Living a Paradigm Shift: Looking Back on Reactions to A New Kind of Science

(This is the second of a series of posts related to next week’s tenth anniversary of A New Kind of Science. The previous post covered developments since the book was published; the next covers its future.)

“You’re destroying the heritage of mathematics back to ancient Greek times!” With great emotion, so said a distinguished mathematical physicist to me just after A New Kind of Science was published ten years ago. I explained that I didn’t write the book to destroy anything, and that actually I’d spent all those years working hard to add what I hoped was an important new chapter to human knowledge. And, by the way—as one might guess from the existence of Mathematica—I personally happen to be quite a fan of the tradition of mathematics.

He went on, though, explaining that surely the main points of the book must be wrong. And if they weren’t wrong, they must have been done before. The conversation went back and forth. I had known this person for years, and the depth of his emotion surprised me. After all, I was the one who had just spent a decade on the book. Why was he the one who was so worked up about it?

And then I realized: this is what a paradigm shift sounds like—up close and personal.

I had been a devoted student of the history of science for many years, so I thought I knew the patterns. But it was different having it all unfold right around me.

I had been building up the science in the book for the better part of 20 years. And I had been amazed—almost shocked—at many of the things I’d discovered. And I knew that communicating it all to the world wouldn’t be easy.

In the early years, I’d just done what scientists typically do, publishing papers in academic journals and giving talks at academic conferences. And that had gone very well. But after I built Mathematica, I started being able to discover things faster and faster. I had a great time. And pretty soon I had material for many tens—if not hundreds—of academic papers. And what’s more, the things I was discovering were starting to fit together, and give me a whole new way of thinking.

What was I going to do with all this? I suppose I could have just kept it all to myself. After all, by that time I was the CEO of a successful company, and certainly didn’t make my living by publishing research. But I thought what I was doing was important, and I really liked the idea of giving other people the opportunity to share the enjoyment of the things I was discovering. So I had to come up with some way to communicate it all. Publishing lots of piecemeal academic papers in the journals of dozens of fields wasn’t going to work. And instead it seemed like the best path was just to figure out as much as I could, and then present it to the world all together in a coherent way. Which in practice meant I had to write a book.

Back in 1991 I thought it might take me a year, maybe two, to do this. But I kept on discovering more and more. And in the end it took nearly 11 years before I finally finished what I had planned for A New Kind of Science.

But whom was the book supposed to be for? Given all the effort I had put in, I figured that I should make it as widely accessible as possible. I’m sure I could have invented some elaborate technical formalism to describe things. But instead I set myself the goal of explaining what I’d discovered using just plain language and pictures. And as it turned out, countless times doing this helped me clarify my own thinking. But it also made it conceivable for immensely more people to be able to read and understand the book.

I knew full well that all this was very different from the usual pattern in science. Most of the time, front-line research gets described first in academic papers written for experts. And by the time it gets into books—and especially broadly accessible ones—it’s not new, and it’s usually been very watered down. But in my case, many years of front-line discoveries would first get described in a broadly accessible book.

Even in the preface I wrote for the book, I expressed concern about how specialist scientists would react to this. But my personal decision was that it was worth it. And when the book came out, it indeed for the most part worked out spectacularly. Most important as far as I was concerned was that a huge spectrum of people were able to read and understand the book. And in fact lots of people specifically thanked me for writing the book so it was accessible to them.

Many specialist scientists were also highly enthusiastic about the book. But much as I had expected, there was a certain component who just assumed that anything presented in a bestselling book couldn’t really be important new science—and pretty much stopped there.

And then there were others for whom the book just seemed irrelevant; they were happy with their ways of doing and thinking about science, and they weren’t interested—at least at that time—in any particular injection of new ideas.

But what about people whose work was in some way or another directly connected to issues discussed in the book? I have to say that by and large I expected a very positive reaction from such people. After all, I had put all this meticulous work into studying things that they were interested in—and I believed I had come up with some exciting results. And what’s more, I personally knew many of these people—and lots of them had benefited greatly from my efforts to develop the field of complex systems research some 15 or so years earlier.

