A New Kind of Science

Rating:
Summary: impressive computation, but not science
Review: The 1200 page book displays an impressive amount of detail-thousands of figures and clever algorithms. However, it is not very deep science. Science means predicting new observations or explaining existing ones more elegantly. Wolfram does little of this. He makes a huge number of philosphical speculations about re-engineering science, that could be siginificant in the future, if anyone does flesh them out in a scientific way.
The other major scienific failure is lack of citing related work that was published before his, even if he did discover these thing in parallel. The book reminded me of Isaac Newton's Biblical cosmologies: an impressive display of calculation, but not scientifically significant.

Some good things: it is an exhaustive catalog of CA algorithms, documented with endless figures. It speculates on how CAs may help most branches of science. The 400 pages of footnotes seem more interesting than main text. I probably wait until the book reaches remainder shelves and buy it as a reference.

Rating:
Summary: the I's have it
Review: I was very, very disappointed in this book ... had expected something disciplined and original. Instead (and I believe unintentionally) it comes off as an extended commercial for -- Mathematica! Stephen Wolfram! If you are new to topics of evolution and complexity, and you find a germ of inspiration here (somewhere within the book's overwhelming mass of pages, first-person pronouns, "beliefs," 2-D diagrams of simple automata -- but no room for references!), then good for you. I do appreciate the author's evident sense of wonder. Unfortunately, much of that wonder is wasted on a narcissistic insistence that the Wonder is Wolfram's Alone (courtesy Mathematica). Here's the irony: yes, beautiful things emerge from reiterative interactions; yet the author walls himself off from direct intellectual interaction (an editor, maybe?), and so the force of his ideas is self-limited and rapidly spent.

Rating:
Summary: A Crushing Disappointment
Review: After waiting a long time for ANKOS to appear, a quick review revealed my worst fears: not only is this author megalomaniacal, he has also completely misrepresented his work. Far from being a new kind of science, his work is merely a deeper (and, in fairness, sometimes more creative) look at results available for years from others fully his equal. It is a bitter disappointment to have been fooled into thinking that the publication of this work would result in a landmark of scientific thought. True scientific luminaries will not, after all, have to slide down the bench to make room for another place.

Rating:
Summary: Careful
Review: There's a danger in confusing two different things together. One can use affine fractals to draw pictures of mountain landscapes, but the rules of fractal construction teach you absolutely nothing about the physics or geology of mountain formation. Likewise, you will learn nothing about leopards simply from constructing patterns that look like leopard spots. Computational universality is very powerful: you can compute any computable number or function, but the way that those numbers and functions appear empirically in nature will remain not explained. To believe that nature is like a ca says nothing unless the program is specified. where did the program come from? I recommend instead the chapters on symmetry as the basis of physical law in Wigner's Symmetries and Reflections, a very beautiful book.

Rating:
Summary: A New Cure for Insomnia
Review: Stephen Wolfram's "A New Kind of Science" could have used an editor. The text is highly repetitive and boring. This is an intellectually soft book. Astonishingly, the book has no bibliography. Wolfram mentions very few other scientists by name in the main text; Godel is among the few who are mentioned in the main text, in the chapter on the so-called "Principle of Computational Equivalence," where it is stated that thanks to Wolfram's discoveries, Godel's incompleteness theorems should no longer be seen as surprising. At long last, Wolfram has provided a context in which the incompleteness theorems appear inevitable, he writes, dismissing the work of dozens of researchers in the field of logic and recursion theory. The book is full of Biblical sounding pronouncements alerting the reader to the importance of what he is about to read; these reach a climax in the final chapter on the Principle of Computational Equivalence, which is supposed to have implications not only for physics, but for mathematics, philosophy and--one of Wolfram's favorite phrases (aside from his liberal use of the pronoun "I")--"elsewhere."

Wolfram's Principle of Computational Equivalence is stated in vague terms; attempts by several professional mathematician colleagues of mine to locate a precise statement of the principle met without success. Here is an attempt to restate the principle; it rests on the assumption that any physical process can be "viewed as a computation." This is ancient and goes back at least to the mechanism of the 18th Century. The Principle, as far as we could determine, is that any two physical processes that aren't "obviously simple" are of "equivalent complexity." For example, the physical process of hitting a golf ball already contains within it the computational "complexity" and "sophistication" of your favorite universal partial function of classical recursion theory. These are vague claims; moreover, attempts to make them more precise seem to falsify them.

