Cryptonomicon
by Neal Stephenson
Average Customer Review:
Mass Market Paperback (05 November, 2002)
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Editorial Review

Neal Stephenson enjoys cult status among science fiction fans and techie types thanks to Snow Crash, which so completely redefined conventional notions of the high-tech future that it became a self-fulfilling prophecy. But if his cyberpunk classic was big, Cryptonomicon is huge... gargantuan... massive, not just in size (a hefty 918 pages including appendices) but in scope and appeal. It's the hip, readable heir to Gravity's Rainbow and the Illuminatus trilogy. And it's only the first of a proposed series--for more information, read our interview with Stephenson.

Cryptonomicon zooms all over the world, careening conspiratorially back and forth between two time periods--World War II and the present. Our 1940s heroes are the brilliant mathematician Lawrence Waterhouse, cryptanalyst extraordinaire, and gung ho, morphine-addicted marine Bobby Shaftoe. They're part of Detachment 2702, an Allied group trying to break Axis communication codes while simultaneously preventing the enemy from figuring out that their codes have been broken. Their job boils down to layer upon layer of deception. Dr. Alan Turing is also a member of 2702, and he explains the unit's strange workings to Waterhouse. "When we want to sink a convoy, we send out an observation plane first.... Of course, to observe is not its real duty--we already know exactly where the convoy is. Its real duty is to be observed.... Then, when we come round and sink them, the Germans will not find it suspicious."

All of this secrecy resonates in the present-day story line, in which the grandchildren of the WWII heroes--inimitable programming geek Randy Waterhouse and the lovely and powerful Amy Shaftoe--team up to help create an offshore data haven in Southeast Asia and maybe uncover some gold once destined for Nazi coffers. To top off the paranoiac tone of the book, the mysterious Enoch Root, key member of Detachment 2702 and the Societas Eruditorum, pops up with an unbreakable encryption scheme left over from WWII to befuddle the 1990s protagonists with conspiratorial ties.

Cryptonomicon is vintage Stephenson from start to finish: short on plot, but long on detail so precise it's exhausting. Every page has a math problem, a quotable in-joke, an amazing idea, or a bit of sharp prose. Cryptonomicon is also packed with truly weird characters, funky tech, and crypto--all the crypto you'll ever need, in fact, not to mention all the computer jargon of the moment. A word to the wise: if you read this book in one sitting, you may die of information overload (and starvation). --Therese Littleton ... Read more

Reviews (726)

If you're gonna read this book,
Then you need to ask yourself a something. Do you I have a short attention span? If you do, please stick to watching sitcoms and leave the reading to us vertebrates. The Cryptonomicons time line is non-linear, with each successive chapter taking place at a different location and following a different character. So, if your gonna read this, know that there are many names, places and dates that are going to be crucial to you getting the most out of this book- If you can't be bothered to remember what happened last week on "Will & Grace" don't bother with this book. For god's sake, don't write a review if you read the first couple of pages and decide, "This sucks, it makes me look like a dork when I carry it around and it's heavy too".

With that said, I can honestly say that, apart from about 20 pages of mathematics that I could not fully understand, this was one of the most idea filled and interesting books I've laid my hands on in some time. Stephenson may be a genius of DaVinci proportion, if not that, then at least a teacher of Feynman's caliber.

An exhaustingly amazing novel
I read a lot, a whole lot. I first read this monster from the library the month it came out, decided (after I had recovered from the experience) that it was probably the best thing I'd read in the whole of the `90s, went out and bought a hardback for myself, and set it in a place of honor on my shelves. Nearly six years on, I find that aging has only improved it. I've been working my way slowly through his recent trilogy, but Cryptonomicon is still better. His characters exist in a t least five dimensions and will stick with you from a long, long time. There's Lawrence Waterhouse, math prodigy and buddy of Alan Turing, who becomes one of the key codebreakers of World War II. There's Marine raider Bobby Shaftoe, a survivor of everything the war can throw at him -- except heroism. There's Randy Waterhouse, Lawrence's equally nerdy grandson, master Unix hacker, and generally nice guy. There's America Shaftoe, partly-Filipino granddaughter of Bobby, master deep diver, and all-round tough cookie -- which doesn't keep Randy and Amy from falling in love. There's Avi, Randy's best friend and front-man in all their business ventures -- in this case, building the world's first politically independent data haven, much to the dismay of major governments. There's Lieut. Goto Dengo, engineer for the Nipponese army and builder of the primary hiding place of Japan's stolen billions in gold bullion. And, moving like mist between the two separate generations, there's the _eminence gris_ Enoch Root, Catholic priest, doctor, cryptographer, conspirator, and take-no-prisoners philosopher. Add to this list several dozen supporting players, all equally well realized, and the richness of the narrative texture is unbelievable. Besides the sheer enjoyment you get from Stephenson's Roman-candle style, his highly original metaphors and similes, and his ironic sense of humor, you're gonna learn a lot about cryptography (both the wartime vintage and the present-day digital variety), and about irregular warfare, and a score of other subjects. Yes, it's a huge book -- but it has to be. The heft also allows space for the author's sprawling digressions on topics as diverse as jungle survival, the similarities between computers and church organs, granny-grade furniture, U-boat life, several Holocausts, imprinting of sexual fetishes, Finnish psychology, the neuro-sociological origins of the ancient Greek pantheon, how to divide up an inheritance, the socioeconomic underpinnings of paper currency, and the proper way to eat Cap'n Crunch. It doesn't all advance the plot, but don't worry about it. Every single paragraph in this thing is worth reading, savoring, and storing away for later rethinking. I'll be reading it against in another decade.

Fun for everyone -- not just the hacker community....
Hey, I did my time working in the computing universe -- as a "DEC-10" operator, an "engineering aide" on work study, a UNIX documentation technical editor (for industry, NOT those semi-literate hackers who wrote the BSD manuals, thanks!) and a programmer in Pascal, C and FORTRAN -- but computers still remain glorified and troublesome _appliances_ in my view. So, a 918-page(!) book about hackers had better have more going on than elaborate self-aggrandizement to keep my interest.This story goes well beyond your usual cyberpunk novel, by fully engaging the larger context in which the techno-wizardry occurs.We get to learn lots of fascinating back story involving (real or imagined) events from World War II, bringing home the recognition that the Web and all of our taken-for-granted computer hardware did not come into existence from vacuum.All of this information is woven into stories about very interesting people, whose lives you either envy or recognize as not so very different from your own, after all.I understand that Bobby Shaftoe and friends are present some of Stephenson's other books, and I'll be looking for them.To echo a previous reviewer, I do hope, though, to see more fully-realized female characters in Stephenson's future work.Say, one with a Ph.D. and a sense of adventure, but not necessarily built like an Olympic athlete or with Heinlein-esque inflated breasts? ... Read more

Isbn: 0060512806
Subjects:  1. Espionage/Intrigue    2. Fiction    3. Fiction - Espionage / Thriller    4. Historical - General    5. Literary    6. Science Fiction    7. Science Fiction - High Tech    8. Thrillers   

Alan Turing: The Enigma
by Andrew Hodges, Douglas Hofstadter
Average Customer Review:
Paperback (01 March, 2000)
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Editorial Review

Alan Turing died in 1954, but the themes of his life epitomize the turn of the millennium. A pure mathematician from a tradition that prided itself on its impracticality, Turing laid the foundations for modern computer science, writes Andrew Hodges:

Alan had proved that there was no "miraculous machine" that could solve all mathematical problems, but in the process he had discovered something almost equally miraculous, the idea of a universal machine that could take over the work of any machine.

During World War II, Turing was the intellectual star of Bletchley Park, the secret British cryptography unit. His work cracking the German's Enigma machine code was, in many ways, the first triumph of computer science. And Turing died because his identity as a homosexual was incompatible with cold-war ideas of security, implemented with machines and remorseless logic: "It was his own invention, and it killed the goose that laid the golden eggs."

Andrew Hodges's remarkable insight weaves Turing's mathematical and computer work with his personal life to produce one of the best biographies of our time, and the basis of the Derek Jacobi movie Breaking the Code. Hodges has the mathematical knowledge to explain the intellectual significance of Turing's work, while never losing sight of the human and social picture:

In this sense his life belied his work, for it could not be contained by the discrete state machine. At every stage his life raised questions about the connection (or lack of it) between the mind and the body, thought and action, intelligence and operations, science and society, the individual and history.

