It was quite interesting to read how he grew up in an environment of anti-Semitism in Hungary yet his parents seemed to promote a funny type of mish-mash of beliefs such as having Christmas presents! In fact, many aspects of von Neumann's personal and spiritual side, including his early conversion to Catholocism and later call for a priest as he lay dying are unfortunately only hinted at.

I point this out because the other aspects of von Neumann's character, his prodigious mathematical talent and his fervent belief that the US strike first with atomic bombs against the then-developing USSR, are quite evident here. What comes across is a general sense that von Neumann was very arrogant about his knowledge and ability to solve everything within the theoretical world. It appears that von Neumann truly believed he was the most intelligent mathematician at that time and one gets the feeling that anyone who might have come close (John Nash comes to mind) was downplayed as working on something 'trivial'.

Luckily, we also get a glimpse into von Neumann's marriage where his mathematical abilities certainly didn't help him to acheive much happiness. Judging by the many references to his constant fights and stream of rather childish letters his emotional development lagged far behind his other abilities. This is also seen in his one-upmanship demonstrated during the many parties he and his wife threw for colleagues during his years at Princeton.

But it is the interplay of his arrogance with the development of the atomic bomb that is the most interesting. It is scary to see how close the world came to all-out war due to the constant preaching by von Neumann (and some of the others in RAND) that game theory absolutely demonstrated that the US must strike first or there could be no resolution to the developing political conflict. I suspect von Neumann's seemingly purposive (probably due to his ego) ignorance of Turing played a deeper role here since one wonders why he didn't develop the theories, later put forward by Chaitin and Kolmogorov, about the limitations of knowledge.

That is, it is surprising how arrogant he was based on the fact that Godel was there at the same time! Oh well, it is lucky for us that we can look back and read about the history with the knowledge that people didn't take von Neumann as seriously as Dr. Strangelove - since it certainly appears that von Neumann could have been used as the basis for that character.

Anyway, this is certainly worth reading for a fascinating glimpse into the times. One just hopes that the arrogance and ego will one day fade so that we can move the hands of the 'doomsday' clock back.

As fascinating as all this was (and he tells the story well), I was most interested in the final third of the book which discusses games other than the prisoner's dilemma: chicken, the volunteer's dilemma, deadlock, stag hunt, the largest-number game, and especially the dollar auction. The games are described not just in terms of numerical payouts, but in situations that can be imagined in real life. And Poundstone also mentions game theory in relation to evolution, and tit for tat strategies in iterated prisoner's dilemmas.

This is a book for the general reader. You need not be a mathematician to understand the contents. Indeed, it is a pretty simple book, and you will only learn basic aspects of game theory if you haven't encountered it before. What you can expect is a story about von Neumann and the cold war and the interesting paradoxes that such situations create.

You see, it's one big story that consists of several sub-stories. In part it's a biography (intellectual and otherwise) of John von Neumann, one of the greatest mathematicians of the twentieth century. It's also a popular exposition of game theory and some of the decision-theoretic puzzles that arise in it (most obviously the one of the book's title). And it's _also_ a history of the Cold War, at least on its strategic side.

You pretty much have to be William Poundstone to weave all this together into a coherent and readable narrative. Fortunately, William Poundstone _is_ William Poundstone, and he pulls it off with panache.

There's something here for everybody. My favorite parts are the chapters on the various game-theoretic dilemmas (including a _very_ nice exposition of Robert Axelrod's _The Evolution of Cooperation_ that correctly captures what Axelrod did and did not show in his famous computer tournaments). But the biography of von Neumann is fascinating too; great mathematicians tend to be odd and interesting characters, and von Neumann was one of the greatest. And all the Cold War-era history is riveting in its own right, even apart from its relationship to von Neumann (who may have been at least one of the real-life models for Dr. Strangelove).

Poundstone is a fine writer with a real gift for this sort of thing. If even one of the strands in this tale sounds engaging to you, you can rest assured that Poundstone will manage to keep you engaged in the other two as well.

Look for his other books too. I especially recommend _Labyrinths of Reason_.

