A New Kind of Science

On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day.

Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

Book Description
This long-awaited work from one of the world's most respected scientists presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.

Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.

Written with exceptional clarity, and illustrated by more than a thousand original pictures, this seminal book allows scientists and non-scientists alike to participate in what promises to be a major intellectual revolution.

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 Dunbar
Sugar Land, TX


An insider's perspective   February 20, 2005
Kovas Boguta (Boston, MA)
115 out of 161 found this review helpful

Having spent much of the last three years thinking about the contents of this book and doing research in the program it establishes, I feel that it is finally time to set the record straight about what this book is and what it means.

First, what it does not say. It does not say the universe is a cellular automaton. It does not say we need to throw away existing science. It does not say that every other scientist is the world is an idiot. It does not claim every single minute idea contained within it is new, original, or revolutionary.

What it does say, however, is nevertheless as revolutionary as it is inevitable.
The fundamental basis for this book, and the science that it tries to build, is the idea that experimental methods are the only way to discover and understand the computational mechanisms that exist in our universe, and indeed to understand the nature of computation itself. Furthermore, it establishes a set of theoretically grounded principles about how these experiments should be conducted, and how their results connect to the rest of science.

Despite deeply confused claims to the contrary in some other reviews, this core idea is new. This is fairly easily verified -- just flip to Chapter 3 and ask, how many other scientists search through billions of register machines to discover interesting, complex behavior? Who else enumerates the 4096 s2k2 Turing machines and catalogues the computations they perform? This new kind of science is all about enumerating the *very simplest* computational systems and analyzing their behavior without biases towards any existing scientific tradition. This kind of research is simply not done in computer science, mathematics, physics, or the vague field of complexity theory.

Within the first 5 chapters, Wolfram establishes beyond a shadow of a doubt that complex behavior is ubiquitous in even the simplest of computational systems. Clearly, these systems do interesting things, and from a purely intellectual perspective deserve to be a pure field of study, much like pure mathematics. But so what? The rest of the book is dedicated to answering that question.

The fact that complexity is so easy to systematically generate suggests a radical approach to science in general. Traditionally, science looks for interesting things in the natural world, and then develops theories to explain certain aspects of their behavior. What Wolfram effectively is suggesting is that by exploring the computational universe, we can start by enumerating and understanding the theories themselves, and then going to the natural world and find places where they apply. At first this sounds crazy and counterintuitive, and from our traditional intuition we "know" that it cannot possibly work. But this book is all about challenging the traditional intuition using actual facts and ultimately fairly simple although abstract arguments.

Much of the criticism of the book - even by supposedly reputable scientists - is so laughably superficial that it barely warrants a response. But I will give one anyway. Critics complain that Wolfram does not give mathematical definitions of complexity, yet one of Wolfram's *main points* is that such definitions are impossible or at best useless. Critics complain that others - Fredkin and Zuse - first had the idea of the universe as a cellular automaton, yet Wolfram explicitly states that he does *not* think that the universe is a cellular automaton. Critics complain that computational methods are already commonplace, but ignore Wolfram's point that they should be leveraged in accordance to the computational realities of the universe. Critics complain that the book is unreadable, yet Wolfram over and over again captures in a single elegant picture what takes several pages of overcomplicated jargon in technical papers. Critics complain that Wolfram's ideas are too vague to be applicable, yet almost every other page contains an experiment that displays his methodology in action. Critics in the same breath say that the book gives no evidence for its claims while at the same time saying it is too big and sprawling. Critics complain that Wolfram has no respect for the ideas of others, yet they do not have enough respect for Wolfram's ideas to judge them on their merits, rather than the style in which they are presented. Critics say that everyone already knows about the power of simple programs. Oh really? Then why is science continuing to be done in ignorance of their consequences? Why is there already no field of empirically, systematically studying very simple computational systems? Because they are too boring? Not likely.

The book does have flaws. First, it doesn't make clear enough the distinction between studying simple programs for their own sake, and using simple programs in applications to the natural world. I also don't think the book makes enough of an effort to show that a science of simple programs is possible - for instance by developing detailed theories of some particular systems. The criticism of existing science is at times difficult to understand - in some instances Wolfram assails it for being computationally reductionist, and in others places he uses more practical issues such as the difficulty of numerical analysis. There is an absolutely ridiculous amount of information in the book, particularly in the notes -- I feel some of it is tangential, and it would have been better to study fewer topics in greater depth. While it didn't bother me, for the sake of others it may have been wise to tone down the use of the first person.

