A New Kind of Science is a controversial book by Stephen Wolfram, published in 2002. It contains an empirical and systematic study of computational models such as cellular automata. Wolfram calls these models simple programs and argues that the scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of science. Image File history File links Newsciendfsdfs. ... This is a list of controversial non-fiction books aimed at the general reader which discuss controversial issues, or are (or were at the time of writing) controversial for other reasons. ... Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in theoretical particle physics, cellular automata, complexity theory, and computer algebra, and is the creator of the computer program Mathematica. ... For album titles with the same name, see 2002 (album). ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... The philosophy of science is the branch of philosophy which studies the philosophical foundations, presumptions and implications of science both of the natural sciences like physics and biology and the social sciences such as psychology and economics. ...

Computation and its implications

The thesis of A New Kind of Science is twofold: that the nature of computation must be explored experimentally, and that the results of these experiments have great relevance to understanding the natural world. Since its crystallization in the 1930s, computation has been primarily approached from two traditions: engineering, which seeks to build practical systems using computations; and mathematics, which seeks to prove theorems about computation. Engineering is the design, analysis, and/or construction of works for practical purposes. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...

Wolfram describes himself as introducing a third major tradition, which is the systematic, empirical investigation of computational systems for their own sake. This is where the "New" and "Science" parts of the book's title originate. However, in proceeding with a scientific investigation of computational systems, Wolfram eventually came to the conclusion that an entirely new method is needed. Traditional mathematics was failing to describe the complexity seen in these systems meaningfully. Through a combination of experiment and theoretical positioning, the book introduces a new method that Wolfram argues is the most realistic way to make scientific progress with computational systems. This difference in method casts A New Kind of Science as a "kind" of science, and allows its principles to be potentially applicable in a wide range of fields. Complexity in general usage is the opposite of simplicity. ...

Simple programs

The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules — essentially, elementary computer programs. In almost any class of computational system, one very quickly finds instances of great complexity among its simplest cases. This seems to be true regardless of the components of the system and the details of its setup. Systems explored in the book include cellular automata in 1, 2 and 3 dimensions, mobile automata, Turing machines in 1 and 2 dimensions, several varieties of substitution and network systems, primitive recursive functions, nested recursive functions, combinators, tag systems, register machines, reversal-addition and a number of other systems. For a program to qualify as simple, there are several benchmarks: A computer program (often simply called a program) is an example of computer software that prescribes the actions (computations) that are to be carried out by a computer. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... An artistic representation of a Turing Machine . ... It has been suggested that this article or section be merged into computable function. ... This article is about a topic in theoretical computer science, and is not to be confused with combinatorial logic, a topic in electronics. ... // Definition A tag system is a triplet (m, A, P), where m is a positive integer; A is a finite alphabet of symbols, one of which is a special halting symbol; P is a set of production rules, assigning some word P(x) to each non-halting symbol x in... In theoretical computer science a register machine is an abstract machine used to study decision problems, similar to how a Turing machine is used. ...

1. Its operation can be completely explained by a simple graphical illustration.
2. It can be completely explained in a few sentences of human language.
3. It can be implemented in a computer language using just a few lines of code.
4. 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. Cellular automata, Turing machines and combinators are examples of such frameworks. Note that some cellular automata have quite complicated detailed rules, and do not 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 percentage of them are capable of producing 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. The term natural language is used to distinguish languages spoken by humans for general-purpose communication from constructs such as computer-programming languages or the languages used in the study of formal logic, especially mathematical logic. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... The Turing machine is an abstract machine introduced in 1936 by Alan Turing to give a mathematically precise definition of algorithm or mechanical procedure. As such it is still widely used in theoretical computer science, especially in complexity theory and the theory of computation. ... A termite cathedral mound produced by a termite colony: a classic example of emergence in nature. ... In computer science, a brute-force search consists of systematically enumerating every possible solution of a problem until a solution is found, or all possible solutions have been exhausted. ...

