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The Golden Ticket: P, NP, and the Search for the Impossible Kindle Edition

3.7 out of 5 stars 3 customer reviews

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Product Description


One of Amazon.com's 2013 Best Science Books

One of Choice's Outstanding Academic Titles for 2013

Honorable Mention for the 2013 PROSE Award in Popular Science & Mathematics, Association of American Publishers

"As Lance Fortnow describes in his new book, The Golden Ticket: P, NP and the Search for the Impossible, P versus NP is 'one of the great open problems in all of mathematics' not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, 'from cures to deadly diseases to the nature of the universe,' even 'an algorithmic process to recognize greatness.'. . . To postulate that P ? NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration--but also of discovery and inquiry, of pleasures pleasingly delayed."--Alexander Nazaryan, New Yorker

"Fortnow effectively initiates readers into the seductive mystery and importance of P and NP problems."--Publishers Weekly

"Fortnow's book is just the ticket for bringing one of the major theoretical problems of our time to the level of the average citizen--and yes, that includes elected officials."--Veit Elser, Science

"Without bringing formulas or computer code into the narrative, Fortnow sketches the history of this class of questions, convincingly demonstrates their surprising equivalence, and reveals some of the most far-reaching implications that a proof of P = NP would bring about. These might include tremendous advances in biotechnology (for instance, more cures for cancer), information technology, and even the arts. Verdict: Through story and analogy, this relatively slim volume manages to provide a thorough, accessible explanation of a deep mathematical question and its myriad consequences. An engaging, informative read for a broad audience."--J.J.S. Boyce, Library Journal

"[This] as-yet-unsolved problem--identified by mathematicians as the P-NP problem--raises fundamental questions about just how far society can ride the technological wave triggered by the computer revolution. Fortnow unfolds a fascinating dual-track story of how this problem first emerged, Western researchers encountering it while trying to maximize computer efficiency, Russian analysts confronting it while puzzling over the persistent need for perebor ('brute force search'). Readers watch as the P-NP problem attracts investigators in cryptography, biology, quantum physics, and social networking--and frustrates them all. Fortnow allows nonspecialist readers to glimpse the conceptual difficulties here (try 'nondeterministic polynomial time,' for example). But he mercifully frames his discussion largely in nontechnical terms. Even readers averse to mathematics will share in the intellectual stimulation of pondering a riddle compelling us to ask what we should hope for--and fear--in replacing human brains with computer algorithms. A provocative reminder of the real-world consequences of a theoretical enigma."--Bryce Christensen, Booklist

"The definition of this problem is tricky and technical, but in The Golden Ticket, Lance Fortnow cleverly sidesteps the issue with a boiled-down version. P is the collection of problems we can solve quickly, NP is the collection of problems we would like to solve. If P = NP, computers can answer all the questions we pose and our world is changed forever. It is an oversimplification, but Fortnow, a computer scientist at Georgia Institute of Technology, Atlanta, knows his stuff and aptly illustrates why NP problems are so important."--Jacob Aron, New Scientist

"Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science."--Rob Hardy, Commercial Dispatch

"A great book. . . . [Lance Fortnow] has written precisely the book about P vs. NP that the interested layperson or IT professional wants and needs."--Scott Aaronson, Shtetl-Optimized blog

"[The Golden Ticket] is a book on a technical subject aimed at a general audience. . . . Lance's mix of technical accuracy with evocative story telling works."--Michael Trick, Michael Trick's Operations Research Blog

"Thoroughly researched and reviewed. Anyone from a smart high school student to a computer scientist is sure to get a lot of this book. The presentation is beautiful. There are few formulas but lots of facts."--Daniel Lemire's Blog

"An entertaining discussion of the P versus NP problem."--Andrew Binstock, Dr. Dobb's

"The Golden Ticket is an extremely accessible and enjoyable treatment of the most important question of theoretical computer science, namely whether P is equal to NP. . . . [I]t is a very pleasant read for those specializing in discrete mathematics, and understandable to anyone with an undergraduate knowledge of mathematics."--Choice

"The book is accessible and useful for practically anyone from smart high school students to specialists. . . . [P]erhaps the interest sparked by this book will be the 'Golden Ticket' for further accessible work in this area. And perhaps P=NP will start to become as famous as E=mc2."--Michael Trick, INFORMS Journal of Computing

"In any case, it is excellent to have a nontechnical book about the P versus NP question. The Golden Ticket offers an inspiring introduction for nontechnical readers to what is surely the most important open problem in computer science."--Leslie Ann Goldberg, LMS Newsletter

"The Golden Ticket does a good job of explaining a complex concept in terms that a secondary-school student will understand--a hard problem in its own right, even if not quite NP."--Physics World

