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{{Short description|Book by Stephen Wolfram}}
{{Undisclosed paid|date=March 2021}}
{{Infobox book
| name             = A New Kind of Science
| image            = A new kind of science.PNG
| caption          =
| author           = [[Stephen Wolfram]]
| illustrator      =
| cover_artist     = 
| country          = United States
| language         = English
| series           =
| subject          = [[Complex systems]]
| genre            = Non-fiction
| publisher        = [[Wolfram Media]]
| pub_date         = 2002
| media_type       = Print
| pages            = 1197 (Hardcover)
| isbn             = 1-57955-008-8
| oclc             = 856779719
| dewey            =
| congress         =
| website          = [https://www.wolframscience.com/nks A New Kind of Science, online]
}}

'''''A New Kind of Science''''' is a book by [[Stephen Wolfram]],<ref>{{cite magazine
 |last=Rosen
 |first=Judith
 |title=Weighing Wolfram's 'New Kind of Science'
 |url=https://www.publishersweekly.com/pw/print/20030113/40516-weighing-wolfram-s-new-kind-of-science.html
 |magazine=Publishers Weekly
 |year=2003}}</ref> published by his company Wolfram Research under the imprint Wolfram Media in 2002. It contains an empirical and systematic study of computational systems such as [[cellular automata]]. Wolfram calls these systems ''simple programs'' and argues that the [[Philosophy of science|scientific philosophy]] and methods appropriate for the study of simple programs are relevant to other fields of science.

== Contents ==
{{More citations needed section|date=April 2022}}

=== Computation and its implications===
The thesis of ''A New Kind of Science'' (''NKS'') is twofold: that the nature of [[computation]] must be explored experimentally, and that the results of these experiments have great relevance to understanding the [[physical world]].<ref>[https://serendipstudio.org/local/scisoc/emergence/DBergerNKS.pdf The World According to Wolfram]</ref>

===Simple programs===
The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules—essentially, elementary [[computer program]]s. In almost any class of a computational system, one very quickly finds instances of great complexity among its simplest cases (after a time series of multiple iterative loops, applying the same simple set of rules on itself, similar to a self-reinforcing cycle using a set of rules). This seems to be true regardless of the components of the system and the details of its setup. Systems explored in the book include, among others, cellular automata in one, two, and three dimensions; [[Mobile automaton|mobile automata]]; [[Turing machine]]s in 1 and 2 dimensions; several varieties of substitution and network systems; recursive functions; nested [[recursion (computer science)|recursive functions]]; [[combinator]]s; [[tag system]]s; [[register machine]]s; and [[Palindromic number|reversal-addition]]. For a program to qualify as simple, there are several requirements:
# Its operation can be completely explained by a simple graphical illustration.
# It can be completely explained in a few sentences of [[human language]].
# It can be implemented in a [[computer language]] using just a few lines of code.
# The number of its possible variations is small enough so that all of them can be computed.

Generally, simple programs tend to have a very simple abstract framework. Simple cellular automata, Turing machines, and combinators are examples of such frameworks, while more complex cellular automata do not necessarily qualify as simple programs. It is also possible to invent new frameworks, particularly to capture the operation of natural systems. The remarkable feature of simple programs is that a significant proportion of them can produce great complexity. Simply enumerating all possible variations of almost any class of programs quickly leads one to examples that do unexpected and interesting things. This leads to the question: if the program is so simple, where does the complexity come from? In a sense, there is not enough room in the program's definition to directly encode all the things the program can do. Therefore, simple programs can be seen as a minimal example of [[emergence]]. A logical deduction from this phenomenon is that if the details of the program's rules have little direct relationship to its behavior, then it is very difficult to directly engineer a simple program to perform a specific behavior. An alternative approach is to try to engineer a simple overall computational framework, and then do a [[brute-force search]] through all of the possible components for the best match.