And Hodges admits what all biographers know, but few admit, about their subjects: "his inner code remains unbroken." Alan Turing is still an enigma. --Mary Ellen Curtin ... Read more

Reviews (19)

interesting portrait of a compelling misfit
The book is well titled as the real Alan Turing was an enigma to many of those who knew him and perhaps even to himself.It is another example of how genius moves to its own rhythms and manages to get noticed in spite of itself.
Turing is, more than anyone else, the father of the modern computer, a man who could visualize something which did not even exist.It was his vision that eventually came to be the most powerful innovation in the last half century.Hodges book explores Turing's entire life and illuminates the context in which apparently arcane and irregular thinking came to have profound ramifications at the right moment and time.

A scientifically useful biography
I read part of this book in 1985 while trying to understand chaotic orbits. The problem was to understand how an orbit can be deterministic and apparently random. When I read Hodges' description of the Turing machine then I realized that it is easy to answer the question, and was able to write down the answer: one simply digitizes the map or ode, initial condition, and all the control parameters in some base of arithmetic, and then studies the action of a (digitized) positive Liapunov exponent on a digit string. I can't comment on the rest of the book, but Hodges does a very good job of presenting Turing's ideas of computable numbers and computable functions. When my collaborator Palmore read the description I refer to here, he said that he nearly fell out of his chair. We solved the problem of computability of chaotic orbits in that era together.

Is there a good book on computability and automata? So far, all the automata texts that I'm aware of are written in a special holy language of abstract computerize.The language erects an unnecessary barrierto understanding the basic ideas. Is Turing's original paper a proof, or an explanation of what he'd understood? I don't know, but I can refer the reader to "Descartes' Dream" by Reuben and Hersch for perespective.

Good biography, perhaps too long.
If you consider to read this book in order to know about Alan Turing's life, definetely this is the book. In it you will learn about the code breakers, about the WWII spy technology and also about the science aplied to War, however, when I read it I found out that sometimes too many pages (550) can make it boring (more than 20 pages dedicate about how to build a subroutine in a program, more than 20 pages about homosexuality laws, more than 20 pages about historic information from India). Being so detailed makes sometimes forget about the main issue. That is why I didn't give it 5 stars. ... Read more

Isbn: 0802775802
Subjects:  1. 1912-1954    2. Biography    3. Biography & Autobiography    4. Biography / Autobiography    5. Biography/Autobiography    6. Computer Science (General)    7. General    8. Great Britain    9. History    10. History & Philosophy    11. Mathematicians    12. Mathematicians And Their Works    13. Military - World War II    14. Scientists - General    15. Turing, Alan Mathison,    16. Biography & Autobiography / Science & Technology    17. Turing, Alan Mathison   

The Theory of the Riemann Zeta-Function (Oxford Science Publications)
by E.C. Titchmarsh
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Paperback (01 March, 1987)
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Reviews (3)

Oxford strong on salas and hille's little o(h)
One does a google search of
"spotter 7, coastwatch, truk lagoon, south pacific"

Up pops the missing associativity quaternion...rather simple.

Now...then Nash's ordinal and quaternions for taste.

If one's sister is a Bonnie PlogerKen Y. Bonnie J. Ploger at Hamline...

The internet religious fall river line.

Ord def for beta called for.

What is the axiomatic language of the Riemann hypothesis?

Ordinality, Zermelo, Schroeder, Peano..Hamilton.

What is the associativity of this "Christian" presence on the
internet other than a sister named Bonnie?

If Nash is right, the zeta function is an onerous axiom.

spotter7, coastwatch, truk lagoon, south pacific

Complete source of the zeta function
This is the true encyclopaedia of the zeta function. Although I prefer Ivic, I always have the feeling that Titchmarsh wants to appear brilliant.

This book cannot be criticized because of the amount of time and effort that must have been spent on it. It was update in 1986 by Heath Brown.
It is useless to summarize the contents because it mainly has everything, and most theorems have several proofs and very long comments.
One thing that is missing is more stuff about prime number distributions (for this, check Ingham, Edward's, and a bit of Ivic's).

It never becomes redundant, and it can either be used a source for additional information, as dictionary, or it can be used in a linear way.

An very comprehesive book for Zeta Function.
Titchmarch is well known in the theory of functions, in this book, he described the Riemann's Zeta function in the most comprehensive way. ( e. g. in the topic of functional equation, he quoted 7 methods) I cannot find any other book more comprehensive than this one. ( though in order the theories, you must have some background knowledge and patience ! ) ... Read more

Isbn: 0198533691
Sales Rank: 577795
Subjects:  1. Applied    2. Functional Analysis    3. Functions, Zeta    4. Mathematics    5. Number Theory    6. Research    7. Theory Of Functions   

Fermat's Last Theorem: The Story of a Riddle That Confounded the World's Greatest Minds for 358 Years
by Simon Singh
Average Customer Review:
Paperback (January, 1998)

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Reviews (4)

A good historical account on 'Maths hardest problem'
A good historical account on a topic in Maths Number Theory. Fermats last theorem showing even those good at maths can also struggle with the subject albeit on a different level

Fermat presented his famous and what looked to be a simple equation, and asked mathematicians of his time to prove it, like he said he could. He never showed anyone how to and it is doubtful that he could, probably only proving it for n=3 &/or n=4.

The book then charts through history those mathematicians that made contributions to the proving of the equation

A good historical account but not exactly riveting, compounded by the fact that the average reader would'nt have a hope in hell of ever understanding the maths involved in proving the theory (thankfully not shown in the book), combined with the knowledge that 'maths hardest problem' is so abstract it doesn't have many practical uses

At least in Singhs next book, 'The Code Book' one can relate to and use many of the discoveries within the book

Fermat's Last Theorem
A theorem is impossible to prove, was written down over three hundred years ago on a book.The one who wrote it didn't know it would become one of the hardest mathematical mysteries in the world.Then Fermat a Jurist, trying to prove with his own intelligence that no power except a square can be divided into two powers with the same exponent.Fermat committed his whole life to proving the theorem of his.His theorem his trying to prove that the Pythagorean Theorem is not a false/true.While mathematical equations and formulas are being talked about in this book, there is also an unforgettable lesson that all should know.Fermat's goal:To the secret of ancient mathematical problem.

P.S.It may be a small book; but it holds so much knowledge

A Very Nice Non-Mathematical Introduction
For all the mathematical colleagues, this book has a minimum amount of notation, maybe little more than you can find in Treasure Island. It is a nice readable book, though, if you read it curled up on your couch with a cup of tea at hand, and nothing on mind.

If you are not a math or science major, you would ask me: why should I read this book? I would answer: because math appeals to a large number of people, and, you got to admit it, in this period of time people must know something about it. This theorem, in addition, had puzzled great mathematicians (even geniuses) for more than three and a half centuries. I think this means that it had passed around so many mathematical schools and fields.

The book starts with some exploration of Greek mathematics, being the base of modern thinking. Here we must see something about the Pythagorean Theorem, because it inspired the Fermat's Last theorem. The author speaks about a nice incident about a Pythagorean being killed for believing that there existed some numbers other than the Rationals (They were called Irrarionals later, even though they are as rational to the modern mathematics as any other numbers, say the quaternions).

He moves then to speak about Fermat, the French mathematician. He mentions that Fermat did not in fact write a proof for his theorem due to the limitation of the margins of his copy of Diaphintine's "Arithmetica,"! this caused the whole mathematical community to suffer 385 years to construct a plausible proof.

After that, we see how Euler proved the case when n = 3. Then Sophie Germain prove it, inspired by Euler, for the Germain prime numbers (which are some special prime numbers). This eliminated most of the cases, yet there still are infinitely many cases to check. The book does not go into technicalities, but you can enjoy reading about the backgrounds of some of brightest mathematicians of the 19th century.

Then comes some account on cryptography, as being the direct application of Number Theory, followed by the story of how Andrew Wiles, the most famous mathematician of our time, came to prove this theorem.

It proved to be even a harder task. It involved some modern up-to-date mathematics ... some fields of Number Theory called: "Elleptic Curves" and "Modular Forms."

Finally, I would like to say that I read this book when I was at my junior year in the department of mathematics at the University of Missouri-Columbia, I DID NOT NEED MUCH MATH TO UNDERSTAND IT. It, as a matter of fact, inspired me to continue my grad studies in the subject of Number Theory; unfortunately my real mathematical interests won the quarrel and I had to settle with Geometry.