One of the difficulties rests with the interpretation of "obviously simple", not to mention that the term "complexity" isn't defined (it appears to be defined "ostensively" by eyeballing the runs of numerous cellular automata), and no notion of "equivalence" is offered. Do we throw away the Chomsky hierarchy? Mathematica is an example of a context-free language; such languages are precisely those recognized by pushdown automata. A language recognizable by a pushdown automaton but not by a deterministic finite state automaton is arguably less "obviously simple" than a regular language (those languages recognizable by precisely the deterministic finite state automata are the regular languages). Do we then conclude, on the basis of the Principle of Computational Equivalence, that the levels of Chomsky Hierarchy above the context-free languages collapse on the basis of this perceived added complexity, and that the context-free, the context-sensitive, and the recursive languages coincide? The principle of computational equivalence is too vague to be of scientific use; if it conflates the levels of any of the various known hierarchical classifications of computational complexity that we have, then it cannot be true. No examples of physical systems of "equivalent computational sophistication" are presented, even though it is asserted that systems which represent "universal" computational processes abound in nature.

Wolfram might argue that I just don't get it; I argue that he just didn't state it, and this is a systemic problem with this intellectually soft book. Wolfram could argue that "obviously simple" means "not universal"; in fact, Wolfram could argue anything without fear of being refuted, since his statements are too vague to admit much of an analysis. Wolfram appears not to want to dirty his hands with precise definitions and statements of his "revolutionary" principles, and would appear to want to leave the enunciation and development of his new science to the next echelon of followers.

Nevertheless, the book can be sporadically inadvertently amusing. I recommend it as a cure for insomnia.

Rating:
Summary: Boring and pointless
Review: I've returned this book after two weeks.

I found it enormously boring, the tedium of going through every variation of a simplistic little updating algorithm is just ludicrous. Hundreds of pages of little black boxes it feels like the whole book is about little black squares.

The main idea of this book: simple rules bringing about the complexity is not new, it is the ultimate goal of every scientific theory. Take the Maxwell equations for example. Four very simple equations completely describing the electromagnetic-field. Of course in most situations these equations are solvable only by approximations but that is still better than Wolfram's theory where the effect of the rules cannot be predicted in any situation. You have to effectively run the updating rules and see what comes out of it.

I was also terribily miffed when I realized that Wolfram uses the words complex and random interchangeably. That is so not the same. A complex system has a reason to be so, it has an underlying complex structure that serves a purpose. But it makes no sense to try to understand a random system since that one has no functionality whatsoever.

In fact it is only well into the book where Wolfram admits to this, that complex and random are the same in his view. Moreover he argues that complexity can be estimated visually, just by looking at a picture you can tell which one is more complex.

I find this kind of reasoning and subjective evaluation unacceptable.

Save your money, this is not science and is extremely boring for a voodoo science book.

Rating:
Summary: a computational race between observer and observed
Review: This book publicizes itself as being a major revolution in science, at least in the eyes of its author. I'd been waiting impatiently for this book for seven months, partly out of a morbid curiosity to see whether or not Mr. Wolfram had lost his mind.

First impressions of the book are: (1) it's size - it's bigger than a college dictionary; (2) it's elegance - all the details (layout, binding, illustrations, etc) are all of the highest quality. And the first five or so chapters are a very easy read - very easy to follow. But as I progressed, I began to feel like while I understood what he was saying, I couldn't always make out why he was saying it. Chapters 7-9 had moments that were either disappointingly short or hard to follow, but still I soldiered on. And with remarkable showmanship, Wolfram has saved his best for last - Chapters 10 and 11 read a bit like a fireworks show, and in Chapter 12 Wolfram drops his biggest bombs. Now maybe I need to reread the whole thing - this time along with the massive body of endnotes!