Simple programs are capable of a remarkable range of behavior. Some have been proven to be universal computers. Others exhibit properties familiar from traditional science, such as thermodynamic behavior, 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 sociological, geological and ecological phenomena. Another feature of simple programs is that 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. The Turing machine is an abstract machine introduced in 1936 by Alan Turing to give a mathematically precise definition of algorithm or mechanical procedure. As such it is still widely used in theoretical computer science, especially in complexity theory and the theory of computation. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Look up continuum in Wiktionary, the free dictionary. ... In chemistry and other physical sciences, percolation is a type of filtering. ... Point attractors in 2D phase space. ... Nighttime traffic captured by a camera over several seconds. ... Crystals are entities of atoms, ions or even polymer strings in which the subunits (i. ... This article or section does not adequately cite its references or sources. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... Ernst Haeckel coined the term oekologie in 1866. ... Complexity in general usage is the opposite of simplicity. ... There are many definitions of complexity, therefore many natural, artificial and abstract objects or networks can be considered to be complex systems, and their study (complexity science) is highly interdisciplinary. ...

Mapping and mining the computational universe

In order to study simple rules and their often complex behaviour, Wolfram believes it is necessary to systematically explore all of these computational systems and document what they do. He believes 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. Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the branch of science concerned with the fundamental laws of the universe. ... Chemistry - the study of atoms, made of nuclei (conglomeration of center particles) and electrons (outer particles), and the structures they form. ...

The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications like those found in biology 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. There are also some forms of production that are in some ways unique to this field of study. For instance, the discovery of computational mechanisms that emerge in different systems but in bizarrely different forms. This article or section does not adequately cite its references or sources. ...

Another kind of production involves the creation of programs for the analysis of computational systems — for 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 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. However, in general Wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe — where they can be witnessed in their clearest forms — and then other fields can pick and choose among these discoveries for those they find relevant.

Systematic abstract science

While Wolfram promotes simple programs as a scientific discipline, he also insists that its methodology will revolutionize essentially every field of science. The basis for his claim is that the study of simple programs is the most minimal possible form of science, which is equally grounded in both abstraction and empirical experimentation. Every aspect of the methodology advocated in NKS 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 NKS allows computational mechanisms to be studied in their cleanest forms, Wolfram believes the process of doing NKS captures the essence of the process of doing science -- and allows that process's strengths and shortcomings to be directly revealed. Abstraction is the process of reducing the information content of a concept, typically in order to retain only information which is relevant for a particular purpose. ...

Wolfram believes 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 leverage them in our favor. For instance, instead of reverse engineering our theories from observation, we can simply enumerate systems and then try to match them to the behaviors we observe. A major theme of NKS style research is investigating the structure of the possibility space. Wolfram feels that science is far too ad hoc, in part because the models used are too complicated and/or 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. Reverse engineering (RE) is the process of taking something (a device, an electrical component, a software program, etc. ... Enumeration is the name given to the generic field of mathematics which deals with counting objects. ...

Philosophical underpinnings

Wolfram believes that one of his achievements is not just exclaiming, "computation is important!", but in providing a coherent system of ideas that justifies computation as an organizing principle of science. For instance, Wolfram's concept of computational irreducibility -- that some complex computations cannot be short-cutted or "reduced" (cf. NP-hard) , 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 explicit computational models may in some cases provide more accurate and rich models of random-looking systems. Philosophy of science is the study of assumptions, foundations, and implications of science, especially in the natural sciences and social sciences. ... Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. ... In computational complexity theory, NP-hard (Non-deterministic Polynomial-time hard) refers to the class of decision problems that contains all problems H such that for all decision problems L in NP there is a polynomial-time many-one reduction to H. Informally this class can be described as containing... Note: The term model is also given a formal meaning in model theory, a part of axiomatic set theory. ...

Based on his experimental results, Wolfram has developed the Principle of Computational Equivalence (see below), which asserts that almost all processes that are not obviously simple are of equivalent sophistication. From this seemingly vague single principle Wolfram draws a broad array of concrete deductions that reinforce many aspects of his theory. Possibly the most important among these is an explanation as to 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 for instance the concept of "heat", but simply a label for all systems whose computations are sophisticated. Understanding this makes the "normal science" of the NKS paradigm possible. The word random is used to express lack of purpose, cause, order, or predictability in non-scientific parlance. ... Complexity in general usage is the opposite of simplicity. ...

At the deepest level, Wolfram believes that like many of the most important scientific ideas, the Principle allows science to be more general by pointing out new ways in which humans are not special. In recent times, it has been thought that the complexity of human intelligence makes us special -- but the Principle asserts otherwise. In a sense, much of Wolfram's ideas are based on understanding the scientific process -- including the human mind -- as operating within the same universe it studies, rather than somehow being outside it.