Simple programs are capable of a remarkable range of behavior. Some have been proven to be [[universal computer]]s. Others exhibit properties familiar from traditional science, such as [[thermodynamics|thermodynamic]] behavior, [[continuum mechanics|continuum]] behavior, conserved quantities, [[percolation]], [[sensitive dependence on initial conditions]], and others. They have been used as models of [[traffic]], material fracture, [[crystal growth]], biological growth, and various [[sociology|sociological]], [[geology|geological]], and [[ecology|ecological]] phenomena. Another feature of simple programs is that, according to the book, making them more complicated seems to have little effect on their overall [[complexity]]. ''A New Kind of Science'' argues that this is evidence that simple programs are enough to capture the essence of almost any [[complex system]].

===Mapping and mining the computational universe===
In order to study simple rules and their often-complex behavior, Wolfram argues that it is necessary to systematically explore all these computational systems and document what they do. He further argues that this study should become a new branch of science, like [[physics]] or [[chemistry]]. The basic goal of this field is to understand and characterize the computational universe using experimental methods.

The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications are often the results of initial forays into the computational jungle. On the other hand, explicit proofs that certain systems compute this or that function are also admissible. Some forms of production are also in some ways unique to this field of study—for example, the discovery of computational mechanisms that emerge in different systems but in bizarrely different forms.

Another type of production involves the creation of programs for the analysis of computational systems. In the ''NKS'' framework, these themselves should be simple programs, and subject to the same goals and methodology. An extension of this idea is that the human mind is itself a computational system, and hence providing it with raw data in as effective a way as possible is crucial to research. Wolfram believes that programs and their analysis should be visualized as directly as possible, and exhaustively examined by the thousands or more. Since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science. But in general, Wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe, where they can be represented in their simplest forms, and then other fields can choose among these discoveries for those they find relevant.

===Systematic abstract science===
While Wolfram advocates simple programs as a scientific discipline, he also argues that its methodology will revolutionize other fields of science. The basis of his argument is that the study of simple programs is the minimal possible form of science, grounded equally in both [[abstraction]] and empirical experimentation. Every aspect of the methodology ''NKS'' advocates is optimized to make experimentation as direct, easy, and meaningful as possible while maximizing the chances that the experiment will do something unexpected. Just as this methodology allows computational mechanisms to be studied in their simplest forms, Wolfram argues that the process of doing so engages with the mathematical basis of the physical world, and therefore has much to offer the sciences.

Wolfram argues that the computational realities of the universe make science hard for fundamental reasons. But he also argues that by understanding the importance of these realities, we can learn to use them in our favor. For instance, instead of [[reverse engineering]] our theories from observation, we can [[enumeration|enumerate]] systems and then try to match them to the behaviors we observe. A major theme of ''NKS''  is investigating the structure of the possibility space. Wolfram argues that science is far too ad hoc, in part because the models used are too complicated and unnecessarily organized around the limited primitives of traditional mathematics. Wolfram advocates using models whose variations are enumerable and whose consequences are straightforward to compute and analyze.

===Philosophical underpinnings===

====Computational irreducibility====
Wolfram argues that one of his achievements is in providing a coherent system of ideas that justifies computation as an organizing [[Philosophy of science|principle of science]]. For instance, he argues that the concept of ''[[computational irreducibility]]'' (that some complex computations are not amenable to short-cuts and cannot be "reduced"), is ultimately the reason why computational models of nature must be considered in addition to traditional [[mathematical models]]. Likewise, his idea of intrinsic randomness generation—that natural systems can generate their own randomness, rather than using chaos theory or stochastic perturbations—implies that computational models do not need to include explicit randomness.

====Principle of computational equivalence====
Based on his experimental results, Wolfram developed the '''principle of computational equivalence'''<!--boldface per WP:R#PLA--> ('''PCE'''): the principle says that [[systems]] found in the [[natural environment|natural world]] can perform [[computation]]s up to a [[maximum|maximal]] ("universal") level of [[computational power]]. Most systems can attain this level. Systems, in principle, compute the same things as a computer. Computation is therefore simply a question of translating [[Input/output|input and outputs]] from one system to another. Consequently, most systems are computationally equivalent. Proposed examples of such systems are the workings of the human brain and the evolution of weather systems.

