Neumann, John Von

Theory of Games and Economic Behavior (Commemorative Edition) (Princeton Classic Editions)

Average customer rating:

An Obvious Classic But . . .
Landmark work but heavy going

Theory of Games and Economic Behavior (Commemorative Edition) (Princeton Classic Editions)
John von Neumann , and Oskar Morgenstern
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0691130612

Book Description

This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.

Customer Reviews:

An Obvious Classic But . . ........2002-10-23

Let me start out by acknowledging that this is THE BOOK that started Game Theory as it exists today. While Bayesian statistics are an obvious precursor, everyone agrees that von Neumann's and Morgenstern's work was ground breaking.

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.

Landmark work but heavy going.......2000-08-23

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.

Customer Reviews:

Well written for the everyday reader.......2007-04-24

As someone familiar with the concept of game theory especially the prisoner's dilemma, I found this book to be particularly informative, on a layman's level. The history/biography of Von Neumann was interesting, and the applications of theory were appropriate. If you are looking for a purely scientific read, this is not for you, but if you are looking to be able to talk about a prisoner's dilemma and have some more cultural literacy, this is a good read.

Definitely worth getting.......2007-03-27

I liked all three of this authority's books. Definitely worth getting, and be prepared for some eye-openers and challenges.

A game we all play..........2006-10-24

So often, truly illuminating discussion of a thing involves an examination of its polarities.

And so, our understanding of physics is enlightened by the interplay between quantum physics and Einsteinian physics, our knowledge of reproduction is enhanced by an exploration of the similarities and differences in the masculine and feminine, our awareness of attraction is enhanced by comprehending the contrast between love and hate and then again indifference.

In this way, in this well written book, Poundstone explores the theoretical side of religion's "golden rule."

As stated by Christ, Hillel, Mohammed, Confucius, Buddha and the holy tractates of Hinduism, Taoism and Shintu, the "golden rule" asks that we not treat others as we ourselves would not wish to be treated. In this way, the "wheel" invented so many times in religious prehistory was again invented by mathematical theoreticians in their off time from inventing hydrogren and nuclear bombs around World War II.

However, in the mathematicians version, the golden rule is reduced to its polarities: the tension between those who co-operate and thereby advance the collective good and those who defect and thereby service their selfish interests. To be sure, people dying for their country, honestly paying all their taxes due and the like all advance societal interests, but how in the end is it that these people are not taken advantage of by those who stay home, retain their taxes for their own private good and the like?

It turns out, according to game theorists that collective good becomes so potent because in the end it is personal good. While one certainly sacrifices in the short run one receives greater benefit by being part of an effective social organization.

And in this way, ultimately the story of game theory takes us on that most fascinating of journeys, to the heart of the golden rule and in that way, to the heart of man's search for meaning itself.

Good, very good.......2006-09-13

An excellent primer on game theory as it explains from scratch theory and vocabulary about it. Usually books give it as granted that everybody gets the basics as if everybody had formal training on game theory, which may not necessarily be the case.
One half of the book is the history of VonNeumann as prime developer of the theory, very well written and enlightening.

great intro to game theory and the life of von Neumann.......2006-09-06

Poundstone does a decent job and I would recomend this book to anyone interested in the history of the subject. I find the life of John von Neumann along with ancedotes about his hyperthymestic memory and practical jokes facinating. He was one of the greatest minds of the twentieth century. My only complaint of Pounderstone's book is that there is prehaps too much history. When dealing with the cold war, we end up with a prisoner's dilemma: both the United States and the Soviet Union have an interest in defecting (obtaining nuclear weapons) no matter what the other country does. If the US obtains weapons and the Soviets do not, then the US gains an advantage. If the US obtains weapons and the Soviets have weapons, then the US is saved from becoming the sucker. But if both the US and the Soviet Union work to make weapons, then both are worse off than had both cooperated. OK, this is all nice and well, I get the point. But do we really need to spend three chapters reading about this? It becomes agonizing to read through if you do not find this stuff interesting. The rest of the book is great. Read about the important characters from Merrill Flood, Melvin Dresher, and Albert Tucker to Robert Axelrod. We also get discussion on other types of social dilemmas such as chicken and stag hunt.