So is it a revolution? I think so. Wolfram shows us a world that is a computational race between observer and observed, where mathematics is (at best) a computational shortcut in this race, and where even relatively simple systems can surpass a complexity threshhold which renders mathematics largely unhelpful. Wolfram makes his case while guiding us through some of the vaguest corners of mathematics and science. While it is not easy to know how current or applicable Wolfram is in all of the dozens of topics he touches upon, I can say that in the areas that I am familiar with, he is either right on or actually introducing major new ideas. His proposal that the universe is discrete rather than continuous is bold to say the least. And his challenge to mathematics is just awesome.

I would say it is a revolution and a lot of fundamental assumptions and models in science will need to be brushed off and updated. There will be a lot more computer modellers out there who won't get nervous if their systems are no longer mathematically provably correct. Also maybe this book will hasten efforts to develop new types of computing - certainly it raises big questions about the potential of quantum computing.

It is worth noting, however, than while he does a pretty convincing job of demonstrating the near-universality of computational irreducibility, he asserts but does not prove a more sweeping principle of computational equivalence.

It will be very interesting to see how the collective reaction plays out. In my opinion comments about ego or grammar here are completely beside the point. For that matter, I wouldn't even say that this book is really about cellular automata, per se.

Rating:
Summary: The Hermit Scientist
Review: Long before "A New Kind of Science," way back in 1950, Martin Gardner (the math games columnist for Scientific American) published an article entitled "The Hermit Scientist," his first publication of a skeptical nature. In 1952 he expanded it into a book called "In the Name of Science" now sold as "Fads and Fallacies in the Name of Science." The book is reviewed in the March 2002 issue of Scientific American by Michael Shermer. Gardner, through Schermer, provide these points to ponder when considering Wolfram and his new book:

"How can we tell if someone is a scientific crank? Gardner writes: (1) "First and most important of these traits is that cranks work in almost total isolation from their colleagues." Cranks typically do not understand how the scientific process operates...that they need to try out their ideas on colleagues, attend conferences and publish their hypotheses in peer-reviewed journals before announcing to the world their startling discovery. Of course, when you explain this to them they say that their ideas are too radical for the conservative scientific establishment to accept. (2) "A second characteristic of the pseudo-scientist, which greatly strengthens his isolation, is a tendency toward paranoia," which manifests itself in several ways: (1) He considers himself a genius. (2) He regards his colleagues, without exception, as ignorant blockheads.... (3) He believes himself unjustly persecuted and discriminated against. The recognized societies refuse to let him lecture. The journals reject his papers and either ignore his books or assign them to "enemies" for review. It is all part of a dastardly plot. It never occurs to the crank that this opposition may be due to error in his work.... (4) He has strong compulsions to focus his attacks on the greatest scientists and the best-established theories. When Newton was the outstanding name in physics, eccentric works in that science were violently anti-Newton. Today, with Einstein the father-symbol of authority, a crank theory of physics is likely to attack Einstein.... (5) He often has a tendency to write in a complex jargon, in many cases making use of terms and phrases he himself has coined."

I would have loved to have been able to read an early copy of "Origin of Species" or "Principia Mathematica" when first released. So I hoped "A New Kind of Science" would be an opportunity to be there when the world changed during my lifetime. If Gardner's criteria are accurate, this ain't the book.

Rating:
Summary: The pinnacle of Ironic Science...
Review: Subtitled: Welcome back to the ether.

To paraphrase Wittgenstein, where to start without going further back? Well, some comments on the 'packaging': very pretty. Lots of trees are going to die for this monumental ode to the problem at the heart of science and unfortunately their deaths are not going to advance the state of knowledge at all. Yes, the quality of the book is impeccable and the typeface, general layout and profuse use of illustrations make it a bargain for the price. One must realize that approximately 1/3 of the book are the additional notes that Wolfram has decided to include to demonstrate how his thesis can be applied to "everything" that has been done in science. But more on that later...

Wolfram has managed to neatly epitomize all that is wrong with science right now. It is unfortunate he appears not to have heard about Robert Rosen in his flurry of referencing and decade of 'researching' since otherwise he might have decided to move on to something actually useful. Or perhaps if he had read Perlovsky or Solomonoff he might have come to some different, and again, useful conclusions.

