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.

Science, Current Events

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On page 27 Wolfram explains "probably the single most surprising discovery I have ever made:" a simple program can produce output that seems irregular and complex.

This has been known for six decades. Every computer science (CS) student knows the dovetailer, a very simple 2 line program that systematically lists and executes all possible programs for a universal computersuch as a Turing machine (TM). It computes all computable patterns, including all those in Wolfram's book, embodies the well-known limits of computability, and is basis of uncountable CS exercises.

Wolfram does know (page 1119) Minsky's very simple universal TMs from the 1960s. Using extensive simulations, he finds a slightly simpler one. New science? Small addition to old science. On page 675 we find a particularly simple cellular automaton (CA) and Matthew Cook's universality proof(?). This might be the most interesting chapter. It reflects that today's PCs are more powerful systematic searchers for simple rules than those of 40 years ago. No new paradigm though.

Was Wolfram at least first to view programs as potential explanations of everything? Nope. That was Zuse. Wolfram mentions him in exactly one line (page 1026): "Konrad Zuse suggested that [the universe] could be a continuous CA." This is totally misleading. Zuse's 1967 paper suggested the universe is DISCRETELY computable, possibly on a DISCRETE CA just like Wolfram's. Wolfram's causal networks (CA's with variable toplogy, chapter 9) will run on any universal CA a la Ulam & von Neumann & Conway & Zuse. Page 715 explains Wolfram's "key unifying idea" of the "principle of computational equivalence:" all processes can be viewed as computations. Well, that's exactly what Zuse wrote 3 decades ago.

Chapter 9 (2nd law of thermodynamics) elaborates (without reference)on Zuse's old insight that entropy cannot really increase in deterministically computed systems, although it often SEEMS to increase. Wolfram extends Zuse's work by a tiny margin, using today's more powerful computers to perform experiments as suggested in Zuse's 1969 book. I find it embarassing how Wolfram tries to suggest it was him who shifted a paradigm, not the legendary Zuse.

Some reviews cite Wolfram's previous reputation as a physicist and software entrepreneur, giving him the benefit of the doubt instead of immediately dismissing him as just another plagiator. Zuse's reputation is in a different league though: He built world's very first general purpose computers (1935-1941), while Wolfram is just one of many creators of useful software (Mathematica). Remarkably, in his history of computing (page 1107) Wolfram appears to try to diminuish Zuse's contributions by only mentioning Aiken's later 1944 machine.

On page 465 ff (and 505 ff on multiway systems) Wolfram asks whether there is a simple program that computes the universe. Here he sounds like Schmidhuber in his 1997 paper "A Computer Scientist's View of Life, the Universe, and Everything." Schmidhuber applied the above-mentioned simple dovetailer to all computable universes. His widely known writings come out on top when you google for "computable universes" etc, so Wolfram must have known them too, for he read an "immense number of articles books and web sites" (page xii) and executed "more than a hundred thousand mouse miles" (page xiv). He endorses Schmidhuber's "no-CA-but-TM approach" (page 486, no reference) but not his suggestion of using Levin's asymptotically optimal program searcher (1973) to find our universe's code.

On page 469 we are told that the simplest program for the data is the most probable one. No mention of the very science based on this ancient principle: Solomonoff's inductive inference theory (1960-1978); recent optimality results by Merhav & Feder & Hutter. Following Schmidhuber's "algorithmic theories of everything" (2000), short world-explaining programs are necessarily more likely, provided the world is sampled from a limit-computable prior distribution. Compare Li & Vitanyi's excellent 1997 textbook on Kolmogorov complexity.

On page 628 ff we find a lot of words on human thinking and short programs. As if this was novel! Wolfram seems totally unaware of Hutter's optimal universal rational agents (2001) based on simple programs a la Solomonoff & Kolmogorov & Levin & Chaitin. Wolfram suggests his simple programs will contribute to fine arts (page 11), neither mentioning existing, widely used, very short, fractal-based programs for computing realistic images of mountains and plants, nor the only existing art form explicitly based on simple programs: Schmidhuber's low-complexity art.