So discussions like the one I described at the beginning of this post at first came as something of a shock. Of course, I had spent quite a few years as an academic, so I was well aware of the petty bickering and backstabbing endemic to that profession. But this was something different: this was people who were somehow deeply upset by what I was doing.

Some of the more sophisticated and forthright of them were pretty explicit with me, at least in person. Typically there was a surface reason for their reaction, and a deeper reason. Sometimes the surface reason related to content, sometimes to form. Those who discussed content fell into two main groups. The first—particularly populated by physicists—said that their immediate reason for being upset was basically that “If what you’re doing is right, we’ve spent our whole careers barking up the wrong tree”. The second group—particularly populated by people who’d studied areas related to complexity—basically said: “If people buy into what you’ve done, it’ll overshadow everything we’ve done”.

To me what was perhaps most striking was that these reactions were often coming from some of the best-established and most senior people in their fields. I suppose at some level it was flattering, but I had certainly not expected this kind of insecurity—not least because I thought it was completely unfounded. Yes, I believed new approaches were needed—that’s why I’d spent so many years developing them. But I saw what I had done as complementing and adding to what had been done before, not replacing or overturning it.

And then there was the matter of form. “You’ve done something that’s academic-like, but you haven’t played by academic rules.” It was true: I wasn’t an academic and I wasn’t operating according to the constraints of academia; I was just trying to invent the best possible ways to do things, given my resources and the discoveries I was making.

A typical issue that came up was how the book was vetted or checked. In academia, there’s the idea that “peer review” is the ultimate method of checking anything. And perhaps in a world where everyone has infinite time, and nobody operates according to their own self-interest, this might be true. But in reality, peer review is fraught with error, often quite corrupt, and even in the best case strongly biased toward avoiding new ideas and maintaining the status quo. And for a piece of work as large, broad and complex as A New Kind of Science, even the basic mechanics of it seemed completely impractical.

So what did I do instead? It was a big exercise in perfectionism. First, we built a large system for automated testing, modeled on what we’d developed over the course of many years for Mathematica. And then we developed a process for getting experts in different areas to look at every page of the book, checking as far as possible every detail. So how did it work out? Impressively well. For even now, 10 years later, after every page of the book has been read and scrutinized by huge numbers of people, and every computational result has been reproduced many times, in all the 1280 pages of the book no errors much beyond simple typos have come to light.

One of the many challenges with the book was the practicality of actually printing and publishing it. Early on, I had hoped that one of the large publishers who wanted to publish the book would be able to handle it. But after awhile it became clear that their production methods and business models could not realistically handle the level of visual quality that the content of the book required. And so, somewhat reluctantly at first, I decided to have Wolfram Media do the publishing instead.

This certainly allowed the book to be printed at higher quality, and to be sold more cheaply. But the setup definitely seemed not to please some academics—particularly, I suspect, because it made clear that the book was simply beyond the reach of any academic network, however powerful that network might be in the academic world. Even if a couple of times I did hear things like “I’m so shocked about [some aspect of your book] that I’m going to campaign my university not to use Mathematica”.

If one looks at a standard academic paper, one of its prominent elements is always a list of references—in principle a list of authorities for statements in the paper. But A New Kind of Science has no such list of references. And to some academics this seemed absolutely shocking. What was I thinking? I always consider history important—both for giving credit and for letting one better understand the context of ideas. And when I wrote A New Kind of Science, I resolved that rather than just throwing in disembodied references, I would actually do the work of trying to unravel and explain the detailed histories of things.

And the result was that of the nearly 300,000 words of notes at the back of the book, a significant fraction are about history. I did countless hours of (often fascinating) primary interviews and went through endless archives—and in the end was rather proud of the level of historical scholarship I managed to achieve. And when it came to traditional references I figured that rather than using yet more printed pages, I should just include in the notes appropriate names and keywords, from which anyone—even with the state of web search in 2002—could readily find whatever primary literature they wanted, at greater depth and more conveniently than from lists of journal page numbers.