The principle can be restated as follows: almost all processes that are not obviously simple are of equivalent sophistication. From this principle, Wolfram draws an array of concrete deductions that he argues reinforce his theory. Possibly the most important of these is an explanation of why we experience [[randomness]] and [[complexity]]: often, the systems we analyze are just as sophisticated as we are. Thus, complexity is not a special quality of systems, like the concept of "heat", but simply a label for all systems whose computations are sophisticated. Wolfram argues that understanding this makes possible the "normal science" of the ''NKS'' paradigm.

===Applications and results===
''NKS'' contains a number of specific results and ideas, and they can be organized into several themes. One common theme of examples and applications is demonstrating how little complexity it takes to achieve interesting behavior, and how the proper methodology can discover this behavior.

First, there are several cases where ''NKS'' introduces what was, during the book's composition, the simplest known system in some class that has a particular characteristic. Some examples include the first primitive recursive function that results in complexity, the smallest [[universal Turing machine]], and the shortest [[axiom]] for [[propositional calculus]]. In a similar vein, Wolfram also demonstrates many simple programs that exhibit phenomena like [[phase transition]]s, [[conserved quantity|conserved quantities]], continuum behavior, and [[thermodynamics]] that are familiar from traditional science. Simple [[computational model]]s of natural systems like [[shell growth in estuaries|shell growth]], [[fluid turbulence]], and [[phyllotaxis]] are a final category of applications that fall in this theme.

Another common theme is taking facts about the computational universe as a whole and using them to reason about fields in a [[holistic]] way. For instance, Wolfram discusses how facts about the computational universe inform [[evolutionary theory]], [[SETI]], [[free will]], [[computational complexity theory]], and philosophical fields like [[ontology]], [[epistemology]], and even [[postmodernism]].

Wolfram suggests that the theory of computational irreducibility may explain how free will is possible in a nominally [[deterministic]] universe. He posits that the computational process in the [[brain]] of the being with free will is so [[Complexity|complex]] that it cannot be captured in a simpler computation, due to the principle of computational irreducibility. Thus, while the process is indeed deterministic, there is no better way to determine the being's will than, in essence, to run the experiment and let the being exercise it.

The book also contains a number of results—both experimental and analytic—about what a particular automaton computes, or what its characteristics are, using some methods of analysis.

The book contains a new technical result in describing the [[Turing completeness]] of the [[Rule 110]] cellular automaton. Very small Turing machines can simulate Rule 110, which Wolfram demonstrates using a 2-state 5-symbol [[universal Turing machine]]. Wolfram conjectures that a particular [[Wolfram's 2-state 3-symbol Turing machine|2-state 3-symbol Turing machine]] is universal. In 2007, as part of commemorating the book's fifth anniversary, Wolfram's company offered a $25,000 prize for proof that this Turing machine is universal.<ref>{{cite web | title=The Wolfram 2,3 Turing Machine Research Prize | url=http://www.wolframscience.com/prizes/tm23/ | access-date=2011-03-31| archive-url= https://web.archive.org/web/20110515032324/http://www.wolframscience.com/prizes/tm23/| archive-date= 15 May 2011 | url-status= live}}</ref> Alex Smith, a computer science student from [[Birmingham]], UK, won the prize later that year by proving Wolfram's conjecture.<ref>{{cite web | title=The Wolfram 2,3 Turing Machine Is Universal! | url=https://www.wolframscience.com/prizes/tm23/solution_news.html | access-date=2007-10-24}}</ref><ref>{{cite web | title=Technical Commentary [on Wolfram 2,3 Turing machine universality proof] | url=https://www.wolframscience.com/prizes/tm23/solution_technical.html | access-date=2007-10-24}}</ref>

