- Title Pages
- Preface
- Acknowledgments
- Sources
- Introduction
- Introduction to Philosophical Perspectives on Emergence
-
1 The Rise and Fall of British Emergentism -
2 On the Idea of Emergence -
3 Reductionism and the Irreducibility of Consciousness -
4 Emergence and Supervenience -
5 Aggregativity: Reductive Heuristics for Finding Emergence -
6 How Properties Emerge -
7 Making Sense of Emergence Jaegwon Kim -
8 Downward Causation and Autonomy in Weak Emergence -
9 Real Patterns - Introduction to Scientific Perspectives on Emergence
-
10 More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science -
11 Emergence -
12 Sorting and Mixing: Race and Sex -
13 Alternative Views of Complexity Herbert Simon -
14 The Theory of Everything -
15 Is Anything Ever New? Considering Emergence -
16 Design, Observation, Surprise! A Test of Emergence -
17 Ansatz for Dynamical Hierarchies - Introduction to Background and Polemics
-
18 Newtonianism, Reductionism and the Art of Congressional Testimony -
19 Issues in the Logic of Reductive Explanations -
20 Chaos -
21 Undecidability and Intractability in Theoretical Physics -
22 Special Sciences (Or: The Disunity of Science as a Working Hypothesis) -
23 Supervenience -
24 The Nonreductivist’s Troubles with Mental Causation - Annotated Bibliography
- About the Authors
- Index
Undecidability and Intractability in Theoretical Physics
Undecidability and Intractability in Theoretical Physics
- Chapter:
- (p.387) 21 Undecidability and Intractability in Theoretical Physics
- Source:
- Emergence
- Author(s):
Stephen Wolfram
- Publisher:
- The MIT Press
This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation.
Keywords: physical process, computation, physical system, theoretical physics, calculation, computational irreducibility, computation theory
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- Title Pages
- Preface
- Acknowledgments
- Sources
- Introduction
- Introduction to Philosophical Perspectives on Emergence
-
1 The Rise and Fall of British Emergentism -
2 On the Idea of Emergence -
3 Reductionism and the Irreducibility of Consciousness -
4 Emergence and Supervenience -
5 Aggregativity: Reductive Heuristics for Finding Emergence -
6 How Properties Emerge -
7 Making Sense of Emergence Jaegwon Kim -
8 Downward Causation and Autonomy in Weak Emergence -
9 Real Patterns - Introduction to Scientific Perspectives on Emergence
-
10 More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science -
11 Emergence -
12 Sorting and Mixing: Race and Sex -
13 Alternative Views of Complexity Herbert Simon -
14 The Theory of Everything -
15 Is Anything Ever New? Considering Emergence -
16 Design, Observation, Surprise! A Test of Emergence -
17 Ansatz for Dynamical Hierarchies - Introduction to Background and Polemics
-
18 Newtonianism, Reductionism and the Art of Congressional Testimony -
19 Issues in the Logic of Reductive Explanations -
20 Chaos -
21 Undecidability and Intractability in Theoretical Physics -
22 Special Sciences (Or: The Disunity of Science as a Working Hypothesis) -
23 Supervenience -
24 The Nonreductivist’s Troubles with Mental Causation - Annotated Bibliography
- About the Authors
- Index