I think any person with some understanding of the notion of mathematics may be very able to enjoy it as much as I did. If you want an introduction to this "mysterious" discipline, this book would provide you the best read. ... Read more

Isbn: 1857026691
Sales Rank: 486014
Subjects:  1. Mathematics    2. Number Theory   

The Codebreakers : The Comprehensive History of Secret Communication from Ancient Times to the Internet
by David Kahn
Average Customer Review:
Hardcover (05 December, 1996)
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Editorial Review

"Few false ideas have more firmly gripped the minds of so many intelligent men than the one that, if they just tried, they could invent a cipher that no one could break," writes David Kahn in this massive (almost 1,200 pages) volume. Most of The Codebreakers focuses on the 20th century, especially World War II. But its reach is long. Kahn traces cryptology's origins to the advent of writing. It seems that as soon as people learned how to record their thoughts, they tried to figure out ways of keeping them hidden. Kahn covers everything from the theory of ciphering to the search for "messages" from outer space. He concludes with a few thoughts about encryption on the Internet. ... Read more

Reviews (24)

Comprehensive
The Codebreakers provides an excellent thorough history of cryptography.(Keeping in mind that it was written in the 1960's.)

I tried to read this book straight through.In retrospect that wasn't the best idea.The writing is very dry.I got through it by stopping to work out the cryptographic systems described with pencil and paper.I guess I understand cryptography better but it took lots of paper and time (well that's cryptography for you;).Well actually I started skimming after a month of that so I didn't quite get through it.What I am trying to illustrate is that the writing is very dry.I'm interested in the subject and I had trouble slugging straight through.Be forewarned.

So what to say what to say?If it happened in cryptography before the 60's then its in here, or at least I don't know the subject well enough to notice omissions.If you are into cryptographic history then get your hot little hands on this book.

I recommend this book highly for university libraries (you need it) and maybe for some public libraries (just so someone can get to it with interlibrary loan).The Codebreakers is great as reference material.Anybody writing a paper on cryptography is going to want it if they are doing a good job with writing that paper.If you are the type of person who would benefit from owning such a reference then you already know who you are and you might just own this book already too.

Truly a History
As a historian, with a particular interest in other than "American History", I found this book particularly compelling.I read the Earlier edition at least three times.

Yes, I found that, at times, the text gets bogged down in minutae that may not appeal to a particular reader, but in a volume of this magnitude, with this scope, and this ambition, that is virtually a lock.

What many of the reviewers don't seem to realize that the book was written in the context of the 1960s and that not only the writing, but also events described must be put into context.David Kahn does an excellent job of doing just that.To illustrate, I might simply point out his portrait of Herbert O. Yardley.One only has to read Yardley's "Education of a Poker Player" to understand just how accurate Kahn was in describing Yardley and his role.

Like all history books of a more specialized nature, there is a serious advantage to having enough background information to understand where events, people, and technology fit into the puzzle.

If you are seriously interested in what went on "behind the scenes" in much of the historical events of the 19th and 20th centuries,this book provides information that is an essential part of the puzzle.

Must be the bible of cryptography
Weighty and thorough.
Between this , Simon Singh and Helen Fouche Gaines, one has reason to assume that an extensive introduction to this field of knowledge has been gained. ... Read more

Isbn: 0684831309
Subjects:  1. Cryptography    2. History    3. History - General History    4. History: American    5. Military - Intelligence/Espionage    6. History / General   

The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
by SIMON SINGH
Average Customer Review:
Paperback (29 August, 2000)
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Editorial Review

People love secrets. Ever since the first word was written, humans have sent coded messages to each other. In The Code Book, Simon Singh, author of the bestselling Fermat's Enigma, offers a peek into the world of cryptography and codes, from ancient texts through computer encryption. Singh's compelling history is woven through with stories of how codes and ciphers have played a vital role in warfare, politics, and royal intrigue. The major theme of The Code Book is what Singh calls "the ongoing evolutionary battle between codemakers and codebreakers," never more clear than in the chapters devoted to World War II. Cryptography came of age during that conflict, as secret communications became critical to both sides' success.

Confronted with the prospect of defeat, the Allied cryptanalysts had worked night and day to penetrate German ciphers. It would appear that fear was the main driving force, and that adversity is one of the foundations of successful codebreaking.

In the information age, the fear that drives cryptographic improvements is both capitalistic and libertarian--corporations need encryption to ensure that their secrets don't fall into the hands of competitors and regulators, and ordinary people need encryption to keep their everyday communications private in a free society. Similarly, the battles for greater decryption power come from said competitors and governments wary of insurrection.

The Code Book is an excellent primer for those wishing to understand how the human need for privacy has manifested itself through cryptography.Singh's accessible style and clear explanations of complex algorithms cut through the arcane mathematical details without oversimplifying.--Therese Littleton ... Read more

Reviews (207)

Very Interesting History
I thought it got off to a bit of a slow start, but about a quarter of the way through it, it became almost impossible to put down.The history of code makers and code breakers is very well put together with inteesting stories.The details on the methods used to break the Enigma ciphers (finding cycles that allow automated searching for correct wheel alignments independent of the scrambling patch cables) was new to me and fascinating.Good description of quantum techniques (which would be the ultimate win for the code makers side of the "arms race").

incredibly interesting
Simon Singh has a true gift for writing. In the wrong hands the material presented in this book could have been dull. Mr. Singh, however, turns this material into what reads likes a page-turning novel. This book is loaded with fastinating information presented in clearly written manner. If you have even the slightest interest in the subject matter, I promise you that you will love this book. One of the things that makes it great is that it looks as deeply at people as it does at the science and math involved. You will find yourself getting attached to the men and women who were so heavily involved in the developments in this subject matter throughtout history. For a top-notch learning and entertainment experience, go read this book now.

Missing History
I saw a book, Fermat's Enigma, many times at the store. Many times I saw it, and walked right by it - not interested. The best thing I can say about "The Code Book" (by the same author) is that before I even finished it I went back to that store and bought Fermat's Engima, not wanting to risk it being sold out.
The Code Book was that good of a read.

Why? It is because it took a subject I knew almost nothing about, and by time I was done made me feel like an expert.In the process I got a precious insight into many historical events I had read about my whole life but, in some part, I had only a superficial understanding.

For example, in College we studied the execution of Mary Queen of Scotts. Our professor told us that the conspiracy was suspect at best and probably was just the result of a vindictive Elizabeth trying to secure her throne. Really?Mr. Singh explains how the Queen's servants broke a code being sent to the Mary and how she authorized an assassination of Elizabeth.By authorizing the assassination, she justified her own execution.An execution which sounds much more rational then "vindictive."At the end, Mr. Singh describes the great dignity Mary displayed at her death and a particularly pathetic scene as her little dog was searching through Mary's effects for Mary, not realizing that she was dead. I can somehow still hear that little dog barking.

This is but one of many stories in this book from Ancient Greece to Modern Washington where Mr. Singh shows (1) the importance of ciphering (2)and its great effect on world history.I almost felt like the FreeMasons were right, there is history and "history." By reading this book, you get a first hand tour of "history" while, at the same time, learning about the incredible changes in the science of spys.

I only had one criticism, which is quite small.Towards the final chapters the author seems more negative as he discusses the tragic ends to many great minds connected to ciphering.I guess there are few nice ways to say bad things but the tone of the book does change. Still, all in all, this is an excellent book which you should read. ... Read more

Isbn: 0385495323
Subjects:  1. Cryptography    2. Data encryption (Computer science)    3. History    4. Language Arts / Linguistics / Literacy    5. Linguistics    6. Military - Intelligence/Espionage    7. Science    8. Science/Mathematics    9. Science / History   

Cryptology (Spectrum)
by Albrecht Beutelspacher, William Watkins, Gerald L. Alexanderson, Dipa Choudhury, William J. Firey, Dan Kalman, Eleanor Lang, Russell L. Merris, Jeffrey L. Nunemacher, Ellen M. Parker
Average Customer Review:
Paperback (05 September, 1996)
list price: $39.95 -- our price: $39.95
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Reviews (4)

The essence of cryptology explained
After nearly 2000 years of being an esoteric branch of pure mathematics, number theory has found an application. And an important one it is. The expansion of the network of the global economy now forces most organizations to send data over public information lines. Without precise, secure encryption/decryption methods, financial trading would be substantially reduced if not essentially halted. Mathematics has indeed come to the rescue in this regard, providing precise, essentially unbreakable codes that are simple to use and understand.
All of cryptology is covered in this work, from the simple substitution cipher to the RSA algorithm. Techniques used to break codes are also demonstrated. Very readable, it is fun to examine the simpler codes and attempt to crack them. The level of mathematics required to understand the material is quite low. Simple algebra and knowledge of modular arithmetic are all that are necessary .
It is probably impossible to understate the simplicity of the RSA encryption algorithm as well as overstate the importance. It is amazing to think that such a simple procedure can guarantee security even when the opposition knows how the encryption was done. This explanation of the RSA encryption methods is the best that this reviewer has ever seen.
Exercises appear at the end of each chapter and it is very unfortunate that no solutions are given. This is a book that can be read for fun, and such books should provide answers to at least some of the questions.
Occupying a niche in the halls of the ivory tower of pure mathematics for nearly two millennia, number theory now forms a pillar of modern society. This book is the best explanation of how the pillar was constructed that is available today. It should be read by all who look down on "applied" mathematics.

