A New Kind of Science. The abbreviation properly refers to the science based on Stephen Wolfram’s book of the same title. Sometimes it is used, loosely, to refer to the book, but the preferred usage for that is “the NKS book“. You can find out more about the book here. You can order a copy here.

It is a new kind of science based on simple programs. Almost all the science that's been done for the past three hundred or so years has been based in the end on the idea that things in our universe somehow follow rules that can be represented by traditional mathematical equations. The basic idea that underlies A New Kind of Science is that that's much too restrictive, and that in fact one should consider the vastly more general kinds of rules that can be embodied, for example, in computer programs.

Instead of asking what mathematical equation some system obeys, it asks what simple program produces the behavior seen in that system. Pure NKS investigates how various types of simple programs typically behave - much as traditional mathematics examines various mathematical equations. Applied NKS then looks for simple programs behind the behavior seen in natural and other systems.

As Kepler noticed orbits seem to follow ellipses, Wolfram noticed things like a seashell pattern that seems to follow a 1-D cellular automaton, and a 2-D hexagonal grid cellular automaton that seems to reproduce the basic forms of snowflakes. Instead of conic sections or differential equations, NKS considers Turing machines, cellular automata, or other similar programs following simple definite rules.

The world of simple programs is another, very general set of formal patterns that real systems can be based on, beyond the equation based patterns investigated in the past. Despite the simplicity of the underlying rules, these programs can exhibit behavior of immense complexity. The book argues that this is the basic mechanism nature uses to produce the wealth of complexity we see all around us.

Stephen Wolfram is the author of A New Kind of Science and the founder and CEO of Wolfram Research, makers of Mathematica.

He worked in physics and cosmology in the late 70s and early 80s, before publishing a series of papers on Cellular Automata in the early 80s. You can find his publications here. In the late 80s he founded Wolfram Research and released the first version of Mathematica. In the 90s he ran his company and researched A New Kind of Science. Since its release in 2002 he has undertaken a number of initiatives to promote NKS, including a lecture series, conferences and summer school, and sponsoring this forum.

The single best way to learn about NKS is to read the NKS book, carefully. You can recreate the experiments by using NKS Explorer, or using the Mathematica code from the notes toward the end of the book - which are also available, free, here. Performing computer experiments and seeing how different parameters change the output seen is a good way to develop your intuition.

There are also other resources to get help learning NKS. You are encouraged to ask questions here on the NKS Forum. Some courses have already been organized to teach NKS, at the high school, college, and graduate level. If there isn’t one yet at your institution, perhaps you can help organize one.

Millions of people have heard about NKS through media coverage of the book. Wolfram has appeared on television and radio explaining NKS, testified before Congress about it, and hundreds of print articles have reviewed the book. You can find a list of media coverage here.

Several hundred thousand people bought the book in the first year. Tens of thousands attended public lectures Wolfram has given at universities, government labs, companies, and other venues.

Public reactions have ranged from enthusiasm to "wait-and-see" to skepticism to outright hostility. Wolfram frequently refers to the turbulence one expects from any paradigm shift. It becomes clear with time that a significant new field has been launched, one full of possibility and promise, whose scope and ultimate significant cannot yet be bounded.

Stephen Wolfram, of course, who continues to work on theoretical NKS problems and on various initiatives to develop the field. A number of Wolfram Research employees work on NKS matters, referred to as the Wolfram Science Group. Reseachers from just about every discipline are making a growing number of contributions to the field - from mathematics, computer science, physics, chemistry, biology, geology, and economics. NKS enthusiasts include educators, university and government researchers, technicians and consultants working with various private companies, as well as journalists, writers, architects, designers, and artists.

Wolfram writes in chapter 1 of the book "My goals in this book are sufficiently broad and fundamental that there have inevitably been previous attempts to achieve at least some of them. But without the ideas and methods of this book there have been basic issues that have eventually ended up presenting almost insuperable barriers to every major approach that has been tried." The NKS book, p. 12.

Wolfram discusses numerous approaches there - artificial intelligence, artificial life, catastrophe theory, chaos, complexity theory, computational complexity, cybernetics, dynamical systems, evolution, experimental mathematics, fractals, general systems theory, nanotechnology, nonlinear dynamics, scientific computing, self-organization, and statistical mechanics. Ibid, pp. 12-16.

Many precursors had a piece of this or that idea that informed the development of NKS. The acknowledgements section on pages xii through xiv of the NKS book mentions several hundred people Wolfram worked with or spoke to during its production. For reference, the contents of his personal library are available online here.

The notes and especially the index of the NKS book are also good places to look for comments about previous fields, their history, and their relation to NKS ideas. Exploring the index entries for various individuals may help trace previous contributions, and clarify the relationship between someone else's previous work and the ideas of NKS. A list of those mentioned in the book's index can be found here.

But in the end, as an integrated subject NKS is essentially a new field with its own approach, rather than part of any of these previous efforts.

Wolfram has said that Mathematica is what made A New Kind of Science possible. First, at a very practical level: it provided the tools Wolfram needed to make the discoveries that underlie A New Kind of Science. Second, at a more abstract level: it showed him that one could really start from scratch and build very big things from very simple elements.

You don't need to know anything about Mathematica to understand A New Kind of Science--just like you don't need to know how computers work inside to use one. But for Wolfram, Mathematica was a crucial step in being able to create A New Kind of Science. And in practice the more comfortable you are using Mathematica, the easier you will probably find doing original research in NKS, yourself. You can order Mathematica here. There is also a student version.

Although one can understand NKS on its own terms without Mathematica, many functions and routines have been written in Mathematica to explore NKS topics. The notes to the book contain executable Mathematica routines for many of the computer experiments Wolfram did. These are also available for download here.

A New Kind of Science Explorer is a separate software program that allows you to recreate many of the book's experiments interactively, with your choice of new parameters. While it is based on Mathematica technology, you do not need Mathematica to use it. You can order it here. A "kit" version with all the same functions plus greater programming flexibility is also available for Mathematica owners, here.

You may see attachments on the forum or elsewhere on the web in Mathematica Notebook format - .nb files. To execute the code they contain or to create such notebooks you need a version of Mathematica. You can read other people's notebooks with MathReader, which is free and available here.

Various reviewers thought the NKS book failed to do justice to their own specialties or oversimplified them, e.g. some chaos theorists who think the randomness seen in chaos does not arise essentially from randomness in initial conditions, and some biologists who think biological machinery is more complicated than the simple programs NKS posits as producing various living structures. Some involved with quantum computing are convinced continuous infinities are not idealizations but are real, and allow essentially greater computational sophistication than the discrete systems NKS considers.

Some reviewers react with incredulity to the idea that all sorts of systems could be based on programs rather than equations, or that everything could be a computation, sometimes confusing either with a claim that everything is a cellular automaton. Others claim one or another idea found in the NKS book is older and originated elsewhere. Some reviewers are anxious to hear falsifiable predictions, others want formal proofs, still others worry that computer experiments should not replace physical experiments.

While practically all of these points merit full discussion and thoughts on them are certainly encouraged in the NKS Forum, many of them stem either from misunderstandings of basic NKS ideas, or from seeing more excluded from consideration by NKS than actually is, or miss subtle distinctions between positions. Sometimes there are substantive disagreements about the real world involved, sometimes different judgments of the role or importance of mechanisms all agree are operating, sometimes quarrels over preferred methods.