Rating: 
Summary: Can the Universe be a Cellular Automaton?
Review: There is much too much here to have digested so soon after publication. But Wolfram's central theme, that the Universe is really a giant Cellular Automaton, runs smack into the Bell Inequality. Any local realistic theory must obey the Bell Inequality, and CA's are as local and realistic as it gets; but the world itself, according to both Quantum Mechanical theory and experimental test, does not always satisfy the Bell Inequality.If Wolfram has found a way around the Bell Inequality, he deserves a Nobel Prize. If he hasn't, his book is fatally disconnected from reality.
Rating:
Summary: Isn't as groundbreaking as hyped
Review: I read some hyped reviews about this one so I checked it out. I wasn't as impressed by the book as I'd expected. The ideas behind the book isn't as new as it's claimed. The fundamental ideas expressed in the book can be summarized into under 10 pages. What takes up so much space is the pictures. The core of the book is Wolfram's speculation on his principal of computational equivalence. What this basically says is that the universe may be considered a giant computer running a huge simulation. The reason why traditional science has hit a dead end (according to him) is that we attempt to use mathematical methods and logic to shortcut this simulation. However, many of the processes are irreducible, so we can't shortcut it with equations and approximations. By doing so we leave out underlying information and therefore can't gain a complete understanding of nature. The other part of the principal is his speculation that there is a practical upper limit to behavioral complexity so that the most complex natural phenomena are of equal or less complexity than his computer experiments. In addition to his observation that complex behavior can arise from simple rules, he speculates that everything in the universe arise from simple processes that are being ran as a huge simulation and that we can understand it through computational simulation. Add a ton of pictures to this plus the notes and your have the book. I would however still recommend you buy it because it has very nice pictures and it's fairly cheap for a hardcover.
Rating: 
Summary: Needs an Editor--or a Movie Director
Review: This book is heavy--about four lbs. by my estimate. I think I'll wait until the movie of it comes out!
Rating:
Summary: A good introduction to cellular automata
Review: In this gargantuan treatise, which has appreciable gravitational pull, the author introduces the reader to the tools and science of cellular automata. Some of the proposals in the book are radical (such as the Principle of Computational Equivalence), some fairly conservative, and some unjustifield, but it does serve to introduce cellular automata from the standpoint of an individual who has been very active in their study and development. The book is long, and space does not permit a detailed review here, but one can read the book in its entirety in a fairly short time frame since the margins are large and there are an abundance of diagrams in the book which take up page space. Also a very large (338 pages) part is devoted to notes in the back of the book.
Different viewpoints on science and mathematics require both formal and empirical justification. The author does this in some areas of the book, but not all, and the ones left open are left to the reader to speculate on. Because of this it is not clear the book will have a major influence on scientific research. One would want more examples of the power of cellular automata in solving difficult problems in mathematics and science before deciding to use them in the everyday practice of scientific research. Throughout the book, the author repeatedly suggests that simple rules in cellular automata can result in complex or "random" behavior, but never really quantifies what he means by randomness. The patterns generated "seem" random to him, as he says repeatedly, but other readers may disagree. He attempts to define it more precisely in his discussions on the processes of perception and analysis, but again the discussion is purely qualitative. In addition, the rule for generating the patterns is known in advance. In actual research however, one is given a collection or pattern of data and attempts to discover the rules behind it. Thus all of the patterns in the book are really quite simple, since the rules are known for generating them. If one is given one of these patterns without knowing the rules, it might be very difficult to find these rules. Such is the headache of modern science. Also, randomness is a concept that depends on the time scale chosen. Transient behavior of physical systems may appear random on short time scales, but for long time scales the system approaches periodic or quasiperiodic behavior. Also, sometimes one can "quench" apparent randomness in a system by a transformation of coordinates, which says that behavior that looked random was only due to a particular coordinate system chosen to characterize the system. The author does distinguish three mechanisms for randomness, one being an explicit introduction of randomness into the rules of the system; another being randomness in the initial conditions; and the third being