Thinking about Gödel and Turing :: essays on complexity 1970-2007 /
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of thes...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, N.J. :
World Scientific,
©2007.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing. This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size co. |
| Beschreibung: | 1 online resource (xix, 347 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812708977 9812708979 1281918679 9781281918673 9786611918675 6611918671 |
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| 520 | |a Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing. This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size co. | ||
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| contents | On the Difficulty of Computations; Information-Theoretic Computational Complexity; Randomness and Mathematical Proof; Godel's Theorem and Information; Randomness in Arithmetic; Paradoxes of Randomness; Complexity and Leibniz; The Limits of Reason; How Real Are Real Numbers?; Is Incompleteness a Serious Problem?; How Much Information Can There Be in a Real Number?; and other papers. |
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| spelling | Chaitin, Gregory J. Thinking about Gödel and Turing : essays on complexity 1970-2007 / Gregory J Chaitin ; with a foreword by Paul Davies. Gödel and Turing Hackensack, N.J. : World Scientific, ©2007. 1 online resource (