Wolfram talks a lot about reversible CAs but little about Edward Fredkin & Tom Toffoli who pioneered this field. He ignores Wheeler's "it from bit," Tegmark & Greenspan & Petrov & Marchal's papers, Moravec & Kurzweil's somewhat related books, and Greg Egan's fun SF on CA-based universes (Permutation City, 1995).

When the book came out some non-expert journalists hyped it without knowing its contents. Then cognoscenti had a look at it and recognized it as a rehash of old ideas, plus pretty pictures. And the reviews got worse and worse. As far as I can judge, positive reviews were written only by people without basic CS education and little knowledge of CS history. Some biologists and even a few physicists initially were impressed because to them it really seemed new. Maybe Wolfram's switch from physics to CS explains why he believes his thoughts are radical, not just reinventions of the wheel.

But he does know Goedel and Zuse and Turing. He must see that his own work is minor in comparison. Why does he desparately try to convince us otherwise? When I read Wolfram's first praise of the originality of his own ideas I just had to laugh. The tenth time was annoying. The hundredth time was boring. And that was my final feeling when I laid down this extremely repetitive book:exhaustion and boredom. In hindsight I know I could have saved my time. But at least I can warn others.

907 of 946 found the following review helpful:

If a million scientists worked on a million experiments ...May 21, 2002
By Thomas Martin
If a million scientists worked on a million experiments for three hundred years, would they learn as much about the universe as Stephen Wolfram does by sitting at his computer for twenty years?

Apparently not, according to Stephen Wolfram.

I'm annoyed with Wolfram for forcing me to poke fun at him like this. I've been waiting for this book a long time, and I genuinely wanted to give it a thumbs up. Unfortunately, Wolfram has made that impossible.

I gave the book three stars, but in fact I consider it almost un-ratable. What do you do with a 1200-page tome that contains a wealth of substantive and fascinating results, but which is insists, at every turn, to draw over-blown and under-supported conclusions from them? I split the difference and gave it a middling rating, but that does not convey the deep ambivalence I feel toward this work.

Given Wolfram's reputation, I expected a certain amount of hubris, and even looked forward to it. Most scientists work hard to suppress the egotism that drives them, but Wolfram's ego is out there in the open. While this can be refreshing, what I found here left me dumbfounded. For Wolfram, all of scientific history is either prelude or footnote to his own work on 1-D cellular automata. On pages 12-16 he breezily sites other work in chaos theory, non-linear dynamics and complexity theory. At the end of the book, there are hundreds of pages of footnotes describing previous history as essentially one damn thing after another - a testament to all the people that didn't see the promised land, as he has.

Wolfram attempts to usurp all credit for the "computational perspective." Assertions such as "the discoveries in this book showing that simple rules can lead to complex behavior" are repeated to the point of exhaustion. But his attempt to shock us falls flat: if that idea was ever radical, it surely would not be considered so today. The other fields that Wolfram casually dismisses have provided strong indications of the power of this principle, as well as the idea that many diverse systems are computationally equivalent. An entire generation of physicists has grown up quite accustom to these notions.

Wolfram did make very substantial and important contributions to the study of complex systems in the early eighties. But he was not the only one, and those studies have not induced a wholesale revision of science. Despite what he would have us believe, the general concepts he espouses are not that radical. It would probably be more accurate to call them expressions of the modern scientific zeitgeist.

Meanwhile, some of Wolfram's specific claims are indeed very novel, but only because they are breathtakingly arrogant. Consider his comments on two famous scientific principles: The second law of thermodynamics, and evolution by means of natural selection. Both these principles date from the mid-nineteenth century. Both have incited considerable controversy, and both have withstood mountains of empirical observations from diverse sources. Wolfram, however, calls both of them into question. Why? Because he has done 1-D cellular automations simulations on his computer that he feels make them suspicious. How does Wolfram expect to be taken seriously when he makes such assertions almost non-chalantly?

