY book of which I am aware which attempts to present Shannon's results to the educated lay reader, and Pierce does a crackerjack job of it. Notwithstanding, this is not a book for the casual reader. The ideas underlying the theory are inherently subtle and mathematical, although there are numerous practical manifestations of them in nature, and in human "information transmission" behavior. On the other hand, this is a work which repays all effort invested in its mastery many times over.
0 of 0 people found the following review helpful.
Two Stars
By Daniel
Hard to read. Not as in "too mathy" or "using complicated language", but just... hard to follow along.
52 of 65 people found the following review helpful.
Good intro but dated
By Glenn L. E. May
The update of this book should have been updated. While it is understandable that at the time of the first print of this book in 1961 the author saw little or no practical use for Shannon's information theory (other than perhaps his channel capacity theorem) it was well known by the second printing in 1980 that it has profound implications in studying biology (and modern technology). For instance in an article published in Nature in 1967, A. L. MacKay showed how the genetic code is highly optimal using Huffman's algorithm. More recently Ardell and Sella (with summaries available on the net) have 'demonstrated that the code's present structure was also shaped by natural selection (though non-Darwinian, see below). In this process, the codons - the triplets of nucleotides that map a particular nucleic acid sequence into proteins - are arranged to minimize the negative effects of genetic error, and to optimize the process of 'readout' of genes during protein synthesis. By permuting all 20 amino acids across all possible codon sets, both groups found that the 'universal' genetic code - the one found in nearly every organism on earth...-falls in the best .0001% of all possible codes and perhaps even better, in terms of its capacity to be an error-correcting code...' By showing modifications are possible in one generation the evidence points away from Crick's thesis of the genetic code being a 'fozen accident' but instead possible Lamarckian beginnings with horizantal gene transfer leading to Carl Woese's early RNA World hypothesis before Darwinian vertical descent begins.
The author also tends to perpetuate the widespread misunderstanding (generally by physicists who tend to contort the meaning away from Shannon's into 'available' states or choices such as with Black Holes) that information is uncertainty; he confuses (readers potentially with) surprise versus information by not taking into account the other half of the necessary equation for information transmission, being noise. He says "The amount of information conveyed by the message increases as the amount of uncertainty as to what message actually will be produced becomes greater." [pg 23] While he clears this up in a later chapter on noise it becomes so technical that it appears most readers of Shannon's theory have been mislead. At this point the scientists (usually physicists who actually work with a different concept of 'available information') typically equate the uncertainty with Kolmogorov complexity and assume that maximum information and complexity is randomess.
For instance consider Philip Nelson's comment in his book Biological Physics that 'random messages carry the most information!' In one footnote of his nearly 600 page book he effectively dismisses all of Nobel Prize winner Shannon's information achievements.
Much of the trouble is with terminology. We think of noise as impure sound. Shannon tried to avoid this problem by introducing the term 'equivocation' but on the other hand this seems to have no intuitive meaning in this context. One really has to go to the math to sort it out. The critical equation to potentially eradicate the confusion does not appear in the book -
R = Hbefore - Hafter
H is an entropy-like formula without Boltzman's constant; however the concepts are very different. (Reportedly Von Neuman told Shannon in the 1940's to call his uncertainty 'entropy, as noone will know what you mean!' Apparently this is still working!) Entropy of the universe apparently increases under the 2nd law of thermodynamics (at least ignoring gravity and extensivity), information begins and ends with life (one needs a recognizer to measure it). A random message in fact carries no information as there is no resolution (reduction) of uncertainty. This is all explained at molecular biologist's Dr. Tom Schneider's website, I know of no other comprehensive source and certainly no book that gets it right. (As yet! 'Hope springs eternal!' A. Pope; 1688 - 1744)
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