Looking at the trajectory of science, it is hard to imagine that the ideas and methods in this book will not grow to be commonplace. On some level, I feel that Wolfram's focus on experiment, exhaustiveness, abstraction, and simplicity just makes sense. The computational universe is like an ultimately idealized analog of the natural one - just as rich in its behavior, but far more amenable to systematic methods. Now that this resource has been identified, we should leverage its power.


Cellular Automata is a powerful idea but is it 42?   May 23, 2002
Adam Lynton (Queensland, Australia)
48 out of 57 found this review helpful

This is obviously a very significant work, worthy of careful attention with a critical eye.

The more recent research in the book has side-stepped the normal peer reviewed processes of scientific journals. This doesn't make it bad and does indeeed make it more accessible...(bye bye calculus in the mainstream text; also celullar automata doesn't really need it)...but it also means the scientific heavy weights haven't tried to pull it apart yet; so potential holes in the claims of the theory may yet surface.

Key book concept => cellular automata => complex processes result from one or two simple augmentation rules being repeatedly applied to an initial cell or row of cells, e.g. color of next cell depends on color of current cell and neighbors. Interesting thing is that whilst the augmentation rules are simple and well defined, some rules lead to a resultant ceullar structure, after several iterations, that appears to be almost random, with structure appearing occassionally, thus the structure has become complex.

Wolfram sites many examples in nature and physics where the cellular automata principle can explain behavior. Biological examples, such as plant growth are amongst the most convincing.

Cellular automata represents a different way of modeling phenomena in nature. Instead of looking at the end resultant complex structure and creating a correspondingly complex equation to describe it, you would look for the simple underlying rule, that through iteration, leads to the structure under analysis. Is there one underlying rule that ultimately defines all the observable complexity in the universe? How's that for a Holy Grail :-).

**The best and most balanced review I have read of Wolfram's book is by Ray Kurzweil. I strongly recommend you read this review. http://www.kurzweilai.net/articles/art0464.html?printable=1**

Enjoy the book...


Review of Wolfram, _A New Kind of Science_   July 14, 2002
Kenneth L. Miner (Lawrence, KS United States)
29 out of 43 found this review helpful

Review of Stephen Wolfram, _A New Kind of Science_

For three hundred years basic science has idealized mathematical models; this book at the very least makes a comprehensive and clear case for the advantages of the modern alternative: computational models. Probably nowhere else will you find such a clear exposition of the topic. The approach utilizes mainly cellular automata, which are fairly easy to understand and can emulate other computational systems. Hardly any of the central questions of science are untouched in this magnificent work, and the amazing thing is, it can be read and pondered by anyone. (Not in one day, though.)

Wolfram begins by developing the basic insights that (a) simple rules can produce systems of great complexity, even of the greatest complexity, which is apparent randomness; and that (b) complexity in systems comes in recurring types which tend to be surprisingly independent of the nature of the systems. From this, after a grand tour of crystal growth, plants and animals, fluid dynamics, financial systems, fundamental physics, cosmology, human perception and analysis, and much else, we arrive at a lengthy discussion of the nature of computation, and finally at Wolfram's grand summation: the Principle of Computational Equivalence. It is this principle that the author believes will eventually revolutionize science.

There is no question that the work is ambitious. Critics of the "Age of Science" often hit hardest at its weakness for speculating beyond the data actually available to the sciences. But there is another level of conjecture, namely, speculation about the future development of science itself, perhaps beyond current understanding of the nature of science. This phenomenon, which might be called metaconjecture, we encounter in its pure form on p. 545 of ANKOS, just about in the middle of the book: to derive all the results of quantum theory from computational models "will certainly take an immense amount of work" but Wolfram believes strongly "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."

There are ways in which this book is a major contribution to the philosophy of science even if the author has exaggerated the significance of his ideas. For one thing, one sees very often in science that weaknesses of a well-established approach are discussed openly only when a new approach is being offered. This book sheds light on the nature of traditional science done almost exclusively in terms of mathematical equations, by contrasting this with his approach of looking at computational models using simple rules (Chapters 1-5). (The issue becomes especially clear at p. 474, where the nature of space is being discussed. Continua such as are presupposed by traditional mathematics do not in general yield the complex behavior Wolfram finds interesting: complex behavior does not emerge from continua.) The book also very usefully discusses the nature of randomness (Chapter 6), the nature of systems based on the satisfaction of constraints as opposed to those based on rules (Chapter 7), and the nature of scientific models (Chapter 8).