Wolfram lacks any hint of balance in assessing the true place of his results. He admits to having been a recluse for years, and it shows. The desire to free oneself of the mainstream community, to allow oneself to be more creative, is understandable and healthy. But one concomitantly loses the critical faculty that derives from being part of a dynamic community. Though Wolfram will likely never see it, what he lost by pulling away from the world has substantially outweighed what he gained. Consequently, his loss has become ours. We did not get the much shorter, but wiser, book that lurks somewhere inside this one.

223 of 236 found the following review helpful:

What it is, and why it disappointsOct 14, 2002

This is a book of ruminations about cellular automata. It is chiefly concerned with the way that the state of a system evolves when deterministic rules are applied to it. The simplest system is a single point in either state 0 or state 1. The transition rule could be that the state "0" changes to state "1", and state "1" changes to state "0". That rule can be expressed as follows.

{1->0, 0->1}

If the system's initial state is 1, then the transition rule (repeatedly applied) yields the following alternating pattern of states.

1
0
1
0
.
.

For hundreds of pages the author discusses the behavior of 1-dimensional automata built from 3-cell transition rules. The 2^3=8 different states of a 3-cell cluster can be written in binary notation from 000 up to 111. The cell in the middle can transition to either of two binary states, yielding a total of 2^8=256 rules. Most rules lead to periodically repeating behaviors, with short periods like the alternating pattern shown above.

An exception is rule 30 (30 in binary is 00011110; these bits the right-hand-side values for the 8 transitions).

rule 30:
{ 111->0, 110->0, 101->0, 100->1, 011->1, 010->1, 001->1, 000->0 }

When applied to an initial state of a single 1 surrounded by 0's, rule 30 generates the following pattern (developing downward from the top row). The array can be displayed as a bitmap of black and white pixels, producing a visualization of the evolving state of the horizontal rows.

..00000000100000000..
..00000001110000000..
..00000011001000000..
..00000110111100000..
..00001100100010000..
..00011011110111000..
..00110010000100100..
..01101111001111110..

What excites many people about such rules (and about replacement grammars in general) is that applying the rule to an input string produces new strings whose characteristics are hard to predict. Plus, the patterns in the resulting visualization look pretty cool and are suggestive of all sorts of things found in nature. It's very easy to write computer code that will generate the patterns based on input rules, so anybody can play the game.

Lots of people have implemented cellular automata and been fascinated that the behavior is so sensitive to the choice of input string and transition rules. Watching the patterns unfold is a bit like playing the slot machines. So many possibilities. So fun to watch. Addictive to play. Great to show your friends. A meme that keeps on meming. Search the Web for "one-dimensional cellular automata" and "applet" and you will find examples that you can run in your browser.

What bothers many readers about the book is that it is like an undergraduate honors project gone haywire. Page after page of printouts of these things. Thousands of them. And with endless streams of the impressions they made on the author. "My Daily Journal of Cellular Automata" would have been a fair title. Wolfram's inflated sense of their importance, and his own, is evident in the copyright statement:

Discoveries and ideas introduced in this book, whether presented at length or not, and the legal rights and goodwill associated with them, represent valuable property of Stephen Wolfram ..

Thus he lays claim to every cellular automaton and any application thereof. Pretty annoying, coming from someone arriving late to the automaton party.

He concludes of the book proper (pp. 844-845, just before his 350 additional pages of "notes") that

.. building on what I have discovered in this book .. there is nothing fundamentally special about us. .. For my discoveries imply that whether the underlying system is a human brain, a turbulent fluid, or a cellular automaton, the behavior it exhibits will correspond to a computation of equivalent sophistication. .. [W]hat my discoveries and the Principle of Computational Equivalence now show is that .. cellular automata can achieve exactly the same level of computational sophistication as anything else.

Wolfram discovery/epiphany appears to be that all algorithms can be computed by a simple model. An example of such a model, called the "Turing machine", is taught every semester to computer science students worldwide.

It excites many people that the physical world is inherently computable, allowing computational simulations to have predictive value. It is bizarre to read Wolfram represent that he is the author of this insight.