The ideas contained in these lectures will come as no great surprise to most scientists today; indeed, I would expect most to simply nod in agreement at most of von Neumann's observations. For example, von Neumann notes that neurons are essentially digital in that they have an all-or-nothing activation energy. However, it is interesting to see how seriously he pursues the idea that the brain may rely upon a mixture of analog and digital encodings; he took absolutely nothing for granted, and may well have been vastly ahead of his time.

Although von Neumann's many references to vacuum tubes and differential analyzers may seem archaic today, his central points remain essentially intact. I'm certain that von Neumann would have felt somewhat vindicated by the explosive advances in semiconductor devices (in both digital and analog incarnations), as well as in machine learning and neurobiology. One can perhaps view von Neumann's lectures as the first glimmerings of what would eventually become fruitful exchanges between computer science and various biological disciplines.

If you are looking for a discussion that will give you some insight into artificial intelligence, neural networks, or brain physiology, then I'm afraid you will likely be disappointed with this book. While many of von Neumann's observations may have been controversial at the time, they have for the most part moved quietly into the collective consciousness of scientists. However, if you have interest in either the historical development of these ideas, or in seeing how one of the preeminent minds of the 20'th century approached this vexing new problem, then it will be worth your time.

What I most enjoyed about this book is von Neumann's methodical and exceedingly cautious approach, coupled with his occasional willingness to speculate. As the vast majority of von Neumann's writings are accessible only to a very small audience, such as his enormously influential treatises on quantum mechanics, geometry, and game theory, and his pioneering work in areas such as functional analysis and operator theory, this little book is perhaps unique in that it lets you in on the ground floor.

The "prima facie" modifier is commonly taken to mean von Neumann saw the brain as "obviously digital," or "patently digital," and that it therefore must resemble a digital computer. But as you read the rest of the book, you quickly discover that this is not what John von Neumann intended. Von Neumann uses words cautiously and precisely, and to him, "Prima facie" means exactly what it says: "on its face."

In 1956, the brain appeared digital. But von Neumann thought this impression might be superficial. He thought that deeper biological investigation might well demonstrate that the nervous system is not, in fact, digital, or not completely digital. He believed it might work in some more sophisticated way, and suggests that perhaps some intermediate signaling mechanism, a hybrid between analog and digital, might be at work in the brain. For this and other reasons he actively resisted labeling the brain as a digital computer.

In the mid 90s, evidence began to appear that von Neumann was probably right to reserve his judgment. These curious new results show that a single nerve impulse is somehow able to convey information to the brain. This signal seems distinctly un-digital. A number of theories have popped up, some attempting to explain this whopping new mystery, others attempting to explain it away. But its impact on neurophysiology, and on conventional computer models of the brain, is pretty shocking. Not to say, devastating. (See Spikes, by Rieke et al, for a readable account of this story.) When the smoke clears, it would not be surprising if people go all the way back to John von Neumann, looking for traction, fresh starting points, and for von Neumann's wonderfully broad sense of what is possible in neurobiology - a sense we have evidently lost to progress in the years since he wrote this splendid essay.

Von Neumann did not include in this book his interesting views on the nervous system of the eye. He was an early adopter of visual memory systems in digital computers, and he was evidently intrigued by the way the retinal cells of the eye are arranged to look backward, that is, toward the screen of the back wall of the eye. Possibly he thought the retinal cells saw back there a thin film diffraction pattern. You can find his interest in the nervous system of the eye remarked in his brother Nicholas Vonneumann's book, John von Neumann as seen by his Brother, and this reminiscence is also paraphrased in Poundstone's Prisoner's Dilemma. Finally, some of the worldly story of von Neumann, his digital computers, and their role in the creation of the hydrogen bomb can be found in MaCrae's biography.

The "prima facie" modifier is commonly taken to mean von Neumann saw the brain as "obviously digital," or "patently digital," and that it therefore must resemble a digital computer. But as you read the rest of the book, you quickly discover that this is not what John von Neumann intended. Von Neumann uses words cautiously and precisely, and to him, "Prima facie" means exactly what it says: "on its face."