==Reception==
{{POV section|date=December 2020}}
Periodicals gave ''A New Kind of Science'' coverage, including articles in ''[[The New York Times]]'',<ref>{{cite news
|last=Johnson|first=George
|title = 'A New Kind of Science': You Know That Space-Time Thing? Never Mind
|work= The New York Times
|date = 9 June 2002
|url=https://www.nytimes.com/2002/06/09/books/review/09JOHNSOT.html|access-date=28 May 2009}}</ref> ''[[Newsweek]]'',<ref>
{{cite news|last=Levy|first=Stephen
|title=Great Minds, Great Ideas
|work=Newsweek|date=27 May 2002
|url=https://www.newsweek.com/id/64625
|access-date=28 May 2009
}}</ref> ''[[Wired magazine|Wired]]'',<ref>{{cite magazine|last=Levy|first=Stephen
|title=The Man Who Cracked The Code to Everything ...
|magazine=Wired 
|date=June 2002
|url=https://www.wired.com/wired/archive/10.06/wolfram.html|access-date=28 May 2009
|archive-url= https://web.archive.org/web/20090527181907/http://www.wired.com/wired/archive/10.06/wolfram.html
|archive-date= 27 May 2009 | url-status= live}}</ref> and ''[[The Economist]]''.<ref>{{cite news
|title=The science of everything
|newspaper=The Economist|date=30 May 2002
|url=http://www.economist.com/printedition/displayStory.cfm?Story_ID=1154164|access-date=28 May 2009}}</ref> Some scientists, including Cosma Shalizi and Scott Aaronson,<ref>{{Cite web |title=Why Stephen Wolfram's research program is a dead end - SingleLunch |url=https://singlelunch.com/2020/04/23/why-stephen-wolframs-research-program-is-a-dead-end/ |access-date=2025-02-03 |website=singlelunch.com |language=en}}</ref> criticized the book and perceived a fatal flaw—that simple systems such as cellular automata are not complex enough to describe the degree of complexity in evolved systems, and observed that Wolfram ignored the research categorizing the complexity of systems. Although critics accept Wolfram's result showing universal computation, they view it as minor and dispute Wolfram's claim of a paradigm shift. Others found that the work contained valuable insights and refreshing ideas.<ref name=Rucker>{{cite journal
|last = Rucker|first = Rudy
|title = Review: A New Kind of Science
|journal=[[American Mathematical Monthly]]|pages = 851–61
|date=November 2003
|doi=10.2307/3647819
|url=https://sjsu.rudyrucker.com/~rudy.rucker/wolfram_review_AMM_11_2003.pdf |archive-url=https://web.archive.org/web/20040328034149/http://sjsu.rudyrucker.com/%7Erudy.rucker/wolfram_review_AMM_11_2003.pdf |archive-date=2004-03-28 |url-status=live
|access-date=28 May 2009
                                 |volume=110|issue = 9
|jstor = 3647819
}}</ref><ref name=Berry>{{cite journal
|last1 = Berry |first1 = Michael
|last2 = Ellis |first2 = John
|last3 = Deutch |first3 =David
|title = A Revolution or self indulgent hype? How top scientists view Wolfram
|journal=[[The Daily Telegraph]]
|date=15 May 2002
|url=http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry343.pdf |archive-url=https://web.archive.org/web/20120519134300/http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry343.pdf |archive-date=2012-05-19 |url-status=live|access-date=14 August 2012}}</ref> Wolfram addressed his critics in a series of blog posts.<ref>{{cite journal
|last = Wolfram|first = Stephen
|title = It's Been 10 Years: What's Happened with ''A New Kind of Science''?
|journal=Stephen Wolfram Blog
|date=7 May 2012|url= https://blog.stephenwolfram.com/2012/05/its-been-10-years-whats-happened-with-a-new-kind-of-science
|access-date=14 August 2012}}</ref><ref>{{cite journal
|last = Wolfram|first = Stephen
|title = Living a Paradigm Shift: Looking Back on Reactions to ''A New Kind of Science''
|journal=Stephen Wolfram Blog
|date=12 May 2012
|url=https://blog.stephenwolfram.com/2012/05/living-a-paradigm-shift-looking-back-on-reactions-to-a-new-kind-of-science
|access-date=14 August 2012}}</ref>