randomness from the environment. The discussion is purely qualitative and leaves the reader wanting as to what tools are needed to detect or distinguish these forms of randomness from each other in the time evolution of the system under study. The detection and use of noise in physical systems is of course of paramount importance to applied science and engineering, and practitioners in these areas will need a more quantitative presentation than what is given by the author. It is clear that the author considers "randomness" as being in some sense fundamental or ontological, since the seemingly random behavior of discrete systems can produce for example, interesting behavior, such as mathematical continuity. Even the characterization of systems or rules as "simple" can be quite difficult to define from a fundamental point of view. The concept of Kolmogorov complexity has shown some headway in defining simplicity, but its elucidation has been omitted from the book, no doubt because of its use of "traditional" mathematics, which the author has steadfastly avoided in the book. There are many examples in "traditional" mathematics however that give the kinds of behavior the author finds fascinating, many of these found in the area of dynamical systems. And here again, the complexity of a problem or system may be dependent on the vantage point of an observer. The inability of "Eve" to decipher the elliptic curve factorization choices of "Bob" and "Alice", makes Eve's situation very complex from her standpoint. Bob and Alice however have chosen a procedure based on a "simple" group operation on elliptic curves. Interestingly, the author has not chosen to discuss quantum computation in this book, in spite of its current importance. His claim that that the Principle of Computational Equivalence is a law of nature that will prohibit systems from carrying out computations more sophisticated than cellular automata and Turing machines suggests that quantum computers can be reduced to these systems, a claim that is profound but difficult to prove. Quantum mechanics and quantum field theory are discussed briefly in the book, but no in-depth suggestions are given as to how to apply cellular automata to resolving difficult and nagging problems in these areas, unfortunately. Speaking now independently of the content of the book, it was written and then delivered to its readers outside the confines of peer-reviewed academic journals. The author is to be applauded for this move, for it shows an independence of spirit and follows a trend that hopefully will increase in the decades ahead. With electronic publishing and Internet postings of scientific results, this leaves readers the privilege of making up their own minds as to the scientific worth of a particular document. Thus one can read this book as the author intended it, and free from the influence of anonymous referees. The author has written it, marketed it, and put his name on it, and he clearly is, and should be, proud of his many achievements to this date. One can disagree with the content of this book, but it is an attempt to view things from a different point of view, and 21st century science needs more of this, not less
Rating:
Summary: Might be good, too sloppily written
Review: I will probably muddle through the book because I suspect the ideas are interesting and important. However, the writing is sloppy. For the author spent a great deal of time arguing his points in his head. And he believes that he must bludgeon you with continuous expressions of how he surprised himself with his results. But as an ordinary mortal whom the author presumes a simpleton, you will be very amazed at the extremely remarkable findings.
I suspect that one quarter of the sentences in the book begin with "and", one quarter with "but", one quarter with "for". The remaining sentences are the ones that add content.
This book needs an editor.
Rating: 
Summary: Science that supersedes mathematics
Review: Stephen Wolfram, math and physics genius and creator of Mathematica, closeted himself away for more than a decade doing research in an area that extends science beyond mathematics and holds great promise for future understanding, Not only that, he's put it all together in a book that requires no real scientific or math background. Wolfram is correct when is says this is a new science, a new way of looking at the world that must be understood on it's own terms. He builds his new science from the bottom up, beginning with the development of a "new intuition" and fundamental understanding that anyone can follow. It took awhile to "let go" of the way I already see and know things; the patterns in which I already experience and comprehend the subject, and then it really took off! A great read!
Rating:
Summary: a new kind of bubble
Review: the book is a nice compilation of mathematical facts at an
elementary level. There is no new science and moreover
no science at all! It is just a long and useful essay.
Rating: 
Summary: Disappointing
Review: Wolfram essentially condemns the mathematical foundations of science and suggests (without proof; but instead a deluge of cellular automata computer experiments) that simple rules can produce complex results that cannot be derived by math as with biology and the real world.