Published in Journal of Recreational Mathematics, reprinted with permission.

Albrecht Rocks!
My friend and I did a project for school on Cryptology and Albrecht Beutelspacher was our savior!!!! If it weren't for this book we would have flunked. In "Cryptology," Beutelpacher has the most amazing pictures which make cryptology fun and easy! I would recommend this book to anyone. Good Job Albrecht!

This is a great book!
This book is great for learning about codes! I could never have done research on codes for a math class without it! Albrecht is a great author and the visuals were very entertaining. I recommend this to anyone who is interested in cryptology!! ... Read more

Isbn: 0883855046
Sales Rank: 403275
Subjects:  1. Business / Economics / Finance    2. Business Writing    3. Computer Data Security    4. General    5. Theory Of Numbers    6. Computers / General    7. Data security & data encryption    8. Secretarial & office skills   

Quicksilver (The Baroque Cycle, Vol. 1)
by Neal Stephenson
Average Customer Review:
Hardcover (23 September, 2003)
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Editorial Review

In Quicksilver, the first volume of the "Baroque Cycle," Neal Stephenson launches his most ambitious work to date. The novel, divided into three books, opens in 1713 with the ageless Enoch Root seeking Daniel Waterhouse on the campus of what passes for MIT in eighteenth-century Massachusetts. Daniel, Enoch's message conveys, is key to resolving an explosive scientific battle of preeminence between Isaac Newton and Gottfried Wilhelm Leibniz over the development of calculus. As Daniel returns to London aboard the Minerva, readers are catapulted back half a century to recall his years at Cambridge with young Isaac. Daniel is a perfect historical witness. Privy to Robert Hooke's early drawings of microscope images and with associates among the English nobility, religious radicals, and the Royal Society, he also befriends Samuel Pepys, risks a cup of coffee, and enjoys a lecture on Belgian waffles and cleavage-—all before the year 1700.

In the second book, Stephenson introduces Jack Shaftoe and Eliza. "Half-Cocked" Jack (also know as the "King of the Vagabonds") recovers the English Eliza from a Turkish harem. Fleeing the siege of Vienna, the two journey across Europe driven by Eliza's lust for fame, fortune, and nobility. Gradually, their circle intertwines with that of Daniel in the third book of the novel.

The book courses with Stephenson's scholarship but is rarely bogged down in its historical detail. Stephenson is especially impressive in his ability to represent dialogue over the evolving worldview of seventeenth-century scientists and enliven the most abstruse explanation of theory. Though replete with science, the novel is as much about the complex struggles for political ascendancy and the workings of financial markets. Further, the novel's literary ambitions match its physical size. Stephenson narrates through epistolary chapters, fragments of plays and poems, journal entries, maps, drawings, genealogic tables, and copious contemporary epigrams. But, caught in this richness, the prose is occasionally neglected and wants editing. Further, anticipating a cycle, the book does not provide a satisfying conclusion to its 900 pages. These are minor quibbles, though. Stephenson has matched ambition to execution, and his faithful, durable readers will be both entertained and richly rewarded with a practicum in Baroque science, cypher, culture, and politics.--Patrick O'Kelley ... Read more

Reviews (242)

Say what?
I can't pick it up.I try and I try, but I cannot finish this book.I keep getting drawn away from it and have read three other titles while that one sits there taunting me.I just do not find it interesting at all.

Tedious
Like many other reviewers, I am big fan of Cryptonomicon and other books by Stephenson, but this bloated, tedious book was a real chore to read.

What went wrong?I had three main issues:

1)no discernible plot; while things indeed happen throughout the 900 page book (how could they not?), these happenings do not really drive any sort of storyline forward (at least for the first 800 pages or so).

2)I didn't care for any of the main characters--besides being generally unsympathetic, they are very much contrived.

3)Despite the massive historical knowledge reflected in the book, it felt very ahistorical, as Stephenson tends to toss in contemporary slang and attitudes at odd moments throughout the book, I guess in an attempt to be clever...

Some reviewers who rave about the book imply that if you don't enjoy this book you don't have the intellect, stamina, or some other attribute necessary to appreciate such a hefty tome.As someone who generally enjoys a good long book, I'm here to tell you that this attitude is completely off-base.

Frankly, I don't see what attraction this book has for anyone, but many people have apparently enjoyed the book very much.In any event please don't buy it just because you enjoy Stephenson's other books, very thick books, or history--you'll be sorely disappointed.

TMR

It's either your thing or it's not
There are some long reviews here and some strong opinions. I'm going to be brief and not nearly so pointed. I really enjoyed this book, but my enjoyment of it comes with an acceptance of some of the flaws others are pointing out. Certainly, don't read this novel if you want a quick plot. Don't read it if you're afraid of big words and have no interest in early human forays into science. On the other hand, do believe that Stephenson is a stunningly imaginative writer. The way he writes this historically-set, often archaic material is so witty and engaging that I like the writing in and of itself. Could you chop out a hundred pages here or there and not notice? Probably, but far too much of our culture nutures short attention spans. Stephenson unapologetically demands a reader to sign on for the long haul, to enjoy each page for itself, without thinking too much about how quickly (or not) they're accumulating. I think the Umberto Eco comparison is apt, but if so Stephenson is a decidely American version. The material is very international, but there's a natural ease and irreverent humor to the author's prose that reminds me of the likes of TC Boyle, strangely enough. Okay, I wasn't as brief as I might have been. But neither is this novel. ... Read more

Isbn: 0380977427
Subjects:  1. Adventure and adventurers    2. Eighteenth century    3. Fiction    4. Fiction - Historical    5. Historical - General    6. Sagas    7. Scientists    8. Seventeenth century    9. Short Stories (single author)    10. Fiction / General   

IC Op-Amp Cookbook (3rd Edition)
by Walter G. Jung
Average Customer Review:
Paperback (02 January, 1986)
list price: $45.00 -- our price: $45.00
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Reviews (4)

Excellent book, LOUSEY printing
I'm holding in my hand a copy of the third edition of Mr. Jung's book, the "IC Op-Amp Cookbook." It just arrived from Amazon.

As an earlier reviewer has pointed out, the printing quality is very poor, particularly in the diagrams. Characters printed in smaller font sizes have a tendency to fill in with ink, so that digits like "8" or letters like "d" tend to be nothing but little blobs. ("Vcc" tends to look like "V**".) The manufacturers' datasheets in the back of the book are nearly unreadable. ("1*00 -- is that number 1500, 1600, 1900 ?") Even in parts of the book printed in larger type, the effect of the edge-bleed is to make reading a painful experience.

So, I am returning the book to Amazon. Based on Mr. Lopez's comments this is clearly not an isolated case of a bad print run. I don't believe (as Mr. Jung implies) that the Lopez review is based on some kind of illegal photocopy.

I've owned both of the previous editions of Mr. Jung's fine book on op amps, and I've very disappointed in what the publisher has done to the third edition. Prentice Hall, shame on you.

Author's response to Jerry Lopez
Mr. Lopez says:

The information is there, but, the print is hardly readable, it is blurred and appears to be a copy of a copy and then reprinted.
A shame. I would suggest not purchasing this book due to the above issue with the print quality.

I say:

Gee, lots of comments occur to me on this. Why didn't he exchange the book? Contact the publisher? Contact the author?

What he describes is similar to what one sees with a poor scanned copy, like the samples pages available here. They suit the purpose, but shouldn't be confused with the real thing. When I pick up a copy of the actual book in question (PH, CR 1997 ISBN 0-13-889601-1), I don't see at all what Lopez suggests is there. The text and graphics print is sharp and readable.

Could he have gotten a bogus copy somehow?

Walt Jung

IC Op-Amp cookbook - hard to read (paperback)
The information is there, but, the print is hardly readable, it is blurred and appears to be a copy of a copy and then reprinted.
A shame. I would suggest not purchasing this book due to the above issue with the print quality. ... Read more

Isbn: 0138896011
Sales Rank: 202656
Subjects:  1. Electronics - Circuits - General    2. Reference    3. Technology & Industrial Arts    4. Technology / Electronics / General   

Swarm Intelligence (The Morgan Kaufmann Series in Evolutionary Computation)
by Russell C. Eberhart, Yuhui Shi, James Kennedy
Average Customer Review:
Hardcover (23 March, 2001)
list price: $73.95 -- our price: $73.95
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Reviews (12)

Good science; not metaphysics : know the difference; win big
You are most likely familiar with the story. In summary form, it is about a group of blind men standing around an elephant each declaring "what an elephant is like" based upon which part of the elephant they are touching -- and elephant is like: a wall (side); a tree trunk (leg); a hose (trunk); a fan (ear); and so on.