Principle of computational equivalence

The principle states that systems found in the natural world can perform computations up to a 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 inputs 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. For the Macintosh operating system, which was called System up to version 7. ... Natural World (sometimes in the past titled Wildlife On One or Wildlife On Two) is a long-running BBC television series on natural history. ... Look up computation in Wiktionary, the free dictionary. ... The largest and the smallest element of a set are called extreme values, or extreme records. ... The largest and the smallest element of a set are called extreme values, or extreme records. ... The term input has a variety of uses in different fields. ... // Information processing In information processing, output is the process of transmitting information by an object (verb usage). ...

Applications and results

There are a vast number of specific results and ideas in the NKS book, and they can be organized into several themes. One common theme of examples and applications is demonstrating how little it takes to achieve interesting behavior, and how the proper methodology can discover these cases.

First, there are perhaps several dozen cases where the NKS book introduces 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 a large number of minimal examples of how simple programs exhibit phenomena like phase transitions, conserved quantities and continuum behavior and thermodynamics that are familiar from traditional science. Simple computational models of natural systems like shell growth, fluid turbulence, and phyllotaxis are a final category of applications that fall in this theme. An artistic representation of a Turing Machine . ... This article does not adequately cite its references or sources. ... In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formulas representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows to establish that certain formulas are theorems of the formal system. ... In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Turbulence is part of daily experience: no microscopes or telescopes are needed to notice the meanders of cigarette smoke, the gracious arabesques of cream poured into coffee or turbulent whirls in a mountain torrent. ... In botany, phyllotaxis is the arrangement of the leaves on the shoot of a plant. ...

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. Holism (from holon, a Greek word meaning entity) is the idea that the properties of a system cannot be determined or explained by the sum of its components alone. ... This article is about biological evolution. ... This article is about the search for extra-terrestrial intelligence. ... Free-Will is a Japanese independent record label founded in 1986. ... As a branch of the theory of computation in computer science, computational complexity theory describes the scalability of algorithms, and the inherent difficulty in providing scalable algorithms for specific computational problems. ... In philosophy, ontology (from the Greek , genitive : of being (part. ... It has been suggested that Meta-epistemology be merged into this article or section. ... Postmodernist architecture of the Stata Center by Frank Gehry Sydney Opera House The term Postmodernism (sometimes referred to as Pomo, Po-Mo, or PoMo [1], [2], [3]) was coined in the early 1960s to describe a dissatisfaction with modern architecture, founding the postmodern architecture. ...

A particularly intriguing suggestion is that the theory of computational irreducibility may provide a resolution to the existence of free will in a nominally deterministic universe. Wolfram posits that if the computational process in the brain of the being with free will is actually complex enough so that it cannot be captured in a simpler computation, due to the principle of computational irreducibility, then while the process is indeed deterministic, there is no better way to determine the being's will than to essentially run the experiment and let the being just decide. The book also contains a vast number of individual results -- both experimental and analytic -- about what a particular automaton computes, or what its characteristics are, using some methods of analysis. Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. ... Free-Will is a Japanese independent record label founded in 1986. ... In animals the brain, or encephalon (Greek for in the head), is the control center of the central nervous system, responsible for thought. ... Free-Will is a Japanese independent record label founded in 1986. ... A complex is a whole that comprehends a number of parts, especially one with interconnected or mutually related parts. ... The term deterministic may refer to: the more general notion of determinism from philosophy, see determinism a type of algorithm as discussed in computer science, see deterministic algorithm scientific determinism as used by Karl Popper and Stephen Hawking deterministic system in mathematics deterministic system in philosophy deterministic finite state machine...

Reception

NKS received extensive media publicity for a scientific book, generating scores of articles in such publications as The New York Times, Newsweek, Wired, and The Economist. It was a best-seller and won numerous awards. NKS was reviewed in a large range of scientific journals. Several themes emerged. On the positive, many reviewers enjoyed the quality of the book's production, and the clear way Wolfram presented many ideas. Many reviewers, even those who engaged in other criticisms, found aspects of the book to be interesting and thought-provoking. On the negative, many reviewers criticized Wolfram for his lack of modesty, poor editing, lack of mathematical rigor, and the lack of immediate utility of his ideas. Concerning the ultimate importance of the book, a common attitude was that of either skepticism or "wait and see". Detailed criticisms are outlined below. Many reviewers and the media focused on the use of simple programs, and cellular automata in particular, to model nature–rather than the more fundamental idea of systematically exploring the universe of simple programs. The New York Times is a daily newspaper published in New York City by Arthur Ochs Sulzberger Jr. ... The Newsweek logo Newsweek is a weekly news magazine published in New York City and distributed throughout the United States and internationally. ... Wired is a full-color monthly magazine and on-line periodical published in San Francisco, California since March 1993. ... The Economist is a weekly news and international affairs publication owned by The Economist Newspaper Ltd and edited in London, UK. It has been in continuous publication since September 1843. ... This article or section does not adequately cite its references or sources. ... Editing may also refer to audio or film editing. ... ... In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained by consuming different bundles of goods and services. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ...