"The whole book is fun to read and can be fully appreciated without any knowledge in (theoretical) computer science. Fortnow's efforts to make the difficult material accessible to non-experts should be commended. . . . The book thus caters to all audiences: from novices with an interest in computational problems to experts with knowledge in theoretical computer science."--Andreas Maletti, Zentralblatt MATH

"This is a fabulous book for both educators and students at the secondary school level and above. It does not require any particular mathematical knowledge but, rather, the ability to think. Enjoy the world of abstract ideas as you experience an intriguing journey through mathematical thinking."--Gail Kaplan, Mathematics Teacher

From the Back Cover

"You will love this book. It's completely accessible and captures the thrill, potential, and heartbreak of an edgy mathematical problem in terms that nonmathematicians will appreciate. After reading The Golden Ticket, I sort of hope P isn't NP after all."--Vint Cerf, Google Vice President and Chief Internet Evangelist and one of the "Fathers of the Internet"

"The P-NP problem is fundamental to computer science, and indeed all of mathematics. This book presents an engaging exposition of the problem, its history, and importance. In the process, it touches on major topics appearing in university computer science courses, all presented in an amusing style requiring no background in mathematics beyond the ability to solve Sudoku puzzles. I highly recommend it."--Stephen Cook, formulator of the P-NP problem

"This book, written by a world-class master of the field, is a grand tour of the most celebrated and profound unsolved problem in computer science. Fortnow's many ingenious explanations make the mysteries of computational complexity accessible to anyone interested in the fundamental questions: what can be computed and how fast can we compute it?"--John MacCormick, author of Nine Algorithms That Changed the Future

"This book is meticulous. Fortnow has really tracked down the history and background of this important and timely subject. Even complexity theorists will benefit from his fine scholarship. The Golden Ticket is the first of its kind--a book for general readers about complexity theory."--William Gasarch, University of Maryland

"Nobody explains the importance of the P-NP problem better than Fortnow."--William J. Cook, author of In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation

Product details

  • Format: Kindle Edition
  • File Size: 6833 KB
  • Print Length: 181 pages
  • Publisher: Princeton University Press (27 Mar. 2013)
  • Sold by: Amazon Media EU S.à r.l.
  • Language: English
  • Text-to-Speech: Enabled
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  • Word Wise: Not Enabled
  • Enhanced Typesetting: Enabled
  • Average Customer Review: 3.7 out of 5 stars 3 customer reviews
  • Amazon Bestsellers Rank: #493,699 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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Format: Hardcover
There is good and bad news early on in this book about the P versus NP problem that haunts computing. The good news is that on the description I expected this to be a dull, heavy going book, and it's not at all. Lance Fortnow makes what could be a fairly impenetrable and technical maths/computing issue light and accessible.

The bad news is that frustratingly he doesn't actually tell you what P and NP mean for a long time, just gives rather sideways definitions of the problem along the lines of `P refers to the problems we can solve quickly using computers. NP refers to the problems to which we would like to find the best solution', and also that he makes a couple of major errors early on, which make it difficult to be one hundred percent confident about the rest of the book.

The errors come in a section where he imagines a future where P=NP has been proved. This would mean you could write an algorithm to very efficiently match things and select from data. Fortnow suggests that our lives would be transformed. This is slightly cringe-making as fictional future histories often are, but the real problem is that he tells us that the algorithm would make it possible to do two things that I think just aren't true.

First he says that from DNA you would be able to identify what a person looks like and their personality. Unfortunately, these are both strongly influenced by epigenetic/environmental issues. Anyone who knows adult identical twins (with the same basic DNA) will know that they can look quite different and certainly have very different personalities. And they will usually have been brought up in the same environment. Fortnow is forgetting one of the oldest essentials of computing - it doesn't matter how good your algorithm is, GIGO - garbage in; garbage out.
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Format: Hardcover
This is a very good book.
Lance Fortnow manages to break down into small pieces, a difficult subject that takes years to master. What is left is a well told story totally accessible from everyone. But, I really think that if you hold a BS in Computer Science, you will find it not only a very good book but it will give you the chance to reorganize your thoughts on the P versus NP Problem.
On the other hand if you had never heard of P vs NP you will be introduced to something that you may not like or be interested in.
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Format: Hardcover Verified Purchase
I don't think it is actually as good as expected. I don't think it as clear. It is mostly a book for fun rather than research.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: HASH(0x8b169570) out of 5 stars 32 reviews
30 of 31 people found the following review helpful
HASH(0x8b199234) out of 5 stars The Million Dollar Problem 1 April 2013
By Rob Hardy - Published on Amazon.com
Format: Hardcover
Everyone knows that computers are getting more powerful and better at doing almost anything. Finding you the fastest route cross country is easy. Translating a page of prose from one language to another is harder, but it's getting better all the time. Finding the shortest route that will get you to all of five different cities, no problem; finding the provably shortest route that will get you to all of a thousand cities - that's a toughie. It's so hard that perhaps no computer, no matter how big or how fast, can ever do it. Perhaps. Are there tasks beyond computing? It is a deep question bridging mathematics and computer science, and it is the subject of _The Golden Ticket: P, NP, and the Search for the Impossible_ (Princeton University Press) by Lance Fortnow. The question is so hard, and so important, that it is one of the seven Millennium Problems for which the Clay Mathematics Institute will give you one million dollars when you prove it. (Programming genius Donald Knuth will also give you a turkey.) This is deeper mathematical territory than most of us will ever penetrate, but Fortnow, a professor of computer science, keeps the explanations light, knowing that those of us reading this sort of book aren't really in the running for the prize, but at the same time showing how important the answer to the question might be for the future of computing.

