A New Kind of Science [Hardcover]

Stephen Wolfram (Author)

Book Description

ISBN-10: 1579550088 | ISBN-13: 978-1579550080 | Publication Date: May 14, 2002 | Edition: 1

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.

Editorial Reviews

Amazon.com Review

Physics and computer science genius Stephen Wolfram, whose Mathematica computer language launched a multimillion-dollar company, now sets his sights on a more daunting goal: understanding the universe. Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems.

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

From Library Journal

Galileo proclaimed that nature is written in the language of mathematics, but Wolfram would argue that it is written in the language of programs and, remarkably, simple ones at that. A scientific prodigy who earned a doctorate from Caltech at age 20, Wolfram became a Nobel-caliber researcher in the emerging field of complexity shortly thereafter only to abscond from academe and establish his own software company (which published this book). In secrecy, for over ten years, he experimented with computer graphics called cellular automata, which produce shaded images on grid patterns according to programmatic rules (973 images are reproduced here). Wolfram went on to discover that the same vastly complex images could be produced by even very simple sets of rules and argues here that dynamic and complex systems throughout nature are triggered by simple programs. Mathematical science can describe and in some cases predict phenomena but cannot truly explain why what happens happens. Underscoring his point that simplicity begets complexity, Wolfram wrote this book in mostly nontechnical language. Any informed, motivated reader can, with some effort, follow from chapter to chapter, but the work as a whole and its implications are probably understood fully by the author alone. Had this been written by a lesser scientist, many academics might have dismissed it as the work of a crank. Given its source, though, it will merit discussion for years to come. Essential for all academic libraries. [This tome is a surprise best seller on Amazon. Ed.] Gregg Sapp, Science Lib., SUNY at Alban.
- Gregg Sapp, Science Lib., SUNY at Albany
Copyright 2002 Cahners Business Information, Inc.

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Product Details

• Hardcover: 1192 pages
• Publisher: Wolfram Media; 1 edition (May 14, 2002)
• Language: English
• ISBN-10: 1579550088
• ISBN-13: 978-1579550080
• Product Dimensions: 9.7 x 8.1 x 2.5 inches
• Shipping Weight: 5.5 pounds (View shipping rates and policies)
• Average Customer Review: 2.8 out of 5 stars  See all reviews (340 customer reviews)
• Amazon Best Sellers Rank: #76,833 in Books (See Top 100 in Books)
  • #55 in Books > Computers & Technology > Computer Science > Modeling & Simulation
  • #59 in Books > Science & Math > Experiments, Instruments & Measurement > Methodology & Statistics

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Customer Reviews

Most Helpful Customer Reviews

2,377 of 2,481 people found the following review helpful:

1.0 out of 5 stars The Emperor's New Kind of Clothes, February 28, 2003

By 

Joe Weiss - See all my reviews

This review is from: A New Kind of Science (Hardcover)

This review took almost one year. Unlike many previous referees (rank them by Amazon.com's "most helpful" feature) I read all 1197 pages including notes. Just to make sure I won't miss the odd novel insight hidden among a million trivial platitudes.

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.

891 of 928 people found the following review helpful:

3.0 out of 5 stars If a million scientists worked on a million experiments ..., May 20, 2002

By 

Thomas Martin (Mesa, Arizona) - See all my reviews
(REAL NAME)   

This review is from: A New Kind of Science (Hardcover)

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.

211 of 221 people found the following review helpful:

1.0 out of 5 stars What it is, and why it disappoints, October 14, 2002

By A Customer

This review is from: A New Kind of Science (Hardcover)

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.