21 of 22 people found the following review helpful
5.0 out of 5 stars The Million Dollar Problem
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...
Published 8 months ago by R. Hardy
4 of 18 people found the following review helpful
3.0 out of 5 stars small errors - big implications
The very first chapter contains the statement "Your hands are the most incredible engineering devices every created." Of course, "every" should be "ever." But what does this imply for the text? Either careless writing or careless editing. Am I being hopelessly overcritical, or am I justifiably reluctant to invest my time in a product which is carelessly presented to...
Published 4 months ago by odyssoma
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21 of 22 people found the following review helpful
5.0 out of 5 stars The Million Dollar Problem,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (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.
33 of 39 people found the following review helpful
5.0 out of 5 stars FINALLY a Really Up to Date Survey of the Biggest Problem in Science,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)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
4.0 out of 5 stars Popularizing P vs NP for the laymen,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)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
5.0 out of 5 stars An account for laypersons of one of the chief open problems in mathematics,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)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
5.0 out of 5 stars Great Book on a Great Topic,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)I really enjoyed this book. It was a light enough read to finish in one sitting on a weeknight within a few hours, but also showed its importance by being able to connect the dots between the P = NP problem to issues in health care, economics, security, scheduling and a number of other problems. And instead of talking in a "professor-like" tone, the author creates illustrative examples in Chapters 2 and 3 that are easy to grasp. These examples form the basis for much of the problems addressed in the book.
This is a book that needed to be written and needs to be on everyone's bookshelf, particularly for those asking questions like "what is mathematics" or "what is mathematics used for". This book answers those questions, and towards the end gives examples (in plain English) of the different branches of mathematics and theoretical computer science, without making it read like a text book.
3 of 3 people found the following review helpful
5.0 out of 5 stars An easy-read intro that gets you wanting to learn more,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)I won't go into details about the book because others have, but it surely is written well, gives good history, and stays very general with logical examples of the problem. The only thing it lacks is clearly going into the logic of why brute force is required for these problems, meaning it doesn't really try to work through a given logical approach to demonstrate the complexity of NP problems. But you will discover this yourself when you try a given problem, and this book is more a setup for more technical books.
3 of 3 people found the following review helpful
5.0 out of 5 stars Great for layreaders but even a blast for computer scientists,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Kindle Edition)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
1 of 1 people found the following review helpful
4.0 out of 5 stars Simple language great concepts,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)I started reading this book keeping my CS background in my mind and I lost the interest because of the vague descriptions of the problems and/or definitions but quickly I realized that this book is intended for non-CS audience. From that point onward I forgot that I'm a grad student in CS and started re-reading the book and I really enjoyed it. Now I use those terms/examples to describe/explain to my non-CS friends what I exactly do :-)
4.0 out of 5 stars Good succinct explanation,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)I especially liked the fact that the author explained the topic well, while resisting the temptation to create a giant book full of repetitious examples. I didn't fully understand some of the analogies but still feel like I have a better understanding of what the P vs. NP problem is - and why it matters to all of us.
4.0 out of 5 stars Popularizing a modern computer science problem,
This review is from: The Golden Ticket: P, NP, and the Search for the Impossible (Hardcover)To understand how a modern automobile functions involves having an understanding of mechanics and electrical systems. To fully grasp an understanding of these systems presupposes a basis in engineering and further still, an understanding of physics. To know physics one must know math. What gives rise to math? Some might say philosophy or perhaps God. If we limit ourselves to the natural world, math will underlie much of what we can or will know. Interest in scientific disciplines will expand and wane, but only math is likely to remain a foundation of them all. Its application permeates throughout the sciences, business, sport and beyond, yet it is largely an abstract field, much of which is just a convenient representation or language to describe what we see or experience happening all around us. In other words, little of it is real, but simply a representation of understanding. Its notation a human invention, a playful language we can mold and shape to fit a problem at hand. This representation of the real suggests that there is something so magical about mathematics that having an understanding of it literally does bring us closer to something much more than the seemingly dull computation school children are all subjected to.
Largely stemming from the field of mathematics came the familiar technology and associated computer science programs we are immersed in today. Out of this field has arisen great excitement and challenge. Perhaps the most famous challenge is the so-called P versus NP problem. Is it the case that P, problems that can be solved in polynomial time or that for which answers can be found quickly and are feasible and efficiently computed, can also be NP or verified efficiently and quickly (and vice versa)? These problems and the importance of which, matter greatly to a number of fields involving computation, including encryption, social network analysis, graph theory (i.e. networking), various scheduling/queuing problems and more. Lance Fortnow is his article turned book, tries to capture the importance of the P versus NP problem for a wide audience. Based on an earlier short article for The Communications of the ACM (which is freely available and I recommend you read it before its conversion to book form), Fortnow covers the history of the problem, its application and what it might mean for the world if P = NP. Mathematicians widely believe, and Fortnow is no exception, that it is likely P does not equal NP. This too has ramifications, but even proving this true is still an open question with significant consequences. For instance, much of the encryption the Internet and computer technology relies upon assumes P is not equal to NP. If proven otherwise, we may witness the most widespread upgrade any set of man-made systems has ever seen.
I'm generally a fan of popular science books, but the best ones require a writer of both immense literary skill and scientific background that most books fall short. Fortnow's addition to this class of books is neither perfect nor poor. He appears to have been a reluctant author, suggesting that the topic is best summed up in two words, "still open". His writing is reasonably clear and concise, but it hardly affords him a place on par with the likes of the best science writers. While I may hold him to a high standard, I can't imagine this book will be widely appreciated by those without an existing interest and background in computer science or mathematics. If you're a discerning reader, I highly recommend finding and starting with his ACM article, which covers the meat of the book in far fewer pages, albeit with a bit more mathematical knowledge assumed of the reader.
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The Golden Ticket: P, NP, and the Search for the Impossible by Lance Fortnow (Hardcover - March 31, 2013)