A New Kind of Science

A New Kind of Science is a book by Stephen Wolfram, 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 scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of science. 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. 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 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, amongst others, cellular automata in one, two, and three dimensions; mobile automata; Turing machines in 1 and 2 dimensions; several varieties of substitution and network systems; recursive functions; nested recursive functions; combinators; tag systems; register machines; 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.