John von Neumann and the Origins of Modern Computing (History of Computing)

Average customer rating:

A superb book on John von Neumann's many contributions to computer science
superb, scholarly book
An Overview of Von Neumann's Contributions to Computing

John von Neumann and the Origins of Modern Computing (History of Computing)
William Aspray
Manufacturer: The MIT Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0262011212

Amazon.com

In the mid 1940s, John von Neumann revolutionized the nascent field of computing by showing that program instructions could be stored in a computer's memory instead of on external panels or punch cards. In John von Neumann and the Origins of Modern Computing, William Aspray details the design and construction of von Neumann's computer systems and explains the broader implications of von Neumann's contributions. Aspray discusses von Neumann's fame in the realms of mathematics, physics, and economics and his remarkable career, which included work as an atomic energy commissioner and as principal scientific adviser to the U.S. Air Force on ballistic missile development. By examining the interplay of science, military, and business, which formed the background for von Neumann's work, Aspray does an excellent job of placing von Neumann's accomplishments in computer science into the context of his other achievements.

Book Description

John von Neumann (1903-1957) was unquestionably one of the most brilliant scientists of the twentieth century. He made major contributions to quantum mechanics and mathematical physics and in 1943 began a new and all-too-short career in computer science. William Aspray provides the first broad and detailed account of von Neumann's many different contributions to computing. These, Aspray reveals, extended far beyond his well-known work in the design and construction of computer systems to include important scientific applications, the revival of numerical analysis, and the creation of a theory of computing.

Aspray points out that from the beginning von Neumann took a wider and more theoretical view than other computer pioneers. In the now famous EDVAC report of 1945, von Neumann clearly stated the idea of a stored program that resides in the computer's memory along with the data it was to operate on. This stored program computer was described in terms of idealized neurons, highlighting the analogy between the digital computer and the human brain. Aspray describes von Neumann's development during the next decade, and almost entirely alone, of a theory of complicated information processing systems, or automata, and the introduction of themes such as learning, reliability of systems with unreliable components, self-replication, and the importance of memory and storage capacity in biological nervous systems; many of these themes remain at the heart of current investigations in parallel or neurocomputing.

Aspray allows the record to speak for itself. He unravels an intricate sequence of stories generated by von Neumann's work and brings into focus the interplay of personalities centered about von Neumann. He documents the complex interactions of science, the military, and business and shows how progress in applied mathematics was intertwined with that in computers.

William Aspray is Director of the Center for the History of Electrical Engineering at The Institute of Electrical and Electronics Engineers.

Customer Reviews:

A superb book on John von Neumann's many contributions to computer science.......2006-06-12

John von Neumann was one of the greatest prodigies of the last century. His right-wing politics and the fact that he made seminal contributions to many fields of science account for his not having won a Nobel prize. Nevertheless many Nobel laureates considered his intellect far superior to theirs.

v.N's many talents account for nobody having yet written a biography that does him justice, as it's very unlikely that anyone with the mind to understand his seminal contributions to many branches of science would have the spare time to write such a book.

Aspray has done an superb job of describing von Neumann's contributions to computer science. By referencing many details in the exhaustive references he enables his readers to quickly find von Neumann's original work if they want to get to the nitty gritty of his contributions and spares the average reader details that would have made the book tedious and unreadable.

I strongly suspect that this will remain the reference book on J. v. N's contributions to computer science; his daughter was quite pleased with it.

superb, scholarly book.......1999-06-17

Unsurpassed quality is the hallmark of this fine book

An Overview of Von Neumann's Contributions to Computing.......1998-10-28

No one has yet written a biography of John von Neumann that sums up both his intellectual achievements and his curious personality. William Aspray's book, John von Neumann and the Origins of Modern Computing, at least makes a good effort at explaining von Neumann's intellectual accomplishments, although it is not a complete biography in explaining the man. Granted, such a biography might be impossible, given the breadth and profundity of von Neumann's contributions to thought. It is hard to conceive of another person who left more of a mark on the twentieth century world of science, with the exception of Einstein himself. For a look at von Neumann the personality, one can find good character sketches of him in Ed Regis's "Who Got Einstein's Office?" and in Joel Shurkin's "Engines of the Mind", but neither of these works presents a complete view of von Neumann's intellectual achivements. Aspray's book does a thorough job of covering von Neumann's thoughts on computing.. It is thorough in dealing with von Neumann's contributions to mathematics, to the building of the IAS computer, to problems in information theory, and outlines more of von Neumann's thought on the analogy between computer processing and the human mind than most writers ever notice. Additionally, von Neumann made contributions to meteorology that are usually overlooked, which Aspray outlines more thoroughly than other writers. The book does not address much about Game Theory (William Poundstone's book, Prisoner's Dilemma, outlines von Neumann's contributions in that field of study), which is another huge area of study that von Neumann pioneered. Aspray's book is required reading for anyone wrestling with John von Neumann's ideas, he outlines perhaps 60% of von Neumann's career better than any other writer, but one wonders when the truly comprehensive biography of von Neumann will be written.