===Scientific philosophy===
A tenet of ''NKS'' is that the simpler the system, the more likely a version of it will recur in a wide variety of more complicated contexts. Therefore, ''NKS'' argues that systematically exploring the space of simple programs will lead to a base of reusable knowledge. But many scientists believe that of all possible parameters, only some actually occur in the universe. For instance, of all possible permutations of the symbols making up an equation, most will be essentially meaningless. ''NKS'' has also been criticized for asserting that the behavior of simple systems is somehow representative of all systems.

===Methodology===
A common criticism of ''NKS'' is that it does not follow established [[scientific methodology]]. For instance, ''NKS'' does not establish [[rigorous]] mathematical definitions,<ref>{{cite journal|last=Bailey|first=David|title=A Reclusive Kind of Science|journal=Computing in Science and Engineering|pages=79–81|date=September 2002|url = https://www.davidhbailey.com/dhbpapers/dhb-wolfram.pdf|access-date=20 March 2021}}
</ref> nor does it attempt to prove [[theorem]]s; and most formulas and equations are written in [[Mathematica]] rather than standard notation.<ref name="autogenerated1">{{cite journal|title=A Mathematician Looks at Wolfram's New Kind of Science|last=Gray|first=Lawrence|journal=Notices of the AMS|year=2003|volume=50|issue=2|pages=200–211|url=https://www.ams.org/notices/200302/fea-gray.pdf |archive-url=https://web.archive.org/web/20030308031909/http://www.ams.org/notices/200302/fea-gray.pdf |archive-date=2003-03-08 |url-status=live}}</ref> Along these lines, ''NKS'' has also been criticized for being heavily visual, with much information conveyed by pictures that lack formal meaning.<ref name=Berry/> It has also been criticized for not using modern research in the field of [[complexity]], particularly works on complexity from a rigorous mathematical perspective. And it has been criticized for misrepresenting [[chaos theory]].

===Utility===
''NKS'' has been criticized for not providing specific results that are immediately applicable to ongoing scientific research.<ref name=Berry/> There has also been criticism, implicit and explicit, that the study of simple programs has little connection to the physical universe and hence is of limited value. [[Steven Weinberg]] has pointed out that no real-world system has been satisfactorily explained using Wolfram's methods.<ref>{{cite news| url=https://www.thefreelibrary.com/In+search+of+a+scientific+revolution%3A+controversial+genius+Stephen...-a0107699603 | work=Science News | title=In search of a scientific revolution: controversial genius Stephen Wolfram presses onward | first=Peter | last=Weiss | year=2003}}</ref> Mathematician [[Steven G. Krantz]] wrote, "Just because Wolfram can cook up a cellular automaton that seems to produce the spot pattern on a leopard, may we safely conclude that he understands the mechanism by which the spots are produced on the leopard, or ''why'' the spots are there, or what function (evolutionary or mating or camouflage or other) they perform?"<ref>{{cite journal|first=Steven G. |last=Krantz |author-link=Steven G. Krantz |title=Review of ''A New Kind of Science'' |journal=Bulletin of the American Mathematical Society |volume=40 |number=1 |pages=143–150 |year=2003 |doi=10.1090/S0273-0979-02-00970-9 |url=https://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00970-9/S0273-0979-02-00970-9.pdf |archive-url=https://web.archive.org/web/20120317130154/http://www.ams.org/journals/bull/2003-40-01/S0273-0979-02-00970-9/S0273-0979-02-00970-9.pdf |archive-date=2012-03-17 |url-status=live}}</ref>