When A New Kind of Science came out, I kept on hearing complaints that it didn’t refer to this or that person or piece of work. And each time I would check. And to my frustration, in almost every case it was right there in the book—with a whole extended historical story. And it wasn’t as if when people actually read it, they disagreed with the history I’d written. Indeed, to the contrary, many times people told me they were impressed at how accurate and balanced my account was—and often that they’d learned new things even about pieces of history in which they were personally involved.

So why were people complaining? I think it was somehow just disorienting for academics not to be able to glance down a definite “references section”—and see papers they’d authored or otherwise knew. But I’m pretty sure it was more an emotional than a functional issue. And as one indication, after the book came out we did the experiment of putting on the web—in standard academic reference format—the list of the 2600 or so books that I’d used in writing A New Kind of Science. And from our web statistics we know that vastly fewer people used this than for example the online version of even one chapter’s worth of historical notes. (Even so, as a matter of completeness, I’m hoping one day to link all my archives of papers to the online book.)

I suppose another feature of the book that did not endear it to some academics was the very intensity of positive reaction that accompanied its release. Within days there were hundreds of articles in the media describing the ideas in the book—with journalists often doing an impressive job of understanding what the book had to say. And then, mostly slightly later, reviews started to appear. Some were detailed and well reasoned; others were quite rushed, and often seemed mainly to be emotional responses—probably more based on reading earlier reviews than on the reading of the actual 1280-page book itself. And after such a positive initial wave of media attention, later (often “catch up”) coverage inevitably tended to swing to the more negative.

Reviews of A New Kind of ScienceWhen the book came out, I had all the reviews we could find diligently archived. And I always intended at some point to systematically read them. But somehow a decade has gone by, and I have not done so. And as I write this post, I have on my desk a daunting pile of printed copies of reviews, as thick as the book itself. But back when they were archived, for reasons I don’t now know, each review was at least put into a “star-rating” category, which we can now use to make a pie chart. And while I’m not sure just how much these statistics really mean, it is perhaps interesting that positive—or at least neutral—reviews overall significantly outweighed negative ones.

So what about the negative reviews? There are certainly some colorful quotes in them. “Why has this undoubtedly brilliant, worthily successful man written such a silly book?… I think it… likely that the book will be forgotten in a few months.” “There’s a tradition of scientists approaching senility to come up with grand, improbable theories. Wolfram is unusual in that he’s doing this in his 40s.” “Is this stuff really that important? Well… maybe. Frankly, I doubt it.” “After looking at hundreds of Wolfram’s pictures, I felt like the coal miner in one of the comic sketches in Beyond the Fringe, who finds the conversation down in the mines unsatisfying: ‘It’s always just “Hallo, ‘ere’s a lump of coal.”’” “With extreme hubris, Wolfram has titled his new book on cellular automata ‘A New Kind of Science’. But it’s not new. And it’s not science.” “It was not the first time the names Wolfram and Newton have been mentioned in the same breath, and I suppose it might be taken as further evidence of an ego bursting all bounds.” And, perhaps my favorite, a whole review simply titled “A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity”.

Realistically, much of the space in these reviews was not devoted to discussing the actual content of the book. High on the list of issues they discussed was that the book had not gone through an academic peer review process, and so could “not be considered an academic work” (not that it was meant to be). Then there were the complaints about the absence of explicit lists of references—often rather misleadingly with no mention of all the detailed historical notes, or perhaps a grudging comment that they were in too small a font.

Another common complaint was that the book was somehow just too grandiose. And for sure, any book with a title like “A New Kind of Science” runs the risk of being characterized that way. To be clear, I believed—and very much still believe—that what’s in A New Kind of Science is very important. In presenting it, though, I suppose I could have somehow tried to hide this. But I was fairly sure that doing so would have a bad effect on people’s ability to understand what was in the book.

The issue is quite familiar to those of us who have written lots of documentation for computer systems: if you have big ideas to communicate, you have to prime people for them—or they inevitably get confused. Because if people think something is a small idea, they’ll try to understand it by straightforwardly extending what they already know. And when that doesn’t work, they’ll just be confused. On the other hand, if you communicate up front that something is big and important, then people will make the effort to understand it on its own terms—and will much more readily be able to place and absorb it. And so—well aware of the potential for being accused of grandiosity—I made the decision that it was better for the science if I was explicit about what I thought was important, and how important I thought it was.