79 of 81 found the following review helpful:

A New Kind of EgoMay 30, 2002

Wolfram does a great deservice for science in his new book. Not for scientists themselves, who can easily find out that more than half the overblown statements in the book are well known old science ideas. But a deservice for the non-scientific reader, who may actually be infused by the mantra that science is just purely speculation, without actually experimentation or show-and-tell.

I can speculate as much as I want about any single model. In fact, if a model is Turing Complete, as a CA is well-known to be, any speculation can always be verified by my model! But science is about proving with experiments one's theories. Or at least showing some interesting predictions that can be made based on chosing the proposed model. But neither of them are present in the book. In fact, in the beginning of the book itself Wolfram warns the reader that scientists are non-believers and will try to destroy his idea.

So he is now in a comfortable place. He has a Turing machine, and can therefore adjust the model to explaining anything. He claims due to the nature of the model he can predict little (interesting, isn't that the decidability problem?), and that
all scientists will atack him because what he believes is true.
This is circular reasoning.

Fractals have shown us that simplicity generates complexity. Even caos models that can be run on hand calculators show that. Or a double pendulum. It is a very well-known result (shown in the 50s/60s) that the game of life is Turing complete (ie. can compute any function given an appropriate program). CA are also Turing complete, so where is the news? I can compute anything. Writing a CA that generates prime numbers amounts to finding the right "program"...

What is disappointing is that most claims are not based on any theory or verification. Let us say that he cannot really run lab experiments to check his ideas. Or even that is too early to predict any new pheonomenon based on his ideas. Well, the least he could do is to use the powerful tools of Complexity Theory (especially Kolmogorov complexity) to measure the complexity of the patterns generated by a CA. Or to at least have some results veryfying the behavior of his set of axioms ... Ok, provide with
some useful examples on how to apply CA to important problems in bioscience, engineering, etc ... Not toy computing (!).

But what he cannot do is to use ideas from other people without giving them proper credit (ok, he puts a tiny side note) or just assume that arrogance, young academic brilliance, or money can justify science. When he claims that all the major revolutions happened like this, I would suggest him to take a look at the first writings of Newton, Gauss, Einstein, Von Neumman, etc ... His predecessors had ideas that revolutionized science, but they always provided results for the scrutiny of other scientists as well. Moreover, their models and ideas could be translated to verifiable statements or allowed new and interesting predictions.

Science is about communication as much as it is about ideas. If one cannot convince other people rationally of the validity of the ideas, and also verify such ideas through experiments (the true hallmark of a scientific theory is checking predictions against experiments) then he is not scientific. He is just creating a cult. Not even a religion, because that assumes that God is not oneself. And Wolfram is convinced he is some kind of
superhero. Well, I finally understand the title of the book. A new kind of science is about follow-the-leader and do not question, have faith, because my ego is the answer you have been waiting (not even 42)...

128 of 135 found the following review helpful:

Not new, not science, or not WolframMay 31, 2002

Of course I didn't read *everything* in this enormous
book, but 100% of the sample passages read so far
can be described by the title of the review. For example,
the idea that the universe may be run by a simple cellular
automaton is not new (I heard it from Edward Fredkin 15 years
ago), and the Principle of Computational Equivalence is
not science, since it is stated so vaguely it can never
be disproved. The one *very nice* new scientific result
found in the book so far, that the rule 110 is computationally
universal, is not due to Wolfram, but to his young
employee Matthew Cook, who does receive some acknowledgment
in the small print in the back of the book, but who was prevented
to publish his work by Wolfram's lawyers for years, while
the Master was finishing his Book.

As a review of ideas close to Wolfram's heart, this
could be an interesting book to read, but it suffers
terribly from repetitious self-congratulations and
high-flying but vague pronounciations. A good editor
should have made the book about 300 pages long, then
I would have probably recommended it. A scientist
who works in isolation needs a high degree of self-criticism
to succeed, and this is exactly what Wolfram sorely lacks.

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