What is wrong with this story, nothing...

The elephant is wisdom not knowledge -- Brahma told me when I was stoned once.You have to walk your path alone but "friends" share information with a select few; not because they're snobs but because they aren't -- a friend in this sense is likewise then someone who might be willing to value what may be told.The seekers of truth lie (no pun here)in the middle; the ignorant take stories out of context needlessly and pervert them to justify positions that are essentially ancilliary to the essentials of their own ancestry, which is what the original story is really directed at.The wise don't listen or write these kinds of reviews.But I heard some other fool talk about there being only the social mind at the expense of the individual mind.Question: perhaps this social mind can correct the job situation in Illinois for example?Or maybe it's too involved in the same obsessions that cripple the individual mind.Question: who provides the therapy for a such a stupid, ineffective, globally small minded polyglot that already assumes the vast majority of people want to hold the piss buckets for those few "bodies" working on important "swarm" thinking projects ("bodies": I don't know what else to call these now reduced appendages) in this love fest -- except love is profitable or it's a crack substitute, and there's no need to sell the science that way; it just makes you cheap.Question: if no one does provide some form of sanity check, what have you already said about me (and you)?

Answer: none of the questions apply, because the story is better than either this review or the other one.Give it some thought while your reading the book and find a place where no one is at -- there you are.

Good, but could have been more concise.
Swarm intelligence is burdened with an awful lot of material that is not core to PSO.A great deal of the book consists of the philosophical ramblings of the authors, rather than technical treatment of the topic at hand.An even larger chunk of the book was devoted to what was essentially a survey of AI: neural nets, evolutionary programming, heuristics, etc.Much too much space was devoted to grounding the reader in AI before proceeding.I must admit, however, that, while I found it out of place, the 'AI primer' part of the book is one of the most useful and lucid I have seen;I just think that it should have been a separate book (and this one should have been much thinner).The material that is specific to PSO is a very small fraction of the book, but is thorough and accessible;there really are few alternatives if one is particularly interested in PSO.However, if you are just interested in emergent behavior, and its applications to AI, take a look at Ant Colony Optimization (Dorigo).It covers ACO, rather than PSO, but is more more readable, and provides a much better technical treatment of the topic, if you want to avoid the philosophy and primer.

Interesting Paradigm
It's an immersive and powerful piece of scientific metrics and theoretical paradigm presentation. It shows that life can be a much deeper form of existence. The book presents the complexities of PSO in its network relativity but can be created using simple algorithms. The basis comes from the behavioural science andsocial patterns of insects such as bees and ants. Their process of colonial interaction and food foraging can be applied as a strong mathematical structure to computational science, robotics, and network technology. At the same time, you can take the exact principles -- in its raw idea -- and apply it to economic structure and business dynamics. I love how this book harks back to the parable of the blind men trying to explain what an elephant is like. ... Read more

Isbn: 1558605959
Sales Rank: 239413
Subjects:  1. Artificial Intelligence    2. Artificial Intelligence - General    3. Computer Bks - General Information    4. Computer Books: Languages    5. Computers    6. Distributed artificial intelli    7. Distributed artificial intelligence    8. Engineering - General    9. General    10. Swarm intelligence    11. Systems engineering    12. Computers / Computer Graphics / General   

A New Kind of Science: A New Kind of Science Explorer bundle
by Stephen Wolfram
Average Customer Review:
Hardcover (01 September, 2002)
list price: $95.00 -- our price: $95.00
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Reviews (4)

A New Kind of Revisionism Redox
Hi, my last review of this book had the title "A New Kind of Plagiarism", since then, very knowledgeable people have pinpointed with exactitude were the plagiarism was (almost the whole book!). A few others still claim that the book is good (how many of them are people who work for Wolfram?), to these people I ask the following question: can you point to a single original idea in the book? (Something that Wolfram actually discovered -because an astounding amount of things he claims are his are in reality other peoples inventions-- and that he did not discover a long time ago and already published). I wonder how many of the positive reviews were written by people who actually went to a University, I ask not as an insult but because If you commit plagiarism when studying in a University you can even get expelled (and they hammer this non-stop when you are in there), why isn't Wolfram "expelled" from the scientific community: simply because he is not in it!. Moreover, this is why he did not make this a scientific article but a book for the public at large; otherwise, the risk of being discovered (as a plagiarist) would have been too great. Guess what? You were discovered! It is amazing how short the memory of the public is. Most people cannot even remember all the fuzz that was made over fractals a while ago, no wonder some of them actually believe Wolfram did something original.These short attention span reviewers do not seem to grasp just how serious scientific fraud is!. Wolfram's book (sorry, I meant to say his copy pasting of other peoples work) should be condemned, no mater how entertaining it might be (or how good it might be as a general introduction to the discipline). Some reviewers think that the notes in the book contain the necessary references: THEY DO NOT. Wolfram is claiming long published (and much commented in popular Science Divulgation books) discoveries by others as his own. As if the plagiarism was not bad enough, the revisionist nature of his "history" of the discipline is unforgivable in itself (trying to erase the actual discoverers of the things he is claiming for himself). This kind of thing might have been permitted in 1950 Russia but in the XXI century in our country it is unbelievable that is being so.As another reviewer pointed out, "In his interview with "The Daily Telegraph" [May 15 2002] titled as "Is this man bigger than Newton and Darwin?" Wolfram remarks on his book as follows: "If other people don't get it, it's their problem, not mine." This is the most horrible attitude toward science I have ever encountered. He makes very little effort to present his what-so-called "New Science" to his peers. " Another reviewer writes:
"If one browses through all the reviews written here, one realizes that those who praise Wolfram are NOT SPECIFIC at all about why he is so great except that he has in general touched almost every aspect of modern science, a non-sense view. On the other hand, readers who have negative viewpoints of the book are very SPECIFIC about their opinion and they express why Wolfram's book is neither revolutionary nor new. "
"Like most people out there I believe that Wolfram owes a big apology to the scientific community and those non-expert enthusiasts who have a huge thirst for science but misled by non-scientists like Wolfram. "
"Mr. Wolfram is the author of Mathematica. Again, he takes the work of hundreds of people without giving them any credit. Disgusting."

"Why Mr. Wolfram can get away with all this. Read the first chapter of Philip Greenspun. If you have money you can invent truth. "

I quote these to wet your appetite for some excellent reviews so please read them all, believe me, they are worth your time, Wolfram's book is not!.

If we could only have a peek at Sasquatch's family photos...
Okay, so the Abominable Snowman walks up and asks if you'd like to see his family photo albums.All 1200+ pages of them.Maybe you don't quite 'get' what Sasquatch is about or why he'd want to share intimate family moments with a complete stranger, but, still, you KNOW you have to have a LOOK.

This is very much the case with Stephen Wolfram's A NEW KIND OF SCIENCE.I picked up my copy from amazon.com for considerably less than $50.00 (US), which, by weight, makes it one of the most reasonably priced books I have ever purchased -- especially among relatively limited printings, which include many, if not the vast majority, of 'standard' works in computer science.

(Hey, for under fifty bucks we should all sample anything capable of creating as much uproar among scientifically literate folks as, say, THE LAST TEMPTATION OF CHRIST created among the [selectively] scientifically oblivious.)

Unlike some other reviewers, I don't fault Wolfram if he fails to communicate as smoothly or as tersely as every reader might like.After all, we are taking part in an information transfer (mind dump?) from a man who, seeking the counsel of intellectual peers, has likely, in the apparent paucity of such during 10 years of secretive research, all too often ended up talking only to HIMSELF!

Nor do I fault Wolfram for a possible titular allusion to Galileo's DIALOGUES ON TWO NEW SCIENCES.Absent gods, pride is not "hubris," in the classical sense.Alas, Wolfram, like Darwin, has pointed the way to mechanisms that explain organized complex structures without apparent intentional, external 'design.'(Doubtless, Darwin didn't invent evolution any more than Wolfram invented cellular automata.But both men are accomplished synthesizers, discovering and/or articulating simple and elegant organizing principles where others encounter only chaos and befuddlement.)

Furthermore, even if we were to sift Wolfram's entire volume and find it devoid of any truly new or original insight, the work would still be invaluable as a compendium of ideas from the fields already referenced, especially chaos, complexity, and self-organizing structures.(If we are sometimes unable to discern between Wolfram's own ideas and someone else's, we can, at least, rejoice in his championing ideas that are important and timely, regardless of 'authorship.')