Average customer rating:

Good balance on technology, sci-fi and military material.
Slow start on a good read
Not Good
flat characters and swis cheese like plot
Why no EMP attempts?

Von Neumann's War (Von Neuman)
John Ringo , and Travis Taylor
Manufacturer: Baen
ProductGroup: Book
Binding: Hardcover

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ASIN: 1416520759

Book Description

New series. Mars is changing. Seemingly overnight the once "Red" planet is turning to gray. Something is happening, something unnatural. A team of, literally, rocket scientists figure out a way to send a probe, very fast, to Mars to determine how and why it is changing. However, when the probe is destroyed well short of the formerly red planet, it's apparent that Mars is being used as a staging ground. The only viable target for that staging ground is Earth. Ranging from rocket design to brilliant paranoids to "in your face" fighting in Iraq, Von Neumann Wars is a fast paced look at what would happen if the earth was attacked by a robot race that, quite accidentally, was bent on destroying civilization.

Customer Reviews:

Good balance on technology, sci-fi and military material........2007-03-15

Book starts slowly to build background for story (which I believe will be followed by additional books to complete it) for half of the book, and passes to fast paced action which is actually very fun to read, although some might find too thick to swallow.
When moving to the book end it climaxes before ending leaving you wanting to know of how the things will eventually end. Hopefully there will more coming soon.

Slow start on a good read.......2007-02-18

Ok, I like this book. It was a bit slow to start. Think of starting fire with two sticks and it took 120 pages to get fire. Once you sit through the set-up, it's a compelling read that cannot be put down. At a guess, I'd sat John Ringo has been hanging out with a scientist because there is a lot more science in this fiction than is usually the case with his works. I suppose that's the Taylor influence? Anyway, great read and kind of a unique variation on the replicating machine plot. Worth reading. Wait for the soft cover though.

Not Good.......2007-01-04

I've read and enjoyed several books by John Ringo over the years but Von Neumann's War is one that I will discard from my bookshelf immediately.

This book was nearly unreadable to me because of the mishmash of styles between Ringo's hard-boiled MIL-SF and co-author Travis M. Taylor's highly technical and verbose style. What resulted was a story that felt very stiff and academic even as it was trying to be a fast-paced thriller.

Overall, this book focuses far too much on the science and not enough on the fiction as it goes on and on about technical minutia but leaves the reader wanting more in terms of character and plot.

I've found that Ringo is at his best when writing alone or collaborating with David Weber. However, his mixed collaborations with other writers such as Travis M. Taylor, in this case, or Julie Cocherane in the case of Cally's War have turned out some of his worst material.

flat characters and swis cheese like plot.......2006-12-04

The book seems to be an attempt to a high paced plot but where Bolo series succeeded this one failed. The characters are flat, the plot is not very well thought through and the ending ... well it seem to come to abrupt, so abrupt that I was looking for possible missing pages. Overall the ending is very much like any idea in the book, - incomplete

Why no EMP attempts?.......2006-11-11

I thought the book as a fairly quick read as SciFi military thrillers go. The authors try to go into a good bit of detail about the science of what is happening. But the do leave out some of the more logical ways to try to defeat the enemy. For one I was shocked that they never tried to create a large EMP via a high atmo nuke or similar. Considering that the invaders are robotic in nature you would think that would have been one of the first things they tried.

Also no attempts at all are made to communicate with the invaders. Not that it would have mattered much, but at least they should have made some attempts to establish first contact.

As far as Von Neumann machine tales go I much perferred the story told in "Spin".

Mathematical Foundations of Quantum Mechanics

Average customer rating:

.. and try to read everything else JvN wrote, too!
Hilbert Space Formulation of QM
Has Strengths and Weaknesses
a classic
Very nice historical approach

Mathematical Foundations of Quantum Mechanics
John von Neumann
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0691028931

Book Description

Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.

Customer Reviews:

.. and try to read everything else JvN wrote, too!.......2005-11-19

von Neumann's account of why he uses the mathematics he does and his critique of the Dirac formalism is worth the price of admission. Those who deride him for avoiding the delta formalism seem to have been seduced by its meretricious computational facility. von Neumann anticipated - actually began in this book and his work on continuous geometry - the modern approach via non-commutative geometry to physics (see Alain Connes), and M-theory.

