A couple of years ago I was reading "New Kind of Science" (NKS) by S. Wolfram, and it presented lot of interesting ideas for a young Physics undergraduate. Now that I am studying Mathematics however, I realise that many ideas of NKS seem to be not so novel afterall, and contained in the Maths literature already, yet with different names.

Is NKS actually presenting novel material?

If yes, what in particular?

If not, what authors have already done this kind of work? Is NKS a "repackaging" of ideas?

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    $\begingroup$ A new kind of self-aggrandisement. $\endgroup$
    – vadim123
    Commented Apr 10, 2015 at 14:25
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    $\begingroup$ Wolfram has a reputation as a bit of an egomaniac. So I'd take it with a grain of salt. Here are some quotes he wrote about himself. "Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." and "Stephen Wolfram is the creator of Mathematica, and a well-known scientist. He is widely regarded as the most important innovator in technical computing today, as well as one of the world's most original research scientists." That's just not the kind of thing you say about yourself. $\endgroup$ Commented Apr 10, 2015 at 14:26
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    $\begingroup$ May be relevant: ams.org/notices/200302/fea-gray.pdf $\endgroup$ Commented Apr 10, 2015 at 14:27
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    $\begingroup$ This may be flagged as offensive...but I've always thought of Stephen Wolfram as a bit of a douche. See Gregory's comments for more details and the litany of egotestical remarks made by Wolfram. He's why we can't have nice things...and why Wolfram|Alpha pro sucks. $\endgroup$ Commented Apr 10, 2015 at 14:36
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    $\begingroup$ Mr. Stephen Wolfram certainly isn't “the most important innovator in scientific and technical computing today” or “the world's most original research scientists”... I am ! :-| $\endgroup$
    – Lucian
    Commented Apr 10, 2015 at 18:04

3 Answers 3


I think the answer to this question is, unfortunately, a little difficult. As many will point out, Wolfram is beyond egotistical and that fact definitely colors the reception of the book. There is a long list of (mostly negative) reviews here. The negativity reaches its apex in the review by Cosma Shalizi. There are some positive reviews as well, though, such as the one by Rudy Rucker.

So, what is NKS? Most correctly, I would say that it is a broad and semi-popular account of Wolfram's work in cellular automata. For those in the field, it clearly builds on the work of others. There are references to this fact in the text but it could certainly be made more explicit. To more clearly see Wolfram's own contributions, you might examine his earlier collection of papers Cellular Automata and Complexity. Rucker lists several of these in his review as well. An honest assessment of his earlier contributions reveal that he is certainly an important researcher in the field and most researchers would be happy to have his body of work. Given the clear antecedents, however, I think that "New Kind of Science" is a definite overstatement. He is in no danger of winning an Abel or Nobel prize.

So, the truth of NKS is certainly somewhere in the huge gulf between a revolutionary (well) new kind of science and (as Shalizi puts it) "utter bat shit insanity".

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    $\begingroup$ Shalizi's review might be one of the most fun literature reviews I've ever read. $\endgroup$
    – user98602
    Commented Apr 10, 2015 at 21:08
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    $\begingroup$ @MikeMiller I actually like the review just because I think it's hysterical, in the same way that harsh reviews can be funny. I don't particularly agree with it, though. $\endgroup$ Commented Apr 11, 2015 at 1:20
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    $\begingroup$ @Newb Of course. But then, a major point that I'm trying to get across in my answer is that, ideally, evaluation of the person should not affect evaluation of his work. As such, this seems to be the wrong place to expand on those experiences. $\endgroup$ Commented Apr 11, 2015 at 10:35
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    $\begingroup$ @DavidRicherby If I wasn't interested, I wouldn't have answered. :) Perhaps, you're implying that I have a conflict of interest? As I am not currently employed at Wolfram Research, I don't believe that I do. I make heavy use of Mathematica in my work but that's hardly a secret and, again, I think that is very separate from my evaluation of NKS. $\endgroup$ Commented Apr 11, 2015 at 14:09
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    $\begingroup$ I see no reason to remove a quote that uses somewhat colorful language (while not being excessive), especially in this case as the author of the post does not even embrace the quote, but instead presents it as an extreme view that in his opinion does not describe the work adequately. (At least this is my understanding of the post.) $\endgroup$
    – quid
    Commented Jun 1, 2018 at 15:44

After reading the reviews that were linked in the comments [1] and @Mark's helpful answer[2][3], I came to a a few conclusions, that answer my questions.

First, let's get something out of the way. Stephen Wolfram is definitely a polariser of opinion. Plus his way of presenting himself and his work are not in the canons of the scientific literature and that is bound to make people upset. Plus, the habit of not mentioning other people's contributions and the legal actions make it more so. But the question is not about Wolfram, the question is about the book and the ideas.

Novel Ideas

It seems to me that the most novel aspect of NKS is the proposed "paradigm shift". Namely, that to proceed in Mathematics and Physics we should abandon constructing more complicated and sophisticated theories. Instead, we should focus our attention to simple programs, such as the Cellular Automata (CA), and instead of trying to prove properties of these, we can learn about them by looking at outputs of simulations.

The validity of this paradigm remains to be proven because, according to the 3 reviews I have read, no real predictions have been made.