In 1956, the brain appeared digital. But von Neumann thought this impression might be superficial. He thought that deeper biological investigation might well demonstrate that the nervous system is not, in fact, digital, or not completely digital. He believed it might work in some more sophisticated way, and suggests that perhaps some intermediate signaling mechanism, a hybrid between analog and digital, might be at work in the brain. For this and other reasons he actively resisted labeling the brain as a digital computer.

In the mid 90s, evidence began to appear that von Neumann was probably right to reserve his judgment. These curious new results show that a single nerve impulse is somehow able to convey information to the brain. This is distinctly un-digital. A number of theories have popped up, some attempting to explain this whopping new mystery, others attempting to explain it away. But its impact on neurophysiology, and on conventional computer models of the brain, is pretty shocking. Not to say, devastating. (See Spikes, by Rieke et al, for a readable account of this story.) When the smoke clears, it would not be surprising if people go all the way back to John von Neumann, looking for traction, fresh starting points, and for von Neumann's wonderfully broad sense of what is possible in neurobiology - a sense of possibilities we have evidently lost in the years since he wrote this splendid essay. He is eloquent on the problem of selecting a memory "organ," and evidently thought the worst choice would be a neuron.

Von Neumann did not include in this book his interesting views on the nervous system of the eye. He was an early adopter of visual memory systems in digital computers, and he was evidently intrigued by the way the retinal cells of the eye are arranged to look backward, that is, toward the screen of the back wall of the eye. Possibly he thought the retinal cells saw back there a thin film diffraction pattern. You can find his interest in the nervous system of the eye remarked in his brother Nicholas Vonneumann's book, John von Neumann as seen by his Brother, and this reminiscence is also paraphrased in Poundstone's Prisoner's Dilemma. Finally, some of the worldly story of von Neumann, his digital computers, and their role in the creation of the hydrogen bomb can be found in MaCrae's biography.

The weaknesses:
(1) the font is a pain to read; it looks like it came off an old typewriter. I wonder why the publishers couldn't put it into a more modern readable form.
(2) Von Neumann writes this book , in part, with the intention to dispel the mathematical nonsense, as he perceives it, of the Dirac delta function. Therefore he casts everything into the unwieldy formalism required to do without the distribution. Indoubtedly he was trying to change the dirac formalism in use in quantum mechanics at the time but was fortunately unsucessful in persuading physicists to use his alternative language.

Summary: I recommend this book for anyone wishing to deepen his or her understanding of the foundations, conceptual and mathematical of quantum theory.

That said, this is not the best written Game Theory text out there. Like all seminal works, it suffers from the basic fact that we've learned a lot of new things since the time it was written. Many people have gone on to build and expand on the insights contained in this book, especially in the area of bargaining and cooperative game theory.

This is a very impressive book to keep on your shelf, and the discussion of poker and the role of bluffing is very interesting, but, owing largely to the 60+ years that have passed since its initial publication, it's not the best reference work or study material available.

Another word of warning: The review below is correct that the level of math that you must understand to fully appreciate this book is quite substantial. This book is more for the mathematically sophisticated who want to develop an appreciation for the origins of game theory.

I'm not even sure I'm qualified to pass judgement on this book, but what I understand, I give 5 stars without hesitation. The authors discuss almost every class of game (2-person, 3-person, zero-sum, non-zero-sum, etc.) and even a very simplified version of poker.

You basically have to be a mathematician to get full value from this book. This book is absolutely full of equations and complex proofs. For a beginner with little math, I'd recommend Game Theory by Morton Davis, or for someone with some university math I'd recommend Games and Decisions by Luce and Raiffa. However, if your math is good, you might as well go straight to this book, which started the whole field of game theory.

Von Neumann was a trained chemical engineer. Although chemistry is usually remarked as the slightest of his credentials, he knew it and used it. This book includes the story of how he applied mathematics and chemistry to the development, delivery and control of explosive weapons - first chemical, and then nuclear.

Von Neumann's work on explosives is a common thread that runs through his work and pulls together many of his interests that - seen in isolation - seem amazingly disparate. His interests in computers, aerodynamics, parlour game theory and even meteorology were all rooted in or entrained by his fascination with explosive weapons. (For a thermonuclear weapon, for example, the weather is a delivery system for fallout.)