It is best to call it the P/NP problem; the abbreviation P comes from "polynomial;" and in giving us the second, Fortnow jokes, "NP (which stands for `nondeterministic polynomial time,' if you really need to know)." He does not get much deeper into polynomials, but P is the group of problems we know computers can solve quickly. NP is a possibly separate group of problems that cannot be solved quickly by any computer program we have now, but if P = NP, then a powerful computer could solve those NP problems as easily as computers are currently solving the P ones. One of the important parts of Fortnow's book is that he shows that the P/NP problem is not something just of interest to mathematicians and computer scientists. It is a critical question in fields as diverse as biology, economics, medicine, and physics. No one has been able to come up with an efficient algorithm that solves any NP problem, which seems to indicate there is no such thing, and that P is not equal to NP. It would be a real surprise if P = NP, but right now there is no proof either way. There are plenty of people working on it. Some of them are the same sort of people who are sure they have proved the classic (and unprovable) problem of trisecting an angle. One computer journal has ruled that it will accept such P/NP proofs from any one author no more often than every two years, because most such attempts are "unreadable or clearly wrong." Fortnow encourages readers to try proving P/NP, "for you cannot truly understand the difficulty of a problem without attempting to solve it," and while his book does not give formal definitions of P/NP that would be the basis for your proof, it has website citations that could start you off. But on the other hand: "Suppose you have actually found a solution to the P versus NP problem," he writes. "How do you get your $1 million check from the Clay Mathematics Institute? Slow down. You almost surely don't have a proof. Realize why your proof doesn't work, and you will have obtained enlightenment."

Not only are you unlikely to get a proof, Fortnow is pessimistic that any mathematician is going to be coming up with one anytime soon. He knows the state of current research on the problem, and says that there is no known line of attack currently being pursued that could lead to a successful proof. Things seem to be at a standstill. He reminds us that it took 357 years to get a proof of Fermat's Last Theorem. While we may continue to butt our heads up against NP problems with merely approximate answers, and while P will increasingly seem not to equal NP, there may be no proof out there ever. Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science.
35 of 41 people found the following review helpful
HASH(0x8b19921c) out of 5 stars FINALLY a Really Up to Date Survey of the Biggest Problem in Science 20 Mar. 2013
By Let's Compare Options Preptorial - Published on Amazon.com
Format: Hardcover Verified Purchase
What an awesome book! P-NP is essentially the question of whether we can find solutions quickly if we can define or know there is a solution quickly-- in layman's terms, it means we know, and then can solve, the traveling salesman problem in "P" -- polynomial -- rather than exponential or infinite time, or not at all. (MAHDI emailed and corrected this by saying: "The second sentence is wrong. P-NP is whether we can find solutions nearly as efficiently as we can verify them. The statement that we can find solutions if we can know there is a solution is a known fact and an easy exercise to prove").

There are a lot of technical books on the topic, but this is the first recent book that explores the golden ticket (finding the ONE in your batch of many that will allow you into Willy Wonka's factory tour) in layman's terms, but without talking down to the reader, and covering and focusing on all the aspects of the question. "How not to prove that P does not equal NP" as the author says, is an example of the complex and convoluted logic that's needed to explore the field of computational complexity.

Most authors, including this one, use public key crytography, factoring, etc. as examples of the "good" things about intractable problems, yet they also point out that if you could solve this problem, all the other millenium prize problems would likely also fall before you! That's more than $5 million US, so this book is definitely worth a careful read! (Ok, little tongue in cheek). The current "go to" text on the topic, from 2010, is Goldreich's P, NP, and NP-Completeness: The Basics of Computational Complexity -- which takes a kind of "text" approach, with problems, exercises, etc., and is a lot more technically oriented (interpret: dry) than Fortnow.

Contents include: The Golden Ticket, The Beautiful World, P and NP, The Hardest Problems in NP, The Prehistory of P vs. NP, Dealing with Hardness, Proving P does not equal NP (which this author believes), Secrets, Quantum, and The Future.