Not to belabor this point, but, depending on the direction from which one approaches a problem, it isn't always clear that s/he has traversed the identical thought processes (or courses of study) as someone else.With no malice aforethought, in mathematics and science we often encounter 'opportunities' for inadvertent reinvention and rediscovery.One author has referred to such as "mathematical epiphanies", alluding to the joy of finding even well-worn truths by and for oneself.In this sense, I feel, Wolfram might be expressing his own delight in making certain ideas his 'own,' even if, in the end, they turn out to be ideas that, with or without his knowledge, he might not have originated.In this respect, I am willing to give him the benefit of the doubt, realizing that others have, for their own reaons, been less charitable.At the same time, I am likewise unwilling to venture a guess regarding that (and how much) of which someone researching and writing in any of Wolfram's many field(s) should or should not have been aware.

In his further defense, however, successful business leaders are often oriented towards results rather than toward bestowing either credit or blame.(I am reminded that the great American patriot Thomas Paine added little to the thoughts of Voltaire, Rousseau, and others from the French Enlightenment.Nevertheless, his popular re-packaging of the 'higher criticism' in THE AGE OF REASON freed minds and pens and tongues that, otherwise, might never have come to know, via the original French, what Paine so eloquently set forth in an iconoclastic salvo the likes of which had not been heard since Luther's theses ignited the Reformation.And, then, even Luther benefitted from a sympathetic publisher!)

If my discussion, up till now, has been somewhat oblique, I have probably read more of Wolfram's book than many of the other reviewers -- far enough, actually, to have made it through the crucial section on "The Principle of Computational Equivalence."Until that point, I must confess, I had been viewing cellular automata as models of and, as such, merely ISOMORPHIC TO... certain natural processes.The great realization, at which we finally arrive, is that THESE machines and the machines at work in natural processes are the SAME [ABSTRACT] MACHINES!(The equivalence of two machines that produce identical outputs from identical inputs is not a revelation -- What is exciting is how Wolfram bridges the gap between the behaviors of man-made machines and naturally occuring 'machines.') Much as Darwin used a brilliant analogy to bridge the apparent gap between artificial and natural selection, Wolfram has articulated a bridge between artificial and natural 'machines' via a unifying computational principle.

I greatly appreciate Wolfram's exposition of some of his own intellectual 'epiphanies' in a form considerably more entertaining than most academic papers... and better organized than many personal journals or research notebooks.If time attests to the impact of these ideas (as I have intimated via comparisons to Galileo, Paine, and Darwin), I believe the time the reader invests to understand them will be well rewarded.

The Emperor's New Kind of Clothes
This review took almost one year. Unlike many previous referees (rank them by Amazon.com's "most helpful" feature) I read all 1197 pages including notes. Just to make sure I won't miss the odd novel insight hidden among a million trivial platitudes.

On page 27 Wolfram explains "probably the single most surprising discovery I have ever made:" a simple program can produce output that seems irregular and complex.

This has been known for six decades. Every computer science (CS) student knows the dovetailer, a very simple 2 line program that systematically lists and executes all possible programs for a universal computer such as a Turing machine (TM). It computes all computable patterns, including all those in Wolfram's book, embodies the well-known limits of computability, and is basis of uncountable CS exercises.

Wolfram does know (page 1119) Minsky's very simple universal TMs from the 1960s. Using extensive simulations, he finds a slightly simpler one. New science? Small addition to old science. On page 675 we find a particularly simple cellular automaton (CA) and Matthew Cook's universality proof(?). This might be the most interesting chapter. It reflects that today's PCs are more powerful systematic searchers for simple rules than those of 40 years ago. No new paradigm though.

Was Wolfram at least first to view programs as potential explanations of everything? Nope. That was Zuse. Wolfram mentions him in exactly one line (page 1026): "Konrad Zuse suggested that [the universe] could be a continuous CA." This is totally misleading. Zuse's 1967 paper suggested the universe is DISCRETELY computable, possibly on a DISCRETE CA just like Wolfram's. Wolfram's causal networks (CA's with variable toplogy, chapter 9) will run on any universal CA a la Ulam & von Neumann & Conway & Zuse. Page 715 explains Wolfram's "key unifying idea" of the "principle of computational equivalence:" all processes can be viewed as computations. Well, that's exactly what Zuse wrote 3 decades ago.

Chapter 9 (2nd law of thermodynamics) elaborates (without reference) on Zuse's old insight that entropy cannot really increase in deterministically computed systems, although it often SEEMS to increase. Wolfram extends Zuse's work by a tiny margin, using today's more powerful computers to perform experiments as suggested in Zuse's 1969 book. I find it embarassing how Wolfram tries to suggest it was him who shifted a paradigm, not the legendary Zuse.

Some reviews cite Wolfram's previous reputation as a physicist and software entrepreneur, giving him the benefit of the doubt instead of immediately dismissing him as just another plagiator. Zuse's reputation is in a different league though: He built world's very first general purpose computers (1935-1941), while Wolfram is just one of many creators of useful software (Mathematica). Remarkably, in his history of computing (page 1107) Wolfram appears to try to diminuish Zuse's contributions by only mentioning Aiken's later 1944 machine.

On page 465 ff (and 505 ff on multiway systems) Wolfram asks whether there is a simple program that computes the universe. Here he sounds like Schmidhuber in his 1997 paper "A Computer Scientist's View of Life, the Universe, and Everything." Schmidhuber applied the above-mentioned simple dovetailer to all computable universes. His widely known writings come out on top when you google for "computable universes" etc, so Wolfram must have known them too, for he read an "immense number of articles books and web sites" (page xii) and executed "more than a hundred thousand mouse miles" (page xiv). He endorses Schmidhuber's "no-CA-but-TM approach" (page 486, no reference) but not his suggestion of using Levin's asymptotically optimal program searcher (1973) to find our universe's code.

On page 469 we are told that the simplest program for the data is the most probable one. No mention of the very science based on this ancient principle: Solomonoff's inductive inference theory (1960-1978); recent optimality results by Merhav & Feder & Hutter. Following Schmidhuber's "algorithmic theories of everything" (2000), short world-explaining programs are necessarily more likely, provided the world is sampled from a limit-computable prior distribution. Compare Li & Vitanyi's excellent 1997 textbook on Kolmogorov complexity.

On page 628 ff we find a lot of words on human thinking and short programs. As if this was novel! Wolfram seems totally unaware of Hutter's optimal universal rational agents (2001) based on simple programs a la Solomonoff & Kolmogorov & Levin & Chaitin.

Wolfram suggests his simple programs will contribute to fine arts (page 11), neither mentioning existing, widely used, very short, fractal-based programs for computing realistic images of mountains and plants, nor the only existing art form explicitly based on simple programs: Schmidhuber's low-complexity art.

Wolfram talks a lot about reversible CAs but little about Edward Fredkin & Tom Toffoli who pioneered this field. He ignores Wheeler's "it from bit," Tegmark & Greenspan & Petrov & Marchal's papers, Moravec & Kurzweil's somewhat related books, and Greg Egan's fun SF on CA-based universes (Permutation City, 1995).

When the book came out some non-expert journalists hyped it without knowing its contents. Then cognoscenti had a look at it and recognized it as a rehash of old ideas, plus pretty pictures. And the reviews got worse and worse. As far as I can judge, positive reviews were written only by people without basic CS education and little knowledge of CS history. Some biologists and even a few physicists initially were impressed because to them it really seemed new. Maybe Wolfram's switch from physics to CS explains why he believes his thoughts are radical, not just reinventions of the wheel.

But he does know Goedel and Zuse and Turing. He must see that his own work is minor in comparison. Why does he desparately try to convince us otherwise? When I read Wolfram's first praise of the originality of his own ideas I just had to laugh. The tenth time was annoying. The hundredth time was boring. And that was my final feeling when I laid down this extremely repetitive book:exhaustion and boredom. In hindsight I know I could have saved my time. But at least I can warn others. ... Read more

Isbn: 1579550207
Sales Rank: 336497
Subjects:  1. Audio Adult: Other    2. Computers / Data Modeling & Design    3. Data Modeling & Design    4. Mathematical Analysis    5. Mathematics    6. Mathematics / Mathematical Analysis    7. Science / General    8. Science / Methodology    9. Cellular automata    10. Computational complexity    11. Computers    12. Electronic data processing    13. Mathematical models    14. Research & Methodology    15. Science   

Cellular Automata and Complexity
by Stephen Wolfram
Average Customer Review:
Paperback (01 January, 1994)
list price: $35.00
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Reviews (1)

Nice coverage of Wolframs published work
This is a nice collection of wolframs work on cellular automata (whichfirst appeared as a number of papers in various physics journals).It is anice coverage of cellular automata, but it would have been nice to givemore credit to von Neuman for his pioneering work in cellular automatatheory.

