Computable universe : understanding and exploring nature as computation / editor, Hector Zenil ; foreword by Sir Roger Penrose.

Format:

Book

Language:

English

Subjects (All):

Mathematical physics.

Computable functions.

Physical Description:

1 online resource (855 p.)

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific Pub., c2013.

Language Note:

English

Summary:

This volume, with a foreword by Sir Roger Penrose, discusses the foundations of computation in relation to nature.It focuses on two main questions: What is computation? How does nature compute?The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications.The volume provides a state-of-the-art collection of technical papers and non-technical essays, re

Contents:

Contents; Foreword R. Penrose; Preface; Acknowledgements; 1. Introducing the Computable Universe H. Zenil; 1. Understanding Computation & Exploring Nature as Computation; 1.1. What is computation? How does nature compute?; 2. The Algorithmic Approach; 2.1. Information and structure in living organisms; 3. Determinism from Quantum Mechanics?; 4. From String Theory to Bit String Theory; 4.1. An algorithmic approach to the problem of fine tuning; 4.2. Black holes as perfect data compressors; References; Historical, Philosophical & Foundational Aspects of Computation

2. Origins of Digital Computing: Alan Turing, Charles Babbage, & Ada Lovelace D. Swade1. The Grand Narrative; 2. Automatic Computation; 3. From Calculation to Computation; 4. Computation as Systematic Method; 5. Formal Description; 6. Ada Lovelace; 7. Legacy of the 19th Century; 8. Turing, Inuence, and the Modern Era; References; 3. Generating, Solving and the Mathematics of Homo Sapiens. E. Post's Views on Computation L. De Mol; 1. Introduction; 2. Why Turing Rules; 3. Two Theses, Two Sides; 3.1. Post's thesis I: Generating sequences and limits of the computable

3.2. Post's thesis II: Solvability and the realm of the computable3.3. \When the bubble of symbolic logic finally burst...""; 4. Some Afterthoughts; References; 4. Machines R. Turner; 1. Abstract Machines; 2. Specification and Implementation; 3. Complexity and Uniformity; 4. Extensional Implementation; 5. The Empirical Perspective; 6. Intensional Stance; References; 5. Effectiveness N. Dershowitz & E. Falkovich; 1. Introduction; 2. Discrete Algorithms; 3. States; 3.1. Abstract states; 3.2. Effective states; 3.3. Oracular states; 4. Transitions; 4.1. Effective transitions

4.2. Classical algorithms5. Effectiveness; 5.1. Algorithms; 5.2. Effective algorithms; 5.3. Relatively effective algorithms; 6. Conclusion; References; 6. Axioms for Computability: Do They Allow a Proof of Church's Thesis? W. Sieg; Background; 1. Church Canons; 1.1. The thesis; 1.2. Semi-circles; 1.3. Symbolic processes; 2. Computors; 2.1. Preliminary step; 2.2. Boundedness and locality; 2.3. Generalizations; 3. Axiomatics; 3.1. Patterns & local operations; 3.2. Axioms & a theorem; 4. Adequacy & Philosophical Errors; References; Postscriptum: Is There a Proof of Church's Thesis?; 1. A proof?

2. Postulates?3. Improvements?; Wilfried Sieg; References; 7. The Mathematician's Bias - and the Return to Embodied Computation S. B. Cooper; 1. Computation Disembodied; 1.1. The Mathematician's bias; 2. The Mathematics of Embodiment?; 3. Emergent Natural Patterns; 4. The Mind as Mathematics?; 5. Embodiment Restored; References; 8. Intuitionistic Mathematics and Realizability in the Physical World A. Bauer; 1. Intuitionistic Understanding of Truth; 2. Synthetic Differential Geometry; 3. The Realizability Interpretation; 4. Realizability in the Real World; References

9. What is Computation? Actor Model versus Turing's Model C. Hewitt

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-283-85071-0

981-4374-30-X

OCLC:

817536625