Criticisms of NKS

The book has attracted several types of criticism and some critics have labeled the book crankery.^[1] A critic (derived from the ancient Greek word krites meaning a judge) is a person who offers a value judgement or an interpretation. ...

Scientific philosophy

A key 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. However, many scientists believe that of all possible parameters, only some actually occur in the universe. That, for instance, of all possible variations of 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. NKS does not establish rigorous mathematical definitions, nor does it attempt to prove theorems.^[2] Along these lines, NKS has also been criticized for being heavily visual, with much information conveyed by pictures that do not have formal meaning. It has also been criticized for not using modern research in the field of complexity, particularly the works that have studied complexity from a rigorous mathematical perspective. Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. ... Look up theorem in Wiktionary, the free dictionary. ... Complexity in general usage is the opposite of simplicity. ...

Critics also note that none of the book's contents were published in peer-reviewed journals, the standard method for distributing new results, and complained he insufficiently credited other scientists whose work he builds on. (Wolfram relegates all discussion of other people to his lengthy endnotes and thus no one is directly credited in the text. But his critics argue that even the endnotes are misleading, glossing over many relevant discoveries and thus making Wolfram's work seem more novel.)^[3] Peer review (known as refereeing in some academic fields) is a process of subjecting an authors scholarly work or ideas to the scrutiny of others who are experts in the field. ...

Utility

NKS has been criticized for not providing specific results that would be immediately applicable to ongoing scientific research. 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 explained using Wolfram's methods in a satisfactory fashion. ^[4] Steven Weinberg (born May 3, 1933) is an American physicist. ...

Principle of computational equivalence

The PCE has been criticized for being vague, unmathematical, and for not making 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. Others suggest it is little more than a rechristening of the Church-Turing thesis. In computability theory the Church-Turing thesis, Churchs thesis, Churchs conjecture or Turings thesis, named after Alonzo Church and Alan Turing, is a hypothesis about the nature of mechanical calculation devices, such as electronic computers. ...

The fundamental theory

Wolfram's speculations of a direction towards a fundamental theory of physics have been criticized as vague and obsolete. It has also been claimed that his model is ruled out by Bell's theorem, although the theorem has been violated by the Bell test experiments which may imply that such computations are possible, or even common, in quantum systems. Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ... In quantum mechanics, Bells Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but can in certain circumstances be violated under quantum mechanics (QM). ...

Natural selection

Wolfram's claim that natural selection is not the fundamental cause of complexity in biology has led some to state that Wolfram does not understand the theory of evolution. A common sentiment is that NKS may explain features like the forms of organisms, but does not explain their functional complexity. Darwins illustrations of beak variation in the finches of the Galápagos Islands, which hold 13 closely related species that differ most markedly in the shape of their beaks. ... This article is about biological evolution. ... Sentiment can refer to: feelings and emotions the literary device sentimentality, which is used to induce an emotional response disproportionate to the situation, and thus to substitute heightened and generally unthinking feeling for normal ethical and intellectual judgment an eighteenth century literary genre called the sentimental novel This is a... Generally, functional refers to something with and able to fulfill its purpose or function. ... Complexity in general usage is the opposite of simplicity. ...

