---
title: "A New Kind of Science"
chunk: 2/4
source: "https://en.wikipedia.org/wiki/A_New_Kind_of_Science"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:33:23.585706+00:00"
instance: "kb-cron"
---

=== 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 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 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 (PCE): the principle says 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 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 transitions, conserved quantities, 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.
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 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 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. Alex Smith, a computer science student from Birmingham, UK, won the prize later that year by proving Wolfram's conjecture.

== Reception ==