One may be puzzled at all the attention given to shapes of leaves and branches, configurations of mollusk shells, pigmentation patterns-until one realizes that traditional science has not been able to say much of anything about them at all! Wolfram chides biologists for the ingenuity they show in trying to explain such things in terms of natural selection; for him, they have developed in spite of, not because of, natural selection. (Wolfram's ideas about the life sciences are perhaps the most interesting in the book.)

I especially liked Wolfram's discussion of entropy. It is often pointed out that the development of life (let alone human life) appears to defy the Second Law of Thermodynamics, which is that all things tend to randomness. But we are always told that while the law holds in general, it may be countered locally. The whole matter appears especially clear when discussed in terms of cellular automata. Why does the Second Law of Thermodynamics appear to hold? For Wolfram it is a result of the following proposition: "No reasonable experiment can ever involve setting up the kind of initial conditions that will lead to decreases in randomness, and... therefore all practical experiments will tend to show only increases in randomness." A reasonable experiment is one in which the process of setting up the experiment is simpler than the process which the experiment is intended to observe (p. 444). So does the law hold? Not really. Systems are quite possible to construct which decrease entropy, e.g. rule 122R with very elaborate initial conditions (p. 443). Rule 37R does not obey the Second Law. Somehow, in such a system, "kinds of membranes form between different regions of the system, and within each region orderly behavior will then occur, at least while the membrane survives." (p. 455) Wolfram drops the discussion there, but he would be the first to admit: "membranes" are, so far at least, just a label for what happens.

Listen to this remark about time (from p. 484):
"Should we really imagine that the complete spacetime history of the universe somehow always exists, and that as time progresses, we are merely exploring different parts of it? Or should we instead think that the universe-more like systems such as cellular automata-explicitly evolves in time, so that at each moment a new state of the universe is in effect created, and the old one is lost?
Models based on traditional mathematical equations-in which space and time appear just as abstract symbolic variables-have never had to make much distinction between these two views. But in trying to understand the ultimate underlying mechanisms of the universe, I believe that one must inevitably distinguish between these views.
And I strongly believe that the second view is the one most likely to provide a meaningful underlying model for our universe."
(That's Aristotelian by the way.)

I recommend the book heartily to anyone interested in the nature of science. Despite what one hears it is not overly long, because only 846 pp. are text, the rest being notes; and it is not expensive because his own company published it.


A dizzying tour of natural law in rose-colored glasses   May 18, 2002
John Tilelli MD (Apopka, FL USA)
54 out of 106 found this review helpful

Since the 16th century, science has attempted to explain reality by the expression of a few immutable laws that seemingly govern their behavior. Newton's laws. Maxwell's equations. The Heisenberg uncertainty principle. Things behaved in a certain way because the law was embedded into them. This point of view is the expression of Christian reductionism (In the beginning was the word.....), that within the seemingly sinful random behavior of real things, that there was an expression of some deeper reality. If the hybridization of red and white sweet peas didn't result in 25% of their offspring being red, but rather 23% or 28%, it didn't matter - the principle of an autosomal recessive trait was the same, and the genetic truth was in itself unchanging. Wolfram turns science on its ear by demonstrating how reality is in some way an expression of the chaos embedded in all behaviors. Perturb some supersymmetry, and all reality is generated. The behavior of nuclei and stars, the leaf of a maple tree, the behavior of socieites. Tweak the void with a tiny change, and like a dinner-bell, voila! all reality is served up. This book is not for the faint of heart, but just about every page is provocative. One will find much to consider, and, like the good meal alluded above, digestion will take far longer than the eating. A tour of Wolfram's software child, Mathematica may help this sometimes baffling reexpression of all science, but is not necessary. Like listening to Beethoven, in which a degree in music appreciation is unnecessary but helpful, formal mathematics opens the door of Wolfram's work a reality unavailable without it, but is in no way necessary to see the beauty of his approach. In the end, the effort of reading it is well worth it, and the hyperbole "Life changing" may not be out of order.