In 1938, von Neumann first became a consultant to the United States military, working at the Aberdeen proving grounds in Maryland. He began by improving the aim of very large guns with explosive shells. It was a surprisingly complicated business because it involved winds aloft, turbulent flow, impacts, and expanding shock fronts of explosive charges. It was on one of his frequent trips to Aberdeen that he encountered one of the University of Pennsylvania engineers working on ENIAC. Von Neumann was unsatisfied with the analog computers then used for weapons work, and plunged into the problem of improving the nascent digital machine. Ultimately he created a digital computer at the Institute for Advanced Studies in Princeton. His purpose in building this particular machine was to use it to complete the design of the hydrogen bomb.

After the war began, von Neumann was sent to England to study the damage inflicted by German bombs during the blitz. He noticed the German bombs were not completely effective because they buried themselves before exploding. Von Neumann used this insight to invent the "air burst" explosive. Thereafter, allied bombs worldwide were fused to go off before they hit the ground. The technique vastly improved their destructive power. Hiroshima was an air burst. At Nagasaki, the bomb was an implosion weapon characterized at Los Alamos as "von Neumann's bomb" because of the implosive detonator he helped develop for it.

MacRae evidently admires von Neumann's accomplishments as a weaponeer, and as a political advocate of weapons development, but he does not quite convey von Neumann's personal sophistication and sense of scientific inquiry.

For example, in developing the digital computer von Neumann talked to a number of neurobiologists. For the most part he believed what they told him and adapted whatever he found useful. His Silliman lectures, reprinted as his book on The Computer and The Brain, includes his credulous precis on the neurobiology of the early 1950s. But von Neumann also noticed and questioned something few neurophysiologists bother themselves about - then or now - which is the fact that the retinal cells of the eye look backward. They are pointed toward the back wall of the eye, and not out at the world. Perhaps these cells see there a thin film diffraction pattern, and not the literal visual picture our brain shows us as an image of the world. Also, in a book by the editor of The Economist, one might expect a bit more on von Neumanns contributions to economics.

Withal, it is difficult to understand why such a civilized, curious, well spoken, socially adroit and erudite man was so intrigued by explosives. To try to make sense of von Neumann you can also read several other books - there exists no single coherent biography. Find "von Neumann and Weiner," two half-biographies in one volume by Heims; The superb Prisoner's Dilemma, by Poundstone; and for historical context, the Rhodes books on the making of the Atomic and Hydrogen Bombs.

After von Neumann's death, his concepts of strategic games were highly elaborated at the RAND corporation, and ultimately became U.S. nuclear policy. MacRae touches on this legacy, but the best book on this great chunk of obscured American history is The Wizards of Armageddon, by Kaplan. It would be interesting to know if von Neumann's theory of parlour games was also used to formulate strategic policy for the Viet Nam disaster. It would not be surprising.

It's true my father never studied for a phd in economics; if you'd just served in world war 2, got a first in economics in Cambridge and been offered a job at The Economist, you'd probably not have seen any practical point in that either. ( If you want to go into who knows what about 21st C futures, internetworking,intangible assets and new economics, I'm sure we can link you to that at http://www.normanmacrae.com )

It may be that some of my father's admiration for Von Neumann also got blended with his world views. But Von Neumann's family -whom my father worked closely with - didn't want any of that blend diluted.

My father was aiming primarily to explain to everyone why Von Neumann was one of the 2 great mathematicians of the 20th century and what background great mathematicians grow up in. In trying to make that accessible to everyone, he clearly doesn't go into the depth of mathematics theory that might stimulate today's hundred greatest living mathematicians. Everyone else will probably find the mathematical content suitable for a biography which they want to learn from.

Moreover, Von Neumann was the first mathematician to insist that the subject's future lay mainly in teamwork facilitated by computing rather than individual mathematical power. Not every academic has understood that point the way Johy would have hoped.

chris macrae, wcbn007@easynet.co.uk Marketing Electronic Learning NETwork http://www.egroups.com/group/melnet2