Wolfram, amongst the very numerous self-references, advances two main ideas that he sees embodying "the new science". The first is the idea that simple programs can have very complex outputs - the concept of the complexity of the output of something like Rule 30 cellular automatons baffling all attempts at compression. The second is his "new" theory of computational equivalence.

Well, there is some news from those sad 'hacks' on the sidelines: the first "idea" is nothing new and, in fact, is simply a logical extension of the framework chosen for the analysis and the "theorem" is perhaps the best illustration of what philosophers refer to as the "gem": tautology. That is, Wolfram's glorious theorem results from his choice of axioms and should not be at all surprising unless one is either too stupid to realize this or else is bent on a program of solipsism.

The universe is not mechanistic. If it were then Wolfram's theory must be taken as an axiom. The first idea, that simple programs can produce results just as complex as very complicated programs, is a logical extension of what we already know about mechanistic frameworks. All of this can easily be demonstrated in a number of ways but perhaps a quick look at the "problem" of induction in formal systems best illustrates why.

Solomonoff's work on Kolmogorov/Chaitin complexity points out that "for practical [computable] induction it is necessary to use computable approximations" (comment added by me). That is, real induction, as practiced by living organisms, is non-computable. AIP, Algorithmic Probability, readily admits that true induction cannot be computable for the moment that one imposes any syntactical-only solution one has already constrained the ability to perform induction. This is the real problem in a mechanistic universe: you are stuck with deduction and a very limited version at that. Now the AIP folks have done lots of work here using rather complex programs to try to escape the problem, like Wittgenstein's fly in the bottle.

So it should be no surprise that at the other end of the extreme, a very small program, one should find great richness in output since one is attempting to impose fewer constraints from the start. But there is news from the outside world that Wolfram should have checked before launching this sad footnote: it won't work. I suggest Perlovsky if one wishes to understand why.

In fact, the AI people realized this limitation a while ago and have feverishly been trying to find ways of "stepping outside" of the mechanistic framework. The crux of this is the simple fact that you need to be non-computable if you want to join the ranks of the living. That is, entailment (causality) is impoverished in a mechanistic framework: how do you ever stop asking "what entails X" without invoking magic? Go and find a copy of Rosen's "Life Itself" and really learn something new.

And this is evident throughout Wolfram's book. We have the ether coming back (he proposes some type of nodal network as the fundamental building block for the universe) and a complete lack of discussion of any of the major problems facing science, particularly physics, such as what is life, why inertial mass equals gravitational mass and why we have so few genomes when mechanistic theory says we should. Even consciousness does not get discussed anywhere in his section on the nature of analysis and perception other than the ugly word "representation" slipping in. A cellular automaton representing to what (go read your Tallis)? One feels we have beaten this horse enough already to even believe it can still be presented by anyone with any serious pretensions to discussing the topic.

This is the worse part of the whole enterprise. There is no new science here, only the same problems with some new band-aids. One hopes we will finally begin to suspect why we are not making more advances and come back to what is crucial: the choice of the framework limits the solution set of the problem. It is time for some new frameworks, not absurd extensions to the existing set.

Don't bother with buying this book, there will be some bargain-basement copies available in a short time.

Rating:
Summary: An Art science - not real science for real problems
Review: I have ordered the book but it has not come yet, but I have been following CA (cellular automata) since it was introduced in other Mathematica books that I have. Based on other reviewers I found, sometimes when I look at to myself too, Wolfram is just playing in his imagination with his computer in playground and lost of touch with "the real" science to solve real problems.

This is like neural network program (this is better than CA, I think), like a black box that does not help scientists or engineers to understand how a system works. He (Wolfram), I bet, does not understand reaction path in biochemical or material design for electronic microchips that build our world.

It is more like an imagination to see a cloud like an airplane, to see certain algorithms produce a crystal structure but does not understand the molecule structure that build the crystal even design the molecule with complicated mathematics.

After all, I will let my imagination follow his imagination and to see if it is useful to solve real problems or not. Maybe CA is just useful as an art. Yes ! It is just a mathematical art. Yes, it is a new kind of science, it is called an art science.

I hope I can enjoy this like a music or like mathematical recreation in old scientific american magazines.