on August 3, 2007
I am an academic economist who knows something about game theory, so when I bought this book I did not hope to learn anything new but just to be entertained by an "illuminating" author during my leisure hours. I was disappointed to the point of anger.
This book is basically a journalist's report based on interviews with a few (probably half a dozen) individuals as the pages are filled with quotes from several academics in good standing. I think it would have been better to simply present many illuminating quotes from these individuals without inserting additional insights that the author gleaned from them, because many of the author's insertions were at best misleading and at worst patently false.
Just for an example, the author keeps insisting that payoff numbers in games are "money" as economists are interested in monetary matters. It might probably be true that von Neumann preferred interpreting payoffs of a game as money, but most practicing economists and game theorists certaintly do not do that.
An annoying repeated phrase is that "xxx told me (in an exclusive interview) that..." where xxx is one of the half dozen individuals mentioned above. Most of what xxx told the author must be correct, relevant and have some meaning but these are simply taken out of context by bits and spread throughout the text.
Also the basic hype about game theory's possibility to be a Theory of Everything seems to come out of (as the author admits) one person's recent writings at Bell Labs. The idea itself presented as such sounds simply outrageous (even to an academic economist like myself) but rather a surpring fact is that game theory's origins are in fact related to such an outrageous idea from physicists, mathematicians and "cyberneticians", one story of which is told in Mirowski, Machine Dreams. Mirowski's book has its own faults, and is a lot more heavy going (with some 500 + pages with small fonts and requiring a lot of knowledge), but at least it shows seriousness and a lot of research the author took to it.
on November 21, 2006
If you read or saw "A Beautiful Mind" and think there was drama in John Nash's creative madness, wait until you plunge into the work that drove him. Even without a background in (or any natural talent for) math, this story swept me up completely and, like previous reviewers, I had a hard time putting the book down. Siegfried expertly ushers the reader into the heart of a branch of mathematics that influences everything from pop culture to Nobel-winning science .. and does so in a way that leaves you feeling awed, inspired, and eager for more.
on December 12, 2006
The movie "A Beautiful Mind" was inspiring and touching. But, it really did not explain Nash's contributions to the world in the form of game theory. Now readers have a chance to understand the theory and practice behind this Nobel Prize winning discovery in Tom Siegfried's book, "A Beautiful Math."
This thorough, historical, mathematical, and metaphorical description of game theory really helps me to see the implications of Nash's discovery. This work influences psychology, evolutionary biology, sociology, anthropology, statistical physics, quantum physics and more. Its far-reaching implications are brought to life within an eloquent explanation that touches on all branches of science.
on July 2, 2007
The book jacket tells us that Seigfried won an award "for interpreting [science] for the public." I'm sure that that award was well deserved, for he has a knack for taking complex ideas and presenting them to a less-educated crowd. His two or three page explanations of concepts that took me weeks (and loads of homework/study) to grasp are nothing short of amazing. He often uses examples or analogies rooted in works of fiction to illustrate his points. The way these works are summarized to include only relevant information, and yet still capture the essence of those stories, is marvelous. Also, unlike many books of this genre, after reading it I did not feel like I needed to re-take any classes or brush up on my math. In fact, the most in-depth math involved (calculating a Nash equilibrium) should be crystal clear to a tenth-grader, and it is conveniently relocated to an appendix so that it doesn't bother any take-your-word-for-it readers.
Why only three stars then? Because this is a book review, and explanatory prowess isn't the only thing that it takes to write a book.
The humor in the book is very hit-and-miss. I wouldn't remove it, because when it hits... it's wonderful, but perhaps he should've gotten a humor-editor, someone to help him decide what to include and what to leave out. For example, Seigfried goes about explaining the mathematical differences between what he calls a "Robinson Crusoe economy" (one in which a single person makes decisions about fixed values) and a "Gilligan's island economy" (one in which each person makes decisions based upon other people, who make decisions based on other people, who...). Seigfried states that,
"Mathematically, that meant that no longer could you simply compute ... for Robinson Crusoe. Your calculations had to accommodate ... for Gilligan, the Skipper too, the millionaire, and his wife, the movie star, the Professor, and Mary Ann."
How cool! But then there are other instances. While using a game between fictional characters Alice and Bob to demonstrate some simple game theory, he inserts parenthetically: "(As I said, Alice would probably tell him to shove it)," directly between two rules of the game. We had already been told that this game was not in Alice's favor, and that it was simplified for the purpose of example. The text is peppered about equally with good, relevant, non-interrupting humor, as it is with not-so-good humor.
Furthermore, while he can explain very-high-level science to a high-school-graduate (and two thumbs up for that) his narration seems to be directed at an audience with a damaged memory. I say this because we are told at least four times that Colin Camerer is into Behavioral Game Theory, and that Neuroeconomics is a fledgling hybrid field.
The organization of the book favors the understanding of game theory over the understanding of its history. One is presented with concepts fundamental to game theory, some uses of it, some game theory developments, some views into advanced game theory; it works very well to foster understanding. With each chunk of theory work, Seigfried includes the history (which I was pleasantly surprised at--it's fascinating) that contributed to that chunk of theory. The problem here is that the first section takes place mostly in the eighteenth century, the second-to-last section in the twenty-first, and the last section in the seventeenth and also the twentieth. The jumping around in time was confusing. I can't say what the best organisational method is, but I don't think this is it.
Lastly, and most importantly, is the hype that he gives game theory. I am interested in it, that's why I picked up the book, and the occasional renewal of that interest was nice, but he takes it a step too far. The reader is told time and time again how freakin' amazing game theory is, it's all true. The problem is that after pages of this game theory hype, and a mid-book discrediting of some evolutionary psychologists who dared disagree, I begin to question how strongly his bias is affecting his writing. It doesn't come across too strongly until the final few pages (which, in my mind, bumped it down from a four-star) in which he compares game theory to a unified field theory, or physics' golden "theory of everything." He says game theory is the theory concerned with everything else (i.e. the social/biological/economic half of everything). I agree that it could be a framework to hold "everything else" together, but that's like saying that all baked goods can be divided between pie, and things-with-frosting. It doesn't include the whole picture, and it does so in a deceptive way.
I should, however, admit that I am subject to the same type of biases as the author. When I read, in that last few pages, that:
"Game theory is not, however, the same as the popular 'Theory of Everything' that theoretical physicists have long sought. That quest is mearly for the equations describing all of nature's basic particles and forces, the math describing the building blocks."
I became quite upset: MEARLY?! that theory is only one of the most important goals of science, ever! Well, you can see that my bias clouds my judgement too, interperet as you will...
So buy this book, I can't stress enough how great the explanations within are, but take it with a grain of salt (and perhaps some of your own research).