Hilbert Space Formulation of QM.......2003-04-10

The ultimate source of Hilbert Space applied to Quantum Mechanics. John von Neumann was the first to systematically formulate QM in such a powerful and elegant vector space. If this is the Bible of QM in HS, Hughes is the missioner! Get the book as well -- The Structure and Interpretation of Quantum Mechanics.

Has Strengths and Weaknesses.......2002-07-30

First the strengths:
(1) The author gives a rigorous proof of the incompatibility of the two theories of quantum mechanics, that is, the evolution of the state vector as determined by Schrodinger's equation and the collapse of the state vector by means of an observation. He does this by the concept of entropy.
(2) He gives a thorough treatment of the "consciousness school" of interpretation, which makes for an interesting,if not entirely convincing read.

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.

a classic.......2000-08-23

As an undergrad, I am sorry that I cannot share the perspectives of professionals as expressed below. After initial introductory courses, I got fascinated by certain untold conceptual issues. And one of the textbooks (probably Griffiths) suggested von Neumann had tried to prove mathematically that the classical formulation is just the furthest the formalism can go and we don't have to worry about underlying complexities. Later, Bohm created a formalism which von Neumann "proves" to be mathematically impossible in this book. I bought this book just to find out how the proof goes. But I got stuck with some tedious proofs on Hilbert space (which he calls a "digression"). This part isn't essential but as the braket notation is not used you need to consult this part. I think at least a strong background in linear algebra is required. Definitly not an introductory textbook. Most useful for those who study history of physics.

Very nice historical approach.......2000-02-01

This is not the kind of book I would recommend to a novice person in the area, but it does give a very interesting view of how was quantum mechanics born. It begins with a thorough discussion about the mathematics of Hilbert spaces and operator theory to later merge Heisenberg's and Schrodinger's theories in one rigorous mathematical theory. It makes some remarks that allows the reader to see how was the 'new' quantum theory born and developed, since it briefly discusses the theories of Heisenberg and Schrodinger in the way they originally stated them. Maybe the most disturbing issue would be the notation since in 1932 dirac had still not developed the bracket formalism.

Average customer rating:

Continuous Geometry
John von Neumann
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Paperback

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Harmonic Analysis

ASIN: 0691058938

Book Description

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry.

This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.

The Computer and the Brain: Second Edition (Mrs. Hepsa Ely Silliman Memorial Lectures)
Average customer rating:

Interesting but no goosebumps

Dated, but always worth reading von Neumann

The un-digital brain.

Clear, maybe even clairvoyant view of the brain.

A great book for exploring the human brain as computer model

The Computer and the Brain: Second Edition (Mrs. Hepsa Ely Silliman Memorial Lectures)
John von Neumann
Manufacturer: Yale University Press
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Binding: Paperback

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John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More

ASIN: 0300084730

Amazon.com

Whether they think that artificial intelligence is impossible or inevitable, most people have highly polarized views on it. John von Neumann, genius, mathematician, and inventor of the nearly ubiquitous computer architecture that bears his name, blazed trails for both camps in The Computer and the Brain. This short book, which was written originally for Yale's Silliman lectures, but published posthumously, summarizes his views on machine and biological intelligence with unprecedented clarity and precision. His understanding of neuroscience was that of a brilliant and strongly motivated amateur at the end of the 1950s--good enough to take on the problem, but by no means matching his comprehension of the machines to which he had devoted much of his professional life. Still, his take on intracranial computation is stunningly prescient--he looks beyond the then-fashionable digital metaphors to suggest a semi-analog strategy that uses parallel processing to make up for its deficiency in speed. Prominent neuroscientific thinkers Paul M. Churchland and Patricia S. Churchland provide a brief, enlightening foreword to this second edition, placing the author's thinking in context and grounding the reader in the scientific milieu that gave rise to The Computer and the Brain. Although his computer architecture slowly is growing obsolete, von Neumann has given us a more lasting legacy in his thinking about thinking. --Rob Lightner

Book Description

With a foreword by Paul M. Churchland and Patricia S. ChurchlandThis book represents the views of one of the greatest mathematicians of the twentieth century on the analogies between computing machines and the living human brain. John von Neumann concludes that the brain operates in part digitally, in part analogically, but uses a peculiar statistical language unlike that employed in the operation of man-made computers. This edition includes a new foreword by two eminent figures in the fields of philosophy, neuroscience, and consciousness.