Looking through reviews, there are some other common themes. One is that A New Kind of Science is a book about cellular automata—or worse, about the idea (not in fact suggested in the book at all) that our whole universe is a giant cellular automaton. For sure, cellular automata are great, visually strong, examples for lots of phenomena I discuss. But after about page 50 (out of 1280), cellular automata no longer take center stage—and notably are not the type of system I discuss in the book as possible models for fundamental physics.

Another theme in some reviews is that the ideas in the book “do not lead to testable predictions”. Of course, just as with an area like pure mathematics, the abstract study of the computational universe that forms the core of the book is not something which in and of itself would be expected to have testable predictions. Rather, it is when the methods derived from this are applied to systems in nature and elsewhere that predictions can be made. And indeed there are quite a few of these in the book (for example about repeatability of apparent randomness)—and many more have emerged and successfully been tested in work that’s been done since the book appeared.

Interestingly enough, the book actually also makes abstract predictions—particularly based on the Principle of Computational Equivalence. And one very important such prediction—that a particular simple Turing machine would be computation universal—was verified in 2007.

There are reviews by people in specific fields—notably mathematics and physics—that in effect complain that the book does not follow the methodology of their field, which is of course why the book is titled “A New Kind of Science”. There are reviews by various academics with varied “it’s been done before” claims. And there are a few reviews with specific technical complaints, about definitions or about phenomena like the emergence of quantum effects from essentially deterministic systems. Sometimes the issues brought up are interesting. But so far as I know not a single review brought up any specific relevant factual issue that wasn’t in some way already addressed in the book.

And reading through negative reviews, the single most striking thing to me is how shrill and emotional most of them are. Clearly there’s more going on than just what’s being said. And this is where the paradigm shift phenomenon comes in. Most people get used to doing science (or other things) in some particular way. And there’s a natural tendency to want to just go on doing things the same way. And there’s no issue with that for people whose subject matter is sufficiently far away—and who can successfully say, “I just don’t care about your new kind of science”. But for people whose subject matter is closer, that doesn’t work. And that’s when the knives really come out.

I have to say that to me (as I discussed in the previous post) the progress of NKS seems quite inexorable, and unavoidable—and indeed a decade after the publication of the book, seems to be progressing well. But I think some of the reviewers of A New Kind of Science convinced themselves that if what they wrote was negative enough they could derail things, and maybe allow their old directions and paradigms to continue unperturbed. And perhaps the mathematical physicist mentioned at the beginning of this post expressed their attitude most clearly when he said in our conversation: “You’re one of the most brilliant people I know… but you should keep out of science”.

There’s lots of analysis that could be done of the dynamics of opinions about A New Kind of Science. In 2002, there were fewer venues than today for public comments to be made. But I suspect that enough existed that it would be possible to piece together much of what happened. And I think it makes a fascinating study in the history of science.

I suppose I am myself by nature a positive person. And no doubt that is a necessary trait if one is going to do the kinds of large projects to which I have devoted most of my life. I am also at this point someone who is much more interested in just doing things than in other people’s assessments of what I do. No doubt others would find attacks on as important a personal project as A New Kind of Science dispiriting. But I have to say that first and foremost my reaction was one of scientific interest. Having studied so much history about paradigm shifts, I found it fascinating to be right in the middle of one myself.

I certainly wondered what one could predict from the dynamics of what was going on. And here history has some interesting lessons. For it suggests that perhaps the single best predictor of good long-term outcomes from potential paradigm shifts is how emotional people get about them at the beginning. So for NKS, all that early turbulence in the end just helps fuel my optimism for its long-term importance and success. And a decade out, not least with everything my previous post discussed, things indeed seem to be well on their way.


