It is a long 1,000 pages book, so it deserves a long 1,000 word review. Not a "new kind of review" with I wrote when I discovered more than I thought. This use of an annoying self-praising 1st person style is certainly a negative side of the book : phrases like "I have discovered vastly more than I ever thought possible" and "what I have done now touches almost every existing area of science, and quite a bit besides". Most reviewers so far agree that it is a remarkable book, but perhaps a bit egoistical, repetitive, longwinded, and with a wrong title. It is not a new kind of science as the title says. Some even argue the content of the "New Kind of Science" book it is neither new nor science. Other scientists like Zuse, Fredkin and Toffoli are mentioned not at all or only in the margin. According to the lack of references to other research work, it is hard to call it a book about a *new* science. It is usual to write a book with a few references only in books about a well-established subject or science. And most of the content of the book is in fact not new. Cellular automata are an important tool, but they are not new and they have shortcomings, too. A weakness of the book is that the author does not mention and emphasize clearly the weak points of the "new science". Darwin devoted in his "Origin of Species" whole chapters to diffculties in his new theory. One weak point is: a turing machine or a CA capable of universal computation can calculate anything, but the price is that you may need a very large amount of time and memory to do it. For a pure CA book it comes a bit too late to be a revelation, for a "New Kind of Science" book it is maybe finished too early. The book contains very interesting sections, and here we come to the positive aspects and the good side of the book. If Stephen Wolfram would have went a bit further, the book would have been a true masterpiece. But unfortunately he stays on save and secure ground, the field of one-dimensional CA. The most interesting parts where the author goes beyond the borders of known science are not in the main text, but in the remarks in the notes section that follows the main text. The book contains about 800 pages without the notes, and then another 350 pages of notes. The main text focusses itself on simple one-dimensional CA. Like Steven Pinker's great book "Words and Rules" the book tries to illuminate the nature of something by choosing a single phenomenon and examining it from every angle imaginable. That phenomenon is for Steven Pinker the topic of regular and irregular verbs, whereas Stephen Wolfram concentrates himself on Cellular Automata and their patterns. This is the weakness of the book - it is not really new science - and at the same times it's strength - the known science and facts are described and explained clearly and good. As a book about CA book it is great. Change the title into "Cellular Automata - the search for a new kind of science", add some references to the work of others, and you have one of the best books on CA ever written. And it points in the right direction. It is not the CA which are fundamentally new, it is the direction in which Stephen Wolfram points: the branches of science dealing with chaos, complexity and complex adaptive systems are relatively new and promising. Complicated formulas and mathematical equations are not very useful here. Science as a whole was fundamentally altered by the application and invention of new mathematics, especially of the differential calculus by Newton and Leibniz. Now science as a whole is altered again by the use of computers to simulate complex systems. Computational models are beginning to replace and extend mathematical models. Multi-agend based simulations replace game theoretical calculations in social sciences. CA replace differential equations in biology, physics and other sciences to explain and describe self-organizing systems. Yet there is no official science of "Complex Adaptive Systems" or "Complexity" similar to mathematics. Steven Strogatz said in his SYNC Book, "I think we may be missing the conceptual equivalent of calculus, a way of seeing the consequences of the myriad interactions that define a complex system." We need to try and check several tools to examine if such a new calculus exists. Stephen Wolfram has done this for CA. He has written a monumental book of high quality, and the content is clear and correct. Although most of the things have been explained, mentioned and discussed before, no one has given such a coherent, comprehensive, detailed and clear view of Cellular Automata in this quality. The style is clear and clean. It is written with clarity and well illustrated. The interesting figures, illustrations and pictures are of excellent quality. A grand and monumental book. Since Galileo scientists and especially Physicists are convinced that nature is written in the language of mathematics. Now even Physicists notice, due to books like this that nature can not completely explained with mathematics. Some parts and patterns can be described better in the language of remarkably simple algorithms and rules. Mathematics can describe and predict certain phenomena and principles in amazing precision. But it is not suitable to explain the evolution and behavior of complex systems. It is often futile and frustrating to attempt to model complex systems using traditional mathematical abstractions. Stephen Wolfram shows clearly there are other ways. Systems with simple local rules can show complex global behavior. This is the red thread that runs through the book, and it is certainly one important part or fiber of the next-generation "C"-science that will extend or combine Cybernetics, Catastrophe theory, Chaos Theory, Complexity Theory and the theory of Complex Adaptive Systems.
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