===Principle of computational equivalence (PCE)===
The '''principle of computational equivalence''' (PCE) has been criticized for being vague, unmathematical, and not making directly verifiable predictions.<ref name="autogenerated1"/><!-- However, Wolfram's group has described the principle as such, not a law, theorem or formula. [They described it as being vague, unmathematical, and not able to make directly verifiable predictions?] --> It has also been criticized for being contrary to the spirit of research in mathematical logic and computational complexity theory, which seek to make fine-grained distinctions between levels of computational sophistication, and for wrongly conflating different kinds of universality property.<ref name="autogenerated1"/> Moreover, critics such as [[Ray Kurzweil]] have argued that it ignores the distinction between hardware and software; while two computers may be equivalent in power, it does not follow that any two programs they might run are also equivalent.<ref name=Kurzweil>{{cite web
|last = Kurzweil|first = Ray
|title = Reflections on Stephen Wolfram's A New Kind of Science
|url=https://www.kurzweilai.net/reflections-on-stephen-wolfram-s-a-new-kind-of-science
|date=13 May 2002
|work=Kurzweil Accelerating Intelligence Blog
}}</ref> Others suggest it is little more than a rechristening of the [[Church–Turing thesis]].<!--  However, the Church-Turing thesis imposes an upper limit while Wolfram's PCE suggests the nonexistence of intermediate degrees of computation sending a computational system either to the upper level (universal) or to the lowest degree. [No. The claim is that intermediate degrees are derived from the complete degree, hence equivalent in "sophistication".] -->

===The fundamental theory (''NKS'' Chapter 9)===
Wolfram's speculations of a direction toward a fundamental theory of physics have been criticized as vague and obsolete. [[Scott Aaronson]], Professor of Computer Science at University of Texas Austin, also claims that Wolfram's methods cannot be compatible with both [[special relativity]] and [[Bell's theorem]] violations, and hence cannot explain the observed results of [[Bell test]]s.<ref>{{cite journal|last=Aaronson|first=Scott|title=Book Review of ''A New Kind of Science'' (Postscript file)|journal=Quantum Information and Computation|volume=2|issue=5|year=2002|pages=410–423|doi=10.26421/QIC2.5-7|url=http://www.scottaaronson.com/papers/nks.ps}}</ref>

[[Edward Fredkin]] and [[Konrad Zuse]] pioneered the idea of a [[Cellular automaton#CA as models of the fundamental physical reality|computable universe]], the former by writing a line in his book on how the world might be like a cellular automaton, later further developed by Fredkin using a toy model called Salt.<ref>{{cite web|url=http://www.math.usf.edu/~eclark/ANKOS_zuse_fredkin_thesis.html|title=ZUSE-FREDKIN-THESIS|work=usf.edu|access-date=2007-02-18|archive-date=2008-09-05|archive-url=https://web.archive.org/web/20080905103801/http://www.math.usf.edu/~eclark/ANKOS_zuse_fredkin_thesis.html|url-status=dead}}</ref> It has been claimed that ''NKS'' tries to take these ideas as its own, but Wolfram's model of the universe is a rewriting network, not a cellular automaton, as Wolfram himself has suggested a cellular automaton cannot account for relativistic features such as no absolute time frame.<ref>{{Cite web | url=https://www.wolframscience.com/nksonline/section-9.7 | title=Fundamental Physics: A New Kind of Science &#124; Online by Stephen Wolfram}}</ref> [[Jürgen Schmidhuber]] has also charged that his work on [[Turing machine]]-computable [[physics]] was stolen without attribution, namely his idea on enumerating possible Turing-computable universes.<ref name=Schmid>{{cite web|last=Schmidhuber|first=Jürgen|title=Origin of main ideas in Wolfram's book "A New Kind of Science"|url=https://www.idsia.ch/~juergen/wolfram.html|publisher=CERN Courier}}</ref>