  1. “And then I realized: this is what a paradigm shift sounds like—up close and personal.” YES! I claim that modified M-theory with Wolfram’s mobile automation is the fundamental theory of the multiverse. The Rañada-Milgrom effect is validated by an easy scaling argument together with the work of Milgrom, McGaugh, and Kroupa. However, everyone ignores the Rañada-Milgrom effect. The Space Roar Profile Prediction yields a precise and decisive test for “A New Kind of Science” (NKS) Chapter 9. To define the Wolframian automaton requires the definitions of the Fredkin delivery machine and the Nambu transfer machine. J. Christian of Oxford, from 2007 to 2012, has made huge progress on his parallelized 7-sphere model, based on teleparallel gravity. Roughly speaking, J. Christian’s theory with the infinite nature hypothesis is the smoothing of the Nambu transfer machine. THIS IS AN ABSOLUTELY ESSENTIAL STEP FOR NKS CHAPTER 9. The Copenhagen interpretation is not entirely true but has some exceptions based on esoteric phenomena involving M-theory. Thus, Bell’s theorem is not 100% valid in all cases.
    J. Christian of Oxford claims to have disproved Bell’s theorem under his assumptions about quantum SU(8) correlations..
    From Joy Christian’s 2009 Azores talk:
    (1) “Bell did not respect the original EPR argument correctly.”
    (2) “Now, I am skipping about thirty-pages of calculations.”
    (3) “ … you can reproduce quantum mechanics locally and realistically …” (Joy Christian: Disproof of Bell’s Theorem”, FQXi Azores Conference 2009)
    J. Christian has been subjected to some vicious attacks, but time shall vindicate his work. He has a PhD with Abner Shimony as thesis advisor.
    IF GENERAL RELATIVITY EXPERTS polish up my paper on the Rañada-Milgrom effect and my paper on the flyby anomaly formula at AND PUBLISH THE IMPROVED PRESENTATIONS IN REFEREED JOURNALS then J. Christian and I would benefit enormously. Paradigm shifts can be rough.

  2. “… perhaps the single best predictor of good long-term outcomes from potential paradigm shifts is how emotional people get at the beginning of them.” YES! Is M-theory essential for the success of NKS Chapter 9? Has J. Christian of Oxford provided a way to establish the smoothing of the Nambu transfer function? Does the empirical validity of the Rañada-Milgrom effect strongly suggest that J. Christian’s parallelized 7-sphere model is empirically valid?
    Most of Christian’s papers can be found on .
    J. Christian has a PhD with Abner Shimony as thesis advisor.
    Scott Aaronson and Joy Christian have had a war of words that can be found online at Aaronson’s blog “Shtetl-Optimized”. Are we witnessing the birth of the physical interpretation of M-theory (or superstring theory)?
    “I don’t think that it has ever happened that a theory that has the kind of mathematical appeal that string theory has has turned out to be wrong. … And in any case I don’t see any alternative to string theory. I don’t see any other way of bringing gravity into the same general theoretical framework as all the other forces of nature.” — Steven Weinberg
    Joy Christian wrote, “… I demonstrated, convincing to me, that scalable quantum computing is impossible in the physical world.” I would say that Christian means that ALL SO-CALLED QUANTUM PHENOMENA, quantum tunneling, quantum wave/particle duality, superconductivity, etc. are examples of Christian’s theory of local realism and NOT the quantum theory. He means that, to his satisfaction, he has mathematically demonstrated GIVEN HIS ASSUMPTIONS ABOUT QUANTUM SU(8) STATES that quantum non-locality is false and EPR local realism is true. I would say that Christian has mathematically established the basis for M-theory and that the Copenhagen interpretation is almost always, but not quite, 100% correct. Bell’s theorem is indeed 100% true within the paradigm of the Copenhagen interpretation, but when the Copenhagen interpretation fails then so does Bell’s theorem. I claim that the empirical validity of the Rañada-Milgrom effect strongly suggests that CHRISTIAN IS CORRECT, UNBELIEVABLE AS IT MIGHT SEEM. I think that Scott Aaronson, Richard Gill, and Florin Moldoveanu have totally failed to understand Christian’s mathematical argument, which is logically sound. The problem is with the physical significance of the introduction of the parallelized 7-sphere. Thomas H. Ray, Edward Eugene Klingman, and Fred Diether are at least minimally competent mathematicians and they support J. Christian for very good reasons. All three of them say that Christian’s argument is mathematically valid. What does this have to do with M-theory? Seiberg-Witten M-theory is perhaps wrong because it implies that the Rañada-Milgrom effect is only approximately true. If modified M-theory with Wolfram’s mobile automaton is the way nature works, then Christian’s parallelized 7-sphere model is the smoothing of the Nambu transfer machine. If M-theory is empirically valid, and nature is infinite, then Christian’s theory of local realism is valid without NKS Chapter. Because M-theory is the only plausible hope for explaining the Rañada-Milgrom effect, it seems as if Christian is basically correct about the fundamental nature of quantum phenomena. The passage of time should dampen emotions and reveal the truth.