There is also an annoying habit for all of his work toconcentrate on deterministic cellular automata, and the mathematics isconstrained to this.Recent work has indicated that the origin ofcomplexity in our universe is from random sources that are preserved.. notthat the complexity all came from the initial conditions.

It isespecially interesting to note in his book how the different rules ofcellular automata play out to create varying degrees of complexity.Ittakes a very specific rule set indeed to allow for interesting complexbehaviors to show up, as evinced by the long search Conway undertook todiscover "life".

Hopefully Wolfram will comment on the recentresearch that indicates that complexity is introduced into our universethrough nondeterministic phenomena.He also should have presented Fredkinsideas about reversible computation to more fully flush out the relationshipbetween cellular automata, computability and reversibility. ... Read more

Isbn: 0201626640
Sales Rank: 230327
Subjects:  1. Cellular automata    2. Computational complexity    3. General    4. Logic    5. Mathematics    6. Science/Mathematics   

Mathematical Theory of Communication
by Claude E. Shannon, Warren Weaver
Average Customer Review:
Paperback (01 October, 1963)
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Reviews (7)

A first!
Where it all began.---The book grew out from an epic scientific paper in 1948, but luckly its author Shannon chose a light touch and a gentle delivery in his presentation. The paper became a book, with a 1949 first edition, which is now a classic, and which has been reprinted a number of times since, ending with the present lovely 1998 edition. It is still the place where readers can learn the essentials, including the two equations of information theory, that are now named after Claude Shannon.

Right from the master
The book about information theory. It is old but contain all the basic concepts. Even better, you can enjoy reading it!

Arguably, the most important paper EVER written!
I think it is fair to say that this book, based on Shannons landmark paper represents what I believe to be, the most important engineering paper ever written in the history of the world (both up to this point, and likely will remain so in the future).In terms of "practical implementation" of theory, it's fair to say that this seminal work has had a far greater contribution to mankind than Einsteins' paper on general and special relativity (just don't say that to a physicists face).

... All to often, famous theorists are relegated to "cult-like" obscurity.Persons like Shannon, Gallager, Forney, Komolgorov may be legendary within a cult-circle of die-hard communication theorists, but are relegated to unfortunate obscurity by the masses.It's rather unfortunate, with todays advanced communication systems, and techniques of coding (Turbo codes, modified LDPC codes, etc..)which push the boundaries to the ultimate limits as defined by Shannon.... that more people (both engineers, and laymen alike) don't recognize the names of early pioneers who started the revolution, and who's theories are the basis for many of our modern luxuries which allow us to download information at such rapid rates.

People often underestimate the deepness of Shannons' work,due to Shannon's writing style.He was one of those rare writers (somewhat like Forney, or Massey) who can actually explain complicated subjects using mere words, without the need for prettying the theory up with fancy math.Comparing the equation filled textbooks of today, versus Shannon's work, one might get the impression that Shannon's work was simplistic. I think it's clear to anyone whos studied his work, that IT WAS NOT SIMPLISTIC. Obviously, there was alot of "behind the scenes" math which Shannon had to go through to actually codify his many theorems. Just because Shannon did not show extensive derivations for each one of his theorems does not mean that he was not a good mathemetician..It merely means that he did not want to write a 1,000 page paper... he wanted to keep it simple (as was the customary writing style in the early to mid 1900's).

In short.. This book should be on YOUR shelf if you dont already own it, and if you are interested in information theory, and the deeper underpinnings of digital communications. I give the book 5 stars, not because it's any kind of elegant literary masterpiece; simply because it is based on the most important paper ever written.... S.A. Hoffman - ... Read more

Isbn: 0252725484
Sales Rank: 47724
Subjects:  1. Mathematical physics    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Telecommunication   

Gödel, Escher, Bach: An Eternal Golden Braid
by Douglas R. Hofstadter
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Paperback (01 January, 1999)
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Editorial Review

Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.

Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.

The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan

Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence. ... Read more

Reviews (203)

The science of self-reference and repetition
What do Godel, Escher and Bach have in common?They're demonstrations of self-referencing paradoxical behavior in 3 different fields: Music, Visual Art and Mathematics.If you can follow the ideas presented in Hofstadter's career building Pulitzer Prize winning work, consider yourself mentally stretched.

Godel's incompleteness theorum refers to itself in proving itself.(If it's true, it can't be.If it can't be true, it is)Escher's art is self-referencing - follow the waterfall down until you realize you are back at the top.Follow the stairs up and around a box, and get back to where you started.Same if you go down.Bach's music rises note by note until it's back where it started.

Attaching the same abstract idea behind each of these ideas is a fantastic synthesis.For some it will seem obvious.Others may consider it nonsense.I consider myself lucky to be in the group that considers themselves stretched.I don't get all of it, but enough to be glad I read it.

One of the great popular science books

This book richly deserved its Pulitzer prize.  It's one of the great pieces of popularscience writing and it's  remarkable that it has lost solittlein 25 years.  You learn the intricacies of Bach's music, of Godel's Incompleteness  theorem, Escher's drawings and DNA replication.Although his purpose seems to have been very general, with everythingtied together looselyas ideas for his future work in artificalintelligence, one could view this as abook about some parts ofcognitive psychology--  how the templates we inherit inour DNAcreate and interpret sounds  and images and theorems and how theseseemto relate to one another via the concepts of recursiveness,tangled hierarchies,and incompleteness.  It is mostly  thelack of these inference engines thataccounts for the fact thatto this day AI has still not been able to make a machine withthe brains of an ant(ie, go out into an arbitrarily complex world,recognize and deal with friend and foe, eat, reproduce, and stayout of the sunand rain and keep doing it for years).
Hisfollowup the next year with Daniel Dennet--`The Mind's I` complementsthis book nicely(see my review).

So one could say that thisis really a psychology text.  It  is about human  behaviorand reasoning-about why we thinkand act the way we do.  But(likeall such discussions until recently) none ofthe explanationsare really explanations.  Nobody at that time had muchunderstandingof  the mental mechanisms involved.  Like most 'explanations` ofbehavior, the comments here are often more interesting forwhat kinds of thingshe tries to use (and omits) than for theactual content.  As with all reasoningand explaining, art, math,music, etc, one now wants to know which of the brainsinferenceengines are activated.  This book and most books and AI  research were largely oblivious to such explanations until quite recently.

 Cognitiveand evolutionary psychology are still not evolvedenough to provide fullexplanations but an interesting start hasbeen made.  Boyer's  `ReligionExplained` is a good place tosee what a modern scientific explanation of  humanbehavior lookslike,and works on art, music and math are sure to appear soon. Pinker's`How the mind  Works` is a  good general survey. They do not explainall of intelligence or thinking but give an idea of how to start. See severalof the recent  texts(ie, 2004 onwards) with evolutionarypsychology in the titleor the web for further info.
Wenow recognize that the bases for art, music, math, philosophy,psychology, sociology, language and religion are found in theautomatic functioning of  templates or inference engines. This is why we canexpect similarities and puzzles and inconsistenciesor incompleteness and often,dead ends. The brain has no generalintelligence but numerous specializedmodules, each  of whichworks on certain aspects of  some problem and theresults arethen added, resulting in the feelings which lead to behavior. Hofstadter, like  everyone, can only generate or recognize explanationsthat areconsistent with the operations of his own inference engines,which  were evolved to deal with such things as resource accumulation,coalitions in small groups, social exchanges and the evaluationof the intentions of other persons. It is amazing they can producephilosophy and science, and not surprising that figuring outhow  they themselves work together to produce consciousness orchoice or spirituality is way beyond reach.

Hedoes not try to deal with the endlessly vexing issue of whetherthese correlations are out there in the world or in here in themind. Yes, weuse our templates, but why did we evolve  thoseand was there anotherpossibility?   Some will say this willall become clear when psychology andgenetics  are sufficientlyadvanced, while others say the same of physics andmathematicsor programming. And, did they all evolve from some  prototype enginein a precambrian invertebrate or did they come much later andfrom many sources?