In a 2002 review of ''NKS'', the Nobel laureate and elementary particle physicist [[Steven Weinberg]] wrote, "Wolfram himself is a lapsed elementary particle physicist, and I suppose he can't resist trying to apply his experience with digital computer programs to the laws of nature. This has led him to the view (also considered in a 1981 paper by Richard Feynman) that nature is discrete rather than continuous. He suggests that space consists of a set of isolated points, like cells in a cellular automaton, and that even time flows in discrete steps. Following an idea of Edward Fredkin, he concludes that the universe itself would then be an automaton, like a giant computer. It's possible, but I can't see any motivation for these speculations, except that this is the sort of system that Wolfram and others have become used to in their work on computers. So might a carpenter, looking at the moon, suppose that it is made of wood."<ref>{{Cite journal|author=Weinberg, S.|title=Is the Universe a Computer?|journal=The New York Review of Books|date=24 October 2002|volume=49 |issue=16 |url=https://www.nybooks.com/articles/15762}}</ref>

===Natural selection===
Wolfram's claim that [[natural selection]] is not the fundamental cause of complexity in biology has led journalist Chris Lavers to say that Wolfram does not understand the [[theory of evolution]].<ref>{{cite news|last=Lavers|first=Chris|title=How the cheetah got his spots|newspaper=The Guardian|date=3 August 2002|url= https://www.theguardian.com/Archive/Article/0,4273,4473834,00.html|access-date=28 May 2009 | location=London}}</ref>

===Originality===
''NKS'' has been heavily criticized as not original or important enough to justify its title and claims.

The authoritative manner in which ''NKS'' presents a vast number of examples and arguments has been criticized as leading the reader to believe that each of these is original to Wolfram; in particular, one of the most substantial new technical results presented in the book, that the [[Rule 110|rule 110 cellular automaton]] is [[Turing complete]], was not proven by Wolfram. Wolfram credits the proof to his research assistant [[Matthew Cook]].<ref>{{Cite web|url=https://www.wolframscience.com/nks/notes-11-8--history-of-universality-in-1d-cellular-automata/|title = Note (C) for the Rule 110 Cellular Automaton: A New Kind of Science &#124; Online by Stephen Wolfram &#91;Page 1115&#93;}}</ref> But the book's notes section acknowledges many of the discoveries made by these other scientists, citing their names together with historical facts, although not in the form of a traditional bibliography section. Additionally, the idea that very simple rules often generate great complexity is already an established idea in science, particularly in [[chaos theory]] and [[complex systems]].

== See also ==
* [[Digital physics]]
* [[Scientific reductionism]]
* ''[[Calculating Space]]''
* [[Marcus Hutter]]'s "Universal Artificial Intelligence" algorithm

== References ==
{{Reflist|30em}}

== External links ==
* [https://www.wolframscience.com/nks A New Kind of Science] free E-Book
* [https://www.youtube.com/playlist?list=PLxn-kpJHbPx3hhVJh4_dGnomU2_nUzRlh What We've Learned from NKS] YouTube playlist — extensive discussion of each NKS chapter; (As of 2022, Stephen Wolfram discusses the NKS chapters in view of recent developments. [https://www.wolframphysics.org Wolfram Physics Project])

<!--

ARTICLES AND REVIEWS SHOULD BE USED AS REFERENCES, NOT AS EXTERNAL LINKS.