I found nothing new in the book other than his mental extrapolation of his results to the real world without proof. Particularly disappointing was his 'revelation' that the second law of thermodynamics is not universal and that in one of his closed systems of a cellular automata program where no information is lost, complexity increased in violation of the second law. However he obviously chooses the statistical mechanical ('micro') version of the second law which is hotly disputed and condemned already by some and for which the inventor, Boltzman, already confessed over a century ago, is time reversible and could not explain the 'inexorible heat death' of the universe. Many others have suggested that entropy cannot be equated with disorder (for instance K. Denbigh in the UK) and that the proper inviolable 2nd law, which as one reviewer below says has never been disproven in the real world, is the thermodynamic ('macro') one that no one can extract an equal amount of work from a fixed amount of heat. Wolfram also accepts the expansion of the universe as an explanation of Olber's paradox as to why the sky is dark and for the possibility of 'islands' of decreasing entropy where life could begin, with no originality. He can't have it both ways, if life evolves from islands of decreasing entropy, another Boltzman speculation, then his closed cellular automata rules are not the explanation. In addition he has not solved the riddle of disparate reversible micro and irreversible macroscopic evolution which for me would have vindicated his braggadocio and the book might have lived up to the hype of having made a scientific discovery that was a breakthrough.
Wolfram also attacks mathematical physics (ironcially since he made all of his money on Mathematica the software program) by telling us what we already know, the narrow applicability of linear math to the real world. His suggestion that no math will do it is important but unproven. One cannot prove that just because a software program can lead to complexity that mathematics can never get there. If so the Santa Fe and other complexity programs should be disbanded, which appears to be the logical conclusion to his thesis; presumably in favour of total dedication of science to studying 'his' cellular automata, but excluding the math which he says has been isolated to the tractable portion only of the programs and so cannot define the dynamics. He appears to give short shrift to the embryonic but burgeoning field of non-linear dynamics but this is the rival to his own theory. And this promising area is being pursued in other fields such as economics and finance, yet Wolfram's message is they are wasting their time; that only experimenting with programs with a multitude of trial experiments can lead to solutions, which is the design of his book, with thousands of diagrams. I confess I could only marshal enough interest to look at a few of them.
His theory that the universe may be governed by a simple 4 or 5 line algorithm is similar to Rudy Rucker's and Max Tegmark's different theories with the same suggestion, that simple rules may govern the evolution of the universe, Rucker's using algoritmic information theory (in a book named "Mind Tools") and Tegmark's using quantum theory (in an article at the Los Alamos site at xxx.lanl.gov). This is not to say the book is worthless. I think Freeman Dyson's comment quoted in a review below is referring to it's contribution to science being worthless and he may be right. However a much smaller book issued without fanfare would be an interesting addition to semi-fictional populist science (the fiction parts being Wolfram's unproven inferences and speculations). In addition he has stimulated a debate which may grow or wane depening upon whether non-linear scientists wish to return to 'trial and error' science.
Rating:
Summary: Astonishing is the right word for it
Review: Stephen Wolfram is a very clever man, no question about it - Mathematica is a great program. However, he is not as clever as he thinks he is. The astounding hubris that this book represents is in very poor taste. This is a self-published book - it needed a real critique other than from the author himself. He then might have written a really substantial boook. There is a lot here that is interesting, but the idea, I'm afraid, that the author all on his own has discovered something brand new and powerful about the world is rather absurd. I predict that this book will slide into obscurity just like all the others of a sensationalist nature. The back flap copy is unintentionally hilarious -- if you think you could stand this tone throughout then go ahead and read it.
Rating:
Summary: Review made before reading
Review: I read the June Wired article; I read the reviews; I ordered the book. I am a univeral expert as deep as any other thinker / writer here. My review:
Apparently, instead of only one answer [42 according to Douglas-Adams];
instead of only one creator [known by numerous names];
instead of only one pre big-bang singularity [according to 'modern physics'];
there was only one tiny golden rule.
Cool. But who made the rule? (This book illustrates the problem with mathematicians. They write 1200 pages proving something that should be obvious. Some brilliant artist will eventually condense all this into a single image, a dazzling paragraph or a perfect review).
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