A New Kind of Science

Description

This long-awaited work from one of the world's most respected scientists presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments--illustrated in the book by striking computer graphics--Stephen Wolfram shows us how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science, from the origins of apparent randomness in physical systems, to the development of complexity in biology, the ultimate scope and limitations of mathematics, the possibility of a truly fundamental theory of physics, the interplay between free will and determinism and the character of intelligence in the universe. Written with exceptional clarity, and illustrated by nearly a thousand original pictures, this seminal book allows scientists and non-scientists alike to participate in what promises to be a major intellectual revolution. Cover Contents Preface A New Kind of Science 1. The Foundations for a New Kind of Science An Outline of Basic Ideas Relations to Other Areas Some Past Initiatives The Personal Story of the Science in This Book 2. The Crucial Experiment How Do Simple Programs Behave? The Need for a New Intuition Why These Discoveries Were Not Made Before 3. The World of Simple Programs The Search for General Features More Cellular Automata Mobile Automata Turing Machines Substitution Systems Sequential Substitution Systems Tag Systems Cyclic Tag Systems Register Machines Symbolic Systems Some Conclusions How the Discoveries in This Chapter Were Made 4. Systems Based on Numbers The Notion of Numbers Elementary Arithmetic Recursive Sequences The Sequence of Primes Mathematical Constants Mathematical Functions Iterated Maps and the Chaos Phenomenon Continuous Cellular Automata Partial Differential Equations Continuous Versus Discrete Systems 5. Two Dimensions and Beyond Introduction Cellular Automata Turing Machines Substitution Systems and Fractals Network Systems Multiway Systems Systems Based on Constraints 6. Starting from Randomness The Emergence of Order Four Classes of Behavior Sensitivity to Initial Conditions Systems of Limited Size and Class 2 Behavior Randomness in Class 3 Systems Special Initial Conditions The Notion of Attractors Structures in Class 4 Systems 7. Mechanisms in Programs and Nature Universality of Behavior Three Mechanisms for Randomness Randomness from the Environment Chaos Theory and Randomness from Initial Conditions The Intrinsic Generation of Randomness The Phenomenon of Continuity Origins of Discreteness The Problem of Satisfying Constraints Origins of Simple Behavior 8. Implications for Everyday Systems Issues of Modelling The Growth of Crystals The Breaking of Materials Fluid Flow Fundamental Issues in Biology Growth of Plants and Animals Biological Pigmentation Patterns Financial Systems 9. Fundamental Physics The Problems of Physics The Notion of Reversibility Irreversibility and the Second Law of Thermodynamics Conserved Quantities and Continuum Phenomena Ultimate Models for the Universe The Nature of Space Space as a Network The Relationship of Space and Time Time and Causal Networks The Sequencing of Events in the Universe Uniqueness and Branching in Time Evolution of Networks Space, Time and Relativity Elementary Particles The Phenomenon of Gravity Quantum Phenomena 10. Processes of Perception and Analysis What Perception and Analysis Do Defining the Notion of Randomness Defining Complexity Data Compression Irreversible Data Compression Visual Perception Auditory Perception Statistical Analysis Cryptography and Cryptanalysis Traditional Mathematics and Mathematical Formulas Human Thinking Higher Forms of Perception and Analysis 11. The Notion of Computation Introduction Computation as a Framework Computations in Cellular Automata The Phenomenon of Universality A Universal Cellular Automaton Emulating Other Systems with Cellular Automata Emulating Cellular Automata with Other Systems Implications of Universality The Rule 110 Cellular Automaton The Significance of Universality in Rule 110 Class 4 Behavior and Universality The Threshold of Universality in Cellular Automata Universality in Turing Machines and Other Systems 12. The Principle of Computational Equivalence Basic Framework Outline of the Principle The Content of the Principle The Validity of the Principle Explaining the Phenomenon of Complexity Computational Irreducibility The Phenomenon of Free Will Undecidability and Intractability Implications for Mathematics and Its Foundations Intelligence in the Universe Implications for Technology Historical Perspectives Notes General Notes Notes For Chapter 1 Notes For Chapter 2 Notes For Chapter 3 Notes For Chapter 4 Notes For Chapter 5 Notes For Chapter 6 Notes For Chapter 7 Notes For Chapter 8 Notes For Chapter 9 Notes For Chapter 10 Notes For Chapter 11 Notes For Chapter 12 Index Colophon