Customer Reviews:

Interesting but no goosebumps.......2005-01-27

After the quick read that it was this morning I am left uncertain as to exactly how I feel about this book. On the positive side even though one does get the feeling that The Computer and the Brain is slightly dated (1958) it has held up remarkably well despite the extreme rate of technological development. On the negative side though it is a bad sign when the most enjoyable part of a book is the foreword.

The cover of the book basically tells the whole story, apples and oranges- for while as von Neumann recognizes that "the most immediate observation regarding the nervous system is that its functioning is prima facie digital" the connection between them is not as strong as a first glance might suggest.

There doesn't seem to be too much that a study of one can teach us about the other but maybe finding out that lack of an underling connection is just as useful as finding such a connection. While this book is a fairly good recitation of the facts (at least as they were known in 1958) I can't say there is really much here to recommend it to the casual reader- think that only as a reference work can this book gain high praise.

Dated, but always worth reading von Neumann.......2003-07-09

Von Neumann was one of the most celebrated and prolific mathematicians of the 20'th century; his contributions were legion, and always bore unmistakable creativity and elegance. "The Computer and the Brain" is a record of a lecture series that von Neumann delivered at Yale University in 1957. In these lectures, von Neumann set out to explore connections between computing hardware and their biological counterparts; brains. Von Neumann compared neurons with physical computing elements in terms of size, speed, heat dissipation, capacity, etc., in an attempt to discover what, if anything, could be said to unite them or to set them apart. He drew from what had been learned in designing computer instructions and memories in an attempt to glean some insight into what the brain might be doing. Ever the consummate mathematician, von Neumann was guarded in his statements, never over-reaching or confusing speculation with fact.

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 un-digital brain........2000-09-13

Perhaps the most famous and often quoted line in this remarkable book appears on page 39, where von Neumann declares that "The most immediate observation regarding the nervous system is that its functioning is prima facie digital."

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.

Clear, maybe even clairvoyant view of the brain........2000-09-13

Perhaps the most famous and often quoted line in this remarkable book appears at the beginning of Part II, where von Neumann declares that "The most immediate observation regarding the nervous system is that its functioning is prima facie digital."

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.

A great book for exploring the human brain as computer model.......1999-03-30

A book for a limited audience. You have got to be interested in some really seminal, currently unresolved issues of how the great invention of the ALU (arithmetic logic unit) still employed in every computer built to the present day, was a compromise effort by this genius. His thought was to model the human brain, and the ALU succeeded in modeling just a small part, but he was totally frustrated and unsatisfied by the result--for good reason. He points out that the very language of the human brain has not yet been discovered--the orders of magnitude by which its process and results exceed the merely digital high speed comparator we call a computer (my apologies to Bill Gates!) clearly demonstrate the existence of a logic and a mathematics, the simplest rules of which as yet defy all our efforts to understand its workings, while we experience its results every time we think. Depth of logical levels, and depth of arithmetic levels necessary to achieve the requisite results we obtain from our Crays and our PCs are scorned by the human brain in a radical simplicity as yet undiscovered (not in that it does it, but in how it does it: therefore he postulates the existence of a radically, essentially different math and logic inherent in its workings). He lays out the discoveries of Turing, McCullough and Weiner in a brilliant tour de force of known (1955)neurological and cybernetic discoveries, and how they charted his course in creating the ALU. He compares analog and digital and mixed models of computing but (in my opinion) oversimplifies the digital aspect of thinking and memory, deeming them to be the route used by the human brain in performing its unruffled magic. He closes by posing two questions that express the wonderment faced by a high level intelligence when accosted by the facts he was unable to wrap mental arms around: 1)"what essential inferences about the arithmetical and logical structure of the computing machine that the nervous system represents can be drawn from these ...conflicting observations? and 2)what are the logics and mathematics in the central nervous system [that must be]structurally *essentially* different from those languages to which our common experience refers? His fellow researcher, Warren McCullough similarly closed out his life and research by repeating a question that plagued him all his life: What is a number, that a man can know it, and a man that he can know a number?

Book Description

. John von Neumann and Norbert Wiener were mathematician-scientists, both child prodigies born near the turn of the century. As young men each made profound contributions to abstract mathematics.

Computer Pioneers:

Computer Pioneers

Computer Pioneers