It occurred to me that some of the mostcomplex products of human reasoning --superstring  theory andthe associated math--are recursive( in somenontrivial  sense)to quantum field theory, subatomic particle behavior and  theentire universe. Physics unites many areas of the most advanced  mathbecauseit needs  self consistent structures, but since we know math is logicallyproven to be  inescapably incomplete and math is a product of the mind, itseems reasonable  that there must be a sense in which the mind is incompletealso. We expectsince they use math that computers must be incomplete. We knowthatTuring's halting theorem for computation(we can not discover inadvancewhen a computer will stop) is logically equivalent toGodel's incompletenesstheorem.  It might follow that physicswill be incomplete as well and there willbe many physical lawsor phenomena that will never be compatible with orderivable fromthe others.  Or perhaps physics can be complete andselfconsistentin one universe but not in others

Just as he did not go veryfar into the many realms of psychology or  physics, neither did he venture farinto philosophy.  Perhaps the book could havebenefited greatly from anunderstanding of the infinitely subtlerelationships between language, thoughtand reality.  An acquaintance with  Wittgenstein would have helped immensely,especially his'Lectures on  the Foundations of Mathematics: Cambridge, 1939'edited  by Cora Diamond(1990).  It is better to get this onerather than theearlier `Remarks on the Foundations of Mathematics, Vol. 1` edited by RushRhees( as they are based on different setsof notes if you  are really  into ityou should get both).
AlthoughI've never seen anyone say so, W can be regarded as a pioneer incognitive psychology.  All of his  research was thought experimentsandintrospection  into the relations between  language, thoughtand reality. Perhaps  nobody ever approached his talent for describing the mind at work. The point is that Hofstadter istrying to  understand how the mind  works as apreliminary tomaking programs that work the same way(or at least get similarresults)so anyone who is interested in this book(or nearly any area ofphilosophy,language, psychology, or  intellectual  discourse) can look intoWwith great profit(but  be forewarned W may seem very  shallow,but if you jumpin you may never stop swimming)!
Just afterreading  this book I happened  to read  Wittgensteins ``Cultureand  Value``(published the  same  year(1980), but written decadesearlier), and,though it's his least interesting  book, I pickedout a few comments  that maybe regarded  as pertinent to muchof  this book and of course to a large part ofmodern intellectuallife.

 ``There  is no religious denomination  in whichthemisuse of metaphysical  expressions has been responsible for somuch sin asit has in mathematics.``  

 ``People  sayagain  and again that philosophydoesn't really progress, that  we are  still occupied with the samephilosophical problemsas were the Greeks.  But the people who say this don'tunderstandwhy is has to be so.  It is because our language has remained thesame  and keeps seducing us into asking the same  questions.  As long  as therecontinues to be a verb 'to be'  that looks as if it  functions  in the same wasas 'to eat' and 'todrink',  as long as we still  have  the adjectives'identical','true', 'false', 'possible', as long as we continue  totalk of  ariver of time, of an expanse  of space, etc., etc.,people  will keep stumblingover the same  puzzling  difficultiesand  find themselves staring at something which no explanation seems  capable of clearing up.  And what's more, thissatisfiesa longing for the transcendent, because, insofar as people think  they can see `the limits of  human understanding',  they believe of coursethat  they can see beyond  these.``
 
Wheneverone gets philosophical itis relevant to take a step back fromtime to time and see just what is reallygoing on.  Hofstadteris not a  philospher and he does not seem to take thatstep.  Incompleteness  seems well defined in math but what about elsewhere?  In what sense is music or  art or biology incomplete?  And exactly what willcount as a tangled  hierarchy, and recursiveness orself referencing in suchdifferent realms(and as W would say,such different language games)?   Its notreally so clear that the  recursiveness in art, music, biology and math are thesame sort of thing at all an, insofar as they are, what exactly thatmeans.What should count as  ``same` here?

H doesnot address these questions in any depth but one might  find them by far the most interesting theme of the book.  We are tantalized at  theseeming connections but do they mean anything?  Do they go to the core of  ourbeing(how the mind works)? Are they merelythe result of the use of  some of thesame templates by art,math, and music?  Do they relate  to the molecularstructureof  matter or to particle physics and  string theory?  Is ituseful toextend these analogies(or are  they homologies?)almostendlessly further intophilosophy, language,  psychology, biology(e.g.,not only the recursive natureof DNA,  RNA  and proteins, butthe many levels of feedback in the nucleus, cytoplasm,  intercellular,interorgan, intracerebral, exchange  of chemicals andgenes betweennucleus, mitochondria and chloroplasts  as well as with thebacteriaand  viruses that wander in out of  our bodies into other bodiesandother organisms  happily picking up and dropping off genesas they go--tangled,recursive,  hierarchical  and in some sense,incomplete).

Or, to take it further, one  might  findyet more connections between artand music, math and biology, computer programs, physics and chemistry andbiochemistry and add such  dimensions as color, geometric shapes, measurements,self organizing abilities, chaos, and other temporal, spatial or purelypsychological ways(emotions,  sensations, dreams etc).  There are many books inart, music,  math, biology,  psychology,physics and chemistry that alreadytouch upon these  themes butI think the most progress is being made incognitive psychology.The brain is highly recursive in many ways.   We conversewithourselves  internally and many times externally. The  schizophreniccommonly hears voices,  but they rarely say nice  things.

Oneis reminded ofthe cut-ups that William Burroughs  and ByronGysin  created.  They cut up booksor even newspapers  andstuck them back together  randomly.  There was usuallysome perverse kind of logic to the result showing  the hidden threads indiscourse.  Burroughs later did the same thing with films,with similar results.

Of course pursuing hidden relationships between seemingly unconnectedthings  quickly leads to numerology, pyrimidology and madness. One can findcodes or algorithms toconnect or derive anything from anything. Hofstadter doesnotgo  into this here but he mentions it in his next book, The Minds I(1981). I am reminded of string theory which has math so powerful it can probablyexplain any possible  universe and so it is verysuspect as  an explanation ofours. 

He suggest that incompleteness,tangled hierarchies etc may beresponsible  for the emergenceof higher phenomena which do not exist and cannotbe explainedat lower levels(eg, consciousness and in fact, everything)and seemsto be something of a holist( but in other places he seems  clearly behavioristor reductionist). You might say he is suggesting we look for the  explanationof emergence in the bizarre phenomena of the foundations of math,  rather thanin those in the foundations of physics. Given a universe where life ispossible, is it  notinevitably full of  recursiveness, tangled hierarchies,incompleteness etc. 

As H is well aware, Zen can be regarded as using  theseaspects of the  world to trick the mind into stopping-- at which point allrelationships become  irrelevant. However hewas  just starting in Zen at thetime so he does not go  veryfar with  it.  For those who want to go into itfurther, probablythe best and most readable recent books on Zen  are thevariousvolumes  by Osho. 

Its a pity he has not been  able to writeanother  book like this as there is  now a vast amount  ofinformation available about DNA and RNA, the inflationary theory of the  universe, quantumtheory, and the beautiful fusionof string  theory  and advanced math, whichcould greatly extendand  amplifiy  the themes of recursion, tangledness,hierarchies,and  incompleteness.  One could  make a good case that the basicstructure  of the universe has these  properties at its smallestandlargest scales.   Both quantum physics and string theoryhave  complex  sets oflaws  that appear tangled,nested, hierarchical and incomplete--  and so far noone can  unifythem, unless one  accepts string  theory on faith-but nobody cansolve string theory and physics, like mathematics  whichit mirrors (orexpresses?)may remain forever incomplete( Kaku's`Hyperspace` gives a summary upto 1994-see my review).

Itwas one of the few times he stuck  his neck outwhen he predictedthat  the future of AI would involve  recursive programs butareneural nets and fuzzy  logic recursive?   And do these relateat all to howthe brain works or to anything Wittgenstein hasto say about language andreality?  The diligent might want tolook at B.A.  Worthington's book--`SelfConsciousness and SelfReferencing:an interpretation of  Wittgenstein's Tractatus`.

Sincethis book appeared, mathematician Gregory Chaitin has mademajorextensions of incompleteness and alsodeveloped the amazing omeganumberdefining the limits of math(his  popular and tech bookseasy to find on the net and  his most recent  on omega-- Meta Math --appeared in 2005). 

Somereaders will find interesting avaguely similar book ``Labyrinth``  by PeterPesic (2000)  whichuses the  form of the triple fugue to link symbolicmathematicsto the  pursuit  of science.
He does not mention that Godelshowed that (if  the universe is rotating) time  travel is possible(ie,time isrecursive), nor that all theories of physics,  includingquantum  field theory,remain incomplete.  Also the highestproduct of  the  mind--Superstring Theoryis recursive to quantumfield theory and  the  behavior of particles and theentireuniverse. A good bit  of this was known in 1980 and Hofstadterwas aphysicist so it''s surprising it does not appear here. We know that the mostadvanced  physics and the most advancedmath fuse in superstring theory  andthis seems amazingly holistic. Physics must have the  self  consistentstructures of mathematicsbut as math is inescapably  incomplete  does it followthatphysics is also? And worse, as  math is a product of the mind is not themind forever incomplete  too?  Does