This book is truly FUN and READABLE-- Fortnow peppers every page with anecdotes, examples, side stories, cartoons, diagrams, and an amazing array of connections. Past explorations couldn't even have asked if it's possible to scan for the largest Facebook friends lists, because Facebook didn't exist during most of the past P/NP books frames!

If you want a more general intro to computational complexity, Neil Johnson's little triple reprint from 07 to 2012 is outstanding: Simply Complexity: A Clear Guide to Complexity Theory, and is under 10 bucks. For an exploration of how P/NP fits with the other current millenial problems, an outstanding new book is Ian Stewart's Visions of Infinity: The Great Mathematical Problems. To go a level higher, and see how computational complexity fits more generally in Systems Science and systems thinking, Flood's 2010 book is a gem: Dealing with Complexity: An Introduction to the Theory and Application of Systems Science (Language of Science).

NONE of these, however, are as gentle an introduction, with as complete and detailed coverage, as Fortnow. This is a must have if you have any interest in the biggest and toughest and perhaps most important problem of our age. The icing on the cake is the really fun read of a really dry topic!

EMAILERS-- update: For those who want more math on complexity than Fortnow gives, but not beyond advanced undergrad, check out this truly undiscovered gem by Sole: Phase Transitions (Primers in Complex Systems).

Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
13 of 15 people found the following review helpful
HASH(0x8b560188) out of 5 stars Popularizing P vs NP for the laymen 28 April 2013
By haig shahinian - Published on Amazon.com
Format: Hardcover Verified Purchase
A rare popular science book about the P vs NP problem. The author takes care in using concrete examples and simplifying explanations as much as possible, though I think at times he makes it too simple. I especially liked that he included the history of how the problem developed on both sides of the iron curtain during the cold war. This book may be a nice read for people who don't have much of a science or math background, but for those who do I don't think they will get enough out of it compared with just reading some wikipedia articles.
6 of 6 people found the following review helpful
HASH(0x8b5f6618) out of 5 stars An account for laypersons of one of the chief open problems in mathematics 4 May 2013
By Ryan Williams - Published on Amazon.com
Format: Hardcover Verified Purchase
Lance Fortnow's new book is an inspiring, accessible, and imaginative overview of P versus NP that everyone can read and appreciate, which until now has been conspicuously missing from the literature. Within the "folklore" of complexity theory, people have long uttered intuitive phrases to motivate P versus NP in passing, such as "P versus NP is asking whether creativity can be automated by computers." Fortnow takes these intuitions and expands them, like no one else has before: really imagining a world where P = NP, exploring the magic of computing in that world, and arguing why that world is unlikely to exist. He also discusses a historical account of the problem's origins in both the East and West, how people cope with P versus NP in practice, some past attempts at resolving P versus NP, the applications to cryptography, and the relevance of quantum computing. All this in less than 200 pages!

There is an intellectual cost to the immediate accessibility of this book: for example, P and NP are never really formally defined. If you would like to *work* on P versus NP, or (less ambitiously) are looking for a technical overview of the problem, there are many available books to recommend such as Scott Aaronson's new Quantum Computing since Democritus or Sipser's classic textbook Introduction to the Theory of Computation. However, if you're just looking for a high-level explanation of why P versus NP is so important, Fortnow's book is a great place to start.
4 of 4 people found the following review helpful
HASH(0x8b560044) out of 5 stars Great for layreaders but even a blast for computer scientists 17 July 2013
By Eric Siegel - Published on Amazon.com
Format: Kindle Edition Verified Purchase
Having personally neglected computational theory for almost two decades since completing my doctorate in computer science, this read was a blast - not only reminding me of the main themes of the topic, but seeing a bigger perspective around it than I'd ever previously been taught - plus a lot of new aspects have developed over those years (e.g., I still thought of P/NP as being about deterministic versus non-deterministic, rather than today's more common vantage: recognizing versus finding a solution to a problem instance).

The footnote on page 111 is my favorite footnote ever.

Given my background, I wouldn't mind (for the Second Edition?) a 2- or 3-page appendix with a Wikipedia type of entry about the technical details, so I could remind myself and ruminate more deeply without interrupting my transcendental state by running back to an actual computer screen, but that is hardly a criticism of the book, given its purpose.

My work is in machine learning (aka, predictive analytics), and the author touches upon how P/NP relates to my field; tantalizing food for thought. Machine learning is not just optimization, though; beyond optimizing over a training data set, you need to ensure it then continues to perform well over data not used to optimize it. Hmm, how does this play out if P=NP?

Eric Siegel, Ph.D.
Founder, Predictive Analytics World
Author, Predictive Analytics: The Power to Predict Who Will Click, Buy, Lie, or Die
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