  3. thanks for this posting… i immersed myself into your book for a better part of 2 years… usually at my favorite coffee shop… some folks were gettting worried about me… and encouraged me to read other books… but the book was so fascinating… that i couldn’t put it down… now that wolframalpha is out… those same folks… are different towards me now that they see some results from the book… thanks again… for writing… a new kind of science… and as far as i am concerned… you are a new kind of isaac newton…

  4. “… a whole new way of thinking.” Does Stephen Wolfram need J. Christian’s parallelized 7-sphere model? In a review of NKS, Scott Aaronson of M.I.T. claimed that the ideas in NKS Chapter 9 seemed to violate Bell’s theorem. J. Christian seems to have proved that, assuming that quantum SU(8) states are nature’s way, Bell’s theorem is false in the paradigm of deterministic M-theory with Christian’s parallelized 7-sphere model. J. Christian shot himself in the foot by claiming that he had a “Disproof of Bell’s Theorem”. Bell’s theorem within the paradigm of the Copenhagen Interpretation IS mathematically valid and is probably physically valid. However, if nature is finite and digital, then the Copenhagen Interpretation should fail for some esoteric M-theoretical phenomena. Is J. Christian’s work mathematically sound?
    I received an e-mail from Thomas H. Ray (May 13th) in a reply to a question as to whether he understood the theory of teleparallel gravity. His answer was in part, “I’m not a PhD. I’m also not a physicist, so I am not familiar with many of the more esoteric theories. I do know the mathematics of classical mechanics and relativity quite well, however, …
    I got involved a little over a year ago, because when I became aware (on FQXi) that someone claimed to “disprove” a mathematical theorem, I was compelled to point out that one can’t do that and still use mathematics to describe the physical world. In the process, however, I read all the criticism of Joy’s framework, most of which revolved around a claim of an error that amounts to ” + 1 = – 1.” I recognized early on that there is no such error, that the analytical model obviates such an error.
    Aside from Joy himself and Fred Diether, I haven’t been in close contact with others who might have actually studied Joy’s research — and I have begun to get the impression that that is a very small set, anyway.
    My role is that of waging an honest defense of Joy’s mathematical framework, which I find to be self consistent. I know it’s a quixotic quest, for there isn’t a mathematician in the world who will admit the idea of “disproof” (including me).”
    I claim that the empirical validity of the Rañada-Milgrom effect strongly supports Christian’s theory of local realism.
    (1) According to Steven Weinberg, “String theory is the only game in town.” Attempts to introduce new physics probably must use M-theory in some form.
    (2) Dark matter exists either in the form of particles (approximate Rañada-Milgrom effect) or Milgrom’s MOdified Newtonian Dynamics (MOND) (precise Rañada-Milgrom effect).
    (3) The precise Rañada-Milgrom effect looks promising based upon the empirical evidence.
    (4) Dark matter particles are necessary for the empirical validity of Seiberg-Witten M-theory and perhaps any nondeterministic form of M-theory.
    (5) The precise Rañada-Milgrom effect implies the failure of nondeterministic (i.e. quantum mechanical) M-theory.
    (6) The failure of nondeterministic M-theory implies the success of deterministic M-theory, which in turn implies the success of deterministic M-theory with Christian’s parallelized 7-sphere model, because the latter is the simplest way to get a deterministic form of M-theory.
    Is there any feedback on this?
    What does all this have to do with NKS Chapter 9? In order for the success of modified M-theory computed by Wolfram’s mobile automaton, we need the Fredkin delivery machine and the Nambu transfer machine. We MUST have the smoothing of the Nambu transfer machine in order to get to M-theory. Deterministic M-theory with J. Christian’s parallelized 7-sphere model is the smoothing of the Nambu transfer machine.
    Today is May 14, 2012 CE, the tenth anniversary of the publication of NKS. Deterministic M-theory with Wolfram’s mobile automaton and Christian’s parallelized 7-sphere model should soon lead to the triumph of NKS Chapter 9. The Rañada-Milgrom effect is good news for M-theory, Stephen Wolfram, and Joy Christian.

