A New Kind of Science

There are a vast range of physical, biological, and other systems that we are confronted with that exhibit an immense complexity. Throughout history, it has been seen as perhaps the work of a supernatural being. Also, often when we encounter something that seems complex, we take it for granted that the phenomenon must be the result of an underlying mechanism that is itself complex. The author shows us how simple programs can, in fact, produce great complexity. In regards to physics, the author states, “that thinking in terms of simple programs will make it possible to construct a single truly fundamental theory of physics, from which space, time, quantum mechanics and all the other known feature of our universe will emerge.” We learn in this book, through virtually hundreds of pages of diagrams, how simple initial conditions can produce complex behavior. Wolfram argues that this phenomenon is responsible from most of the complexity we see in nature.There is extensive discussion of cellular automata, where we have simple rules that result in complex behavior- so much in fact that I skipped through some of the material. It is believed that these behaviors are common in nature. An interesting finding is that “adding more complexity to the underlying rules does not yield behavior that it ultimately any more complex.” By chapter four, we are introduced to systems based on numbers. How does their behavior compare with other systems discussed? Even here it is possible to get behavior of considerable complexity by applying a series of operations based on simple arithmetic. Chapter 5 expands things to two dimension and beyond. The next chapter considers completely random initial conditions.Finally, we get to the application of what was covered in the previous chapters – the study of actual phenomena in nature. There seems to be a similarity between the basic mechanisms in nature and those responsible for the phenomena seen in simple programs. It is important to note that even though the models are based on simple programs that may successfully reproduce the behavior of some system even though that system does not actually consist of discrete cells, it is just a model. Models provide “an abstract representation of effects that are important in determining the behavior of a system.” The author provides examples of snowflake formation and fluidic motion. Regarding evolution, it seems that natural selection may not be as important as once thought saying that features in complexity of biological organisms arise in a sense not because of natural selection but despite it. Also, it was noted that the high degree of complexity seen in nature “can arise in a sense quite effortlessly just as a consequence of following certain simple rules of growth.”In the chapter on physics, this idea of simple initial conditions producing complex and seemingly random behavior is applied to the Second Law of Thermodynamics. The author discusses models for continuum fluid mechanics and even the universe. In fact, he believes that most physical laws discovered so far “are not truly fundamental but are emergent features of the large-scale behavior of some ultimate underlying rules.” The discussion veers into topics like gravity, spacetime, and quantum phenomena. It is the author’s “strong belief that in the end it will turn out that every detail of our universe does indeed follow rules that can be represented by a very simple program – and that everything we see will ultimately emerge just from running this program.” Wow, the thought went through my head: could we be living in a simulation? Who knows?The next chapter deals with process of perception and analysis. I skimmed through parts of this section – a bit too much detail for me. But the question becomes could simple mechanisms underlie human thinking? The next chapter covers universality and how “in the end cellular automata can actually be made to emulate almost every single type of system” that has been discussed so far. In fact, a wide range of computations that can be performed by computers can be done by cellular automata.In the final chapter, the author discusses something called the Principle of Computational Equivalence, where one can view all processes whether produced by humans or nature as computations. Another concept discussed is computational irreducibility, which implies that even if one has all the information to work out how some system will behave, it will still take an irreducible amount of computational work to do this. The concepts developed here apply not only to phenomena in nature but can provide new insights on fundamental issues in mathematics as well. Note that in discussing his work, the author supplies literally hundreds of charts, diagrams, and tables to back up his claims. The author concludes the main purpose of the book has been to build a new kind of basic science, but the most important consequence will have been to introduce a vast new range of systems helpful to technology.

This is a stunning book in its physical properties. It's huge, well illustrated, and easy to read. On the negative side, it's too huge to read on an airplane, it's ponderous in reading, it makes my left wrist hurt from holding it up when I read.But overall I highly recommend it for anyone wanting to read how cellular automata can apply to fields showing complexity not solved with tradional mathematical approaches (just about all).I'm appalled by some of the negative reviews of this book here on Amazon. I think alot of these ad hominem attacks are due to the author's over hyping the book before releasing it, and his general ego-centric personality. But, the reviews should be on the book, not the author's personality.I found the book to be very easy to read. Those that say he needed an editor probably did not read the book... particularly the beginning where he describes why he took an informal approach to his writing.Those that claim he grabs credit for Cellular Automata also missed this beginning where he credits those who came before him. Now, I will admit that Wolfram doesn't hesitate to overuse the "I" word, but again... he tells you upfront why he does so. I found it to be only mildly irritating. Scientists are often egotistical, heck... look at Linus Pauling.In this regard I think we could say that Wolfram is egotistical, but in no way showing hubris. I think this is a monumental book, and may defy categorization.The purpose of this book was to show how Cellular Automata are at the base of many things complex and currently beyond description or understanding. To do this he describes Cellular Automata in enough detail so that everyone can understand it, and the experts could not say that something was missed. This is why the book is ponderously slow. I found myself jumping ahead to read his conclusions and theories.I will concur with some other reviewers that it is more computation than theory. I wish the book had been reduced down to 1/3 of the size and more theory and consequences given. However, that would probably defeat Wolfram's long term goals with the book. Again, he describes why he structures the book the way he did in the first part of the book.I'm very pleased with my purchase of this book and recommend it to others that have an interest in mathematics. I particularly liked his discussion of biology and Cellular Automata, and I agree with him that it may offer a better explanatory model than natural selection in evolution.John DunbarSugar Land, TX

Wolfram es uno de los genios modernos que amplía el conocimiento de manera extraordinaria. En este libro abre el mundo matemático con la metamatemática que actualmente se encuentra en desarrollo pues dota a los científicos de las estructuras y el lenguaje necesario para entender la organización formal del conocimiento. Libro que inicia el desarrollo moderno del lenguaje de cómputo y la visión integral del aspecto formal de cualquier conocimiento. Indispensable para cualquier científico que desee investigar a fondo los misterios del conocimiento de su disciplina.

Simplicity,Beyond a level, can generate amazing complexity. Must read one

Très bonne facture. Un peu surpris au début par la couleur - je l’ai prise en gris - dont les variations vont du gris très clair 20% au gris 60% mais finalement séduit car hyper confortable, stable et résistant bien à la chaleur directe.

Thematisch ist das Buch durchaus interessant.Die Ich-Bezogenheit des Autors und des Schreibstils muss man dabei halt ein wenig ausblenden.

Bought it on a lark and as I read it I discovered something transcendent . The book is a profoundly moving emotional experience, an intellectual Rollercoaster, a white knuckle ride to the top of the author's ego where the air is truly rare. If you want to know how it feels to stand on the summit of civilization and gaze down on the poor wretched souls below, this is the book for you.