;Scholar articles
* Leon O Chua, "''A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science''". Singapore; Hackensack, N.J.: World Scientific, 2006. ISBN 981-256-977-4

;Reviews and overviews

*  Wolfram, Stephen, "[http://www.wolframscience.com/reference/quick_takes.html Quick takes on some ideas and discoveries in A New Kind of Science]". Wolfram Media, Inc.
* [http://www.wolframscience.com/conference/2004/ NKS 2004 conference].  Wolfram Media, Inc.
* [http://wolframscience.typepad.com/wolfram_science/ Wolfram's NKS Conference blog], June 2006.
* Clark, Ed, [http://www.math.usf.edu/~eclark/ANKOS_reviews.html Reviews] (the most comprehensive collection of reviews of NKS)
* [http://zenbullets.com/blog/?p=72 Universal Automatism - Everything is Computation]
* Schmidhuber, Juergen [https://www.idsia.ch/~juergen/wolfram.html "A 35 year old kind of science"] (with links to much earlier work on [[digital physics]])
* [[Kovas Boguta]], [http://forum.wolframscience.com/showthread.php?s=b4dcb648c91f4096a166716339679de1&threadid=271 "Comments on a review of NKS"] (an exposition of what NKS actually is, framed as a response to critics)
* [http://books.slashdot.org/books/02/05/21/146210.shtml?tid=134 Review and discussion of ''A New Kind of Science'']. [[Slashdot]].
* Krantz, Steven G., [https://www.ams.org/bull/2003-40-01/S0273-0979-02-00970-9/S0273-0979-02-00970-9.pdf "Book review"]. [[American Mathematical Society]] ([[Portable Document Format|PDF]] document)
* [[Rudy Rucker]], [http://www.rudyrucker.com/pdf/wolfram_review.pdf "Book Review"]. American Mathematical Monthly, November, 2003.
* Stephen Wolfram's lecture at MIT, [http://mitworld.mit.edu/play/147/ "A New Kind of Science"] ([[RealNetworks|Real Media]] video and audio, 1:36:36). Department of Mathematics at MIT, September 15, 2003.
* Naiditch, David, "Divine Secrets Of the Ya-Ya Universe. Stephen Wolfram: A New Kind of Science—or a Not-So-New Kind of Computer Program?", ''[[Skeptic (U.S. magazine)]]'', issue 10-2, 2003.
* Neske, Garrett, "Whatever Happened to Stephen Wolfram? A New Kind of Science Revisited", ''Skeptic (U.S. magazine)'', issue 14-3, 2008.
* [http://uk.geocities.com/joelewisbowen/wolfram.html Critique of the explanatory force of A New Kind of Science] ([https://archive.today/20070725222520/http://uk.geocities.com/joelewisbowen/wolfram.html Archived] 2009-10-23)
* [[Cosma Shalizi|Shalizi, Cosma]] [http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/ "Review of 'Stephen Wolfram's A New Kind of Science': A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity"]
* {{cite web
|last = Kurzweil|first = Ray
|title = Reflections on Stephen Wolfram's A New Kind of Science
|url=https://www.kurzweilai.net/reflections-on-stephen-wolfram-s-a-new-kind-of-science
|date=13 May 2002
|work=Kurzweil Accelerating Intelligence Blog
}}
* Levy, Steven [https://www.wired.com/wired/archive/10.06/wolfram.html The Man Who Cracked The Code to Everything ...] [[Wired (magazine)|Wired]], 2002
* {{cite web |last1=Wolfram |first1=Stephen |title=Lecture given by Wolfram as part of the MIT "Applied Mathematics Colloquium" |url=https://techtv.mit.edu/videos/15901-a-new-kind-of-science |archive-url=http://web.archive.org/web/20170729103222/https://techtv.mit.edu/videos/15901-a-new-kind-of-science |archive-date=2017-07-29}} ([http://web.archive.org/web/20200619005818/https://d3tsb3m56iwvoq.cloudfront.net/transcoded/techtv/732d4d4bee9c4c8c9f923c52ae72253d/hd.mp4]|(MP4 video archived June 18, 2020)])

;Applications
*[http://blog.wolfram.com/2007/08/the_space_of_all_possible_bridge.html The Space of All Possible Bridge Shapes] by Stephen Wolfram, August 3, 2007, a short essay on the future of bridge design written in response to the collapse of the [[I-35W Mississippi River bridge]].

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