Another novel part of the book seems to be the "Principle of Computational Equivalence". It basically means according to [1] that there are two classes of computations: the simple/easily predictable ones, and all the "computationally irreducible", equivalent to each other. This implies that all CA complex enough, or rather, complex looking enough, are Turing equivalent. This principle, apart from not being well defined in the book, also seems to be false, according to the reviewers.

Work has already been done

Turns out a lot of work had been done on CA at the time of publishing. This has been done with the "Old Kind of Science", i.e. with proofs and all. In particular Conway's work on the Game of Life, and the fact of it being Turing equivalent. NKS does contain a lot of info and discussion about 2D CA and other programs, with links to the real world. Some of this is original, some is not.

Then there is the work of mathematicians in complexity theory that can be said to touch the same concepts as NKS.

In the end, NKS does appear to be a repackaging of ideas, in order to call to a new paradigm of doing science. If this will work, remains to be proven.


[1] A very useful, balanced and justified review. Recommended. http://www.ams.org/notices/200302/fea-gray.pdf

[2] Negative review. The arguments about the content are convincing. http://bactra.org/reviews/wolfram/

[3] Positive review. Not as balanced in my opinion. I was not convinced by it. http://sjsu.rudyrucker.com/~rudy.rucker/wolfram_review_AMM_11_2003.pdf

  • $\begingroup$ A reasonable assessment! I would point out, though, that the many of the ideas that he "repackaged" are, in fact, his own. From a personal perspective, I've found his numbering schemes of CAs to be quite useful and his paper Geometry of Binomail Coefficients to be delightful. $\endgroup$ Commented Apr 11, 2015 at 1:25
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    $\begingroup$ @MarkMcClure I don't think anyone would complain about Wolfram repackaging his own ideas: that is inevitable if one is to write a book popularizing those ideas. The problems come when other people's ideas are repackaged. Most of the reviews I've read agree that Wolfram did some great research on CAs in the '80s. $\endgroup$ Commented Apr 11, 2015 at 13:33

The problem is that asking if something is novel in science is actually very tricky because almost every scientific idea is based on previous work. Therefore, I don't think it is very valuable to question whether something is novel or not because it most certainly is not. However, you can ask if a particular work offers something interesting or particularly noteworthy. I will enumerate a few prominent ideas explained in NKS, including previous work (which is more or less what you asked):

  1. A proposed method to analyse complex systems is to explore the computational universe to see what simple programs are able to do and document their behavior using experimental or analytic methods. Previous work: Edward Fredkin and Konrad Zuse proposed the idea that the universe might be a cellular automaton. In 1997, Schmidhuber described a Turing machine capable of computing all possible histories for the universe based on physical laws.

  2. Principle of computational irreducibility. Systems that display complex behavior can not be reduced and we need to run the experiment to see the outcome.

  3. Principle of computational equivalence. Most sufficiently complex systems are computationally equivalent.

  4. Turing completeness of Rule 110. Wolfram conjectured this in 1985. Matthew Cook (who worked as a research assistant to Wolfram) published a proof in 2000 and a legal battle ensued due to a violation of an NDA. Previous work: Conway's Game of Life, Von Neumann's idea of self-replicating machines.

  5. Conjecture that the 2-state 3-symbol Turing machine is universal. Alex Smith proved this conjecture in 2007.

There are other interesting ideas but most of them are extremely speculative and unlikely to be confirmed or falsified by evidence any time soon.

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    $\begingroup$ Thanks for the useful reply. The Reviews I have read say that 2. and 3. in your reply are actually false. They don't present a proof in the review though. Do you know of anybody that proved that? $\endgroup$
    – Andrea
    Commented Apr 11, 2015 at 9:39
  • $\begingroup$ Try not to put much weight on reviews (positive or negative reviews). In this case, reviews are not really appropriate because they are more journalistic in nature than scientific. As far as I know, 2 and 3 have not been proven wrong. They are incompatible with other theories or observations to the same extent that pretty much any theory is incompatible with something else. Instead, we should ask "Does the theory predict something specific?" If so, then we should be able to falsify such predictions. $\endgroup$
    – r_31415
    Commented Apr 11, 2015 at 15:53
  • $\begingroup$ A concrete question: NKS claims that CA rule 30 is computational irreducible, and the principle of computational equivalence would then imply that rule 30 is also Turing equivalent. (This of course assuming that being computationally irreducible means satisfying the "complex enough" criterion) .This could be falsified or confirmed by proof. Has this been done? $\endgroup$
    – Andrea
    Commented Apr 11, 2015 at 16:06
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    $\begingroup$ NKS claims CA rule might be computational irreducible but there is no proof of this, in no small part due to the lack of a well-defined notion of what computational irreducibility actually means. There is also no proof that rule 30 is Turing complete (unlike rule 110). If it is truly a property of every "complex" system in the universe, then it would be pointless to try to define it precisely, in the same way that we can't really define inertia and instead, we generally accept it as a property of our universe. $\endgroup$
    – r_31415
    Commented Apr 11, 2015 at 18:44
  • $\begingroup$ @RobertSmith Actually, most of the reviews linked from this page are scientific (in particular, Lawrence Gray's review in the Notices of the AMS and the review by Cosma Shalizi, who's worked on CAs). This kind of review is such an important part of the scientific process that it's a mandatory part of getting a paper published in a reputable journal. And all the scientific reviews of ANKS that I've read (admittedly, just a handful) have found scientific flaws with the book. $\endgroup$ Commented Apr 12, 2015 at 12:48

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