  5. Dear Mr. Stephen Wolfram:

    Your work is a good & reliable as the Theory of Relativity was when Albert Einstein published his work. Albert Einstein did not care what critics had to say because the Theory of Relativity is reality whether critics like it or not!

    Albert Einstein merely forced his critics to prove the Theory of Relativity to be wrong, which of course, they could not do!

    Best Regards,

    John F. Remillard

  6. An excellent book marking the 10th. anniversary of Wolfram’s A New Kind of Science has recently been published by Springer Verlag under the title Irreducibility and Computational Equivalence: Ten Years After Wolfram’s A New Kind of Science, edited by H. Zenil. It is available through Amazon (, and other sellers, including Springer itself.

    Table of Contents:

    Gregory Chaitin

    Part I Mechanisms in Programs & Nature

    1. Cellular Automata: Models of the Physical World
    Herbert W. Franke

    2. On the Necessity of Complexity
    Joost J. Joosten

    3. A Lyapunov View on the Stability of Cellular Automata
    Jan M. Baetens & Bernard De Baets

    Part II Systems Based in Numbers & Simple Programs

    4. Hyperbolic Cellular Automata
    Maurice Margenstern

    5. Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System
    Karl Mainzer

    6. A New Kind of Science: Ten Years Later
    David H. Bailey

    Part III Social, Biological Systems & Technology

    7. A New Kind of Finance
    Philip Z. Maymin

    8. The Relevance of Computation Irreducibility and Computation Universality in Economics
    K. Vela Velupillai

    9. Exploring the Sources of and Nature of Computational Irreducibility
    Brian Beckage, Stuart Kauffman, Louis Gross, Asim Zia, Gabor Vattay and Chris Koliba

    10. Computational Technosphere and Cellular Engineering
    Mark Burgin

    Part IV Fundamental Physics

    11. The Principle of a Finite Density of Information
    Gilles Dowek and Pablo Arrighi

    12. Do Particles Evolve?
    Tommaso Bolognesi

    13. Artificial Cosmogenesis: A New Kind of Cosmology
    Clément Vidal

    Part V Behavior of Systems & the Notion of Computation

    14. An Incompleteness Theorem for the Natural World
    Rudy Rucker

    15. Pervasiveness of Universalities of Cellular Automata: Fascinating Life-like Behaviours
    Emmanuel Sapin

    16. A spectral portrait of the elementary cellular automata rule space
    Eurico L.P. Ruivo and Pedro P.B. de Oliveira

    17. Wolfram’s Classification and Computation in Cellular Automata Classes III and IV
    Genaro J. Martinez, Juan Carlos Seck Touh Mora and Hector Zenil

    Part VI Irreducibility & Computational Equivalence

    18. Exploring the Computational Limits of Haugeland’s Game as a Two-Dimensional Cellular Automaton
    Drew Reisinger, Taylor Martin, Mason Blankenship, Christopher Harrison, Jesse Squires and Anthony Beavers

    19. Unpredictability and Computational Irreducibility
    Hervé Zwirn and Jean-Paul Delahaye

    20. Computational Equivalence and Classical Recursion Theory
    Klaus Sutner

    Part VII Reflections and Philosophical Implications

    21. Wolfram and the Computing Nature
    Gordana Dodig-Crnkovic

    22. A New Kind of Philosophy. Manifesto for a Digital Ontology
    Jacopo Tagliabue

    23. Free Will and A New Kind of Science
    Selmer Bringsjord

    Cristian Calude