Originality and self-image

NKS has been heavily criticized as not being original or important enough to justify its title and claims. Edward Fredkin and Konrad Zuse pioneered the idea of a computable universe, and specifically the idea of the universe as a cellular automaton.[1] It has been claimed that NKS tries to take these ideas as its own. Juergen Schmidhuber has been a particularly vocal critic in this regard, throwing in the additional charge that his work on Turing machine-computable physics was stolen without attribution. Edward Fredkin was an early pioneer of digital physics (in recent work he uses the term digital philosophy (DP)). His main contributions include his work on reversible computing and cellular automata. ... Konrad Zuse (1992) Statue in Bad Hersfeld Konrad Zuse (June 22, 1910 – December 18, 1995) was a German engineer and computer pioneer. ... Jürgen Schmidhuber (born 1963 in Munich) is a computer scientist and artist known for his work on machine learning, universal Artificial Intelligence (AI), artificial neural networks, digital physics, and low-complexity art. ... An artistic representation of a Turing Machine . ... Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the branch of science concerned with the fundamental laws of the universe. ...

It has been claimed that the core idea that very simple rules often generate great complexity is already an understood and established idea in science-particularly in chaos and complexity research. 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 ideas was original to Wolfram. In particular, the most substantial new technical result presented in the book, that the rule 110 cellular automaton is Turing complete, was not proven by Wolfram, but by his research assistant, Matthew Cook. Some have argued that the use of computer simulation is ubiquitous, and instead of starting a paradigm shift NKS just adds justification to a paradigm shift that has already occurred. // The rule 110 cellular automaton is a one-dimensional two-state cellular automaton with the following rule table: Rule 110, like the Game of Life, exhibits what Stephen Wolfram calls Class 4 behavior, which is neither completely random nor completely repetitive. ... In computability theory a programming language or any other logical system is called Turing-complete if it has a computational power equivalent to a universal Turing machine. ... Matthew Cook was born in Morgantown, West Virginia, in 1970 and grew up in Evanston, Illinois. ... A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. ... Paradigm shift is the term first used by Thomas Kuhn in his 1962 book The Structure of Scientific Revolutions to describe a change in basic assumptions within the ruling theory of science. ...

See also

• Emergence
• Cellular automaton
• Rule 110 cellular automaton
• Scientific reductionism
• Philosophy of science

A termite cathedral mound produced by a termite colony: a classic example of emergence in nature. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology. ... // The rule 110 cellular automaton is a one-dimensional two-state cellular automaton with the following rule table: Rule 110, like the Game of Life, exhibits what Stephen Wolfram calls Class 4 behavior, which is neither completely random nor completely repetitive. ... The term scientific reductionism has been used to describe various reductionist ideas about science. ... Philosophy of science is the study of assumptions, foundations, and implications of science, especially in the natural sciences and social sciences. ...

External articles

Citations and notes

1. ^ http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/
2. ^ http://www.ams.org/notices/200302/fea-gray.pdf
3. ^ http://www.ams.org/notices/200302/fea-gray.pdf
4. ^ http://www.sciencenews.org/articles/20030816/bob10.asp

Official site

• Wolfram, Stephen, A New Kind of Science. Wolfram Media, Inc., May 14, 2002. ISBN 1-57955-008-8
• Wolfram, Stephen, "Quick takes on some ideas and discoveries in A New Kind of Science". Wolfram Media, Inc.
• NKS 2004 conference. Wolfram Media, Inc.
• InformationSpace. Causal set exploration tool which supports 1 dimensional causal sets such as those found in the book.
• Wolfram's NKS Conference blog, June 2006.
• WolframTones: An Experiment in a New Kind of Music

Scholar articles

• Leon O Chua, "A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science". Singapore ; Hackensack, N.J. : World Scientific, 2006. ISBN 9812569774

Reviews and overviews

• Clark, Ed, Reviews (the most comprehensive collection of reviews of NKS)
• Universal Automatism - Everything is Computation
• Amazon.com, book reviews (ranked by votes)
• Schmidhuber, Juergen "A 35 year old kind of science" (with links to much earlier work on digital physics)
• Kovas Boguta, "Comments on a review of NKS" (an exposition of what NKS actually is, framed as a response to critics)
• Review and discussion of A New Kind of Science. Slashdot.
• Krantz, Steven G., "Book review". American Mathematical Society (PDF document)
• Rudy Rucker, "Book Review". American Mathematical Monthly, November, 2003.
• Stephen Wolfram's lecture at MIT, "A New Kind of Science" (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 Magazine, issue 10-2, 2003.
• Critique of the explanatory force of A New Kind of Science
• Shalizi, Cosma "Review of 'Stephen Wolfram's A New Kind of Science': A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity"
• Reflections on Stephen Wolfram's 'A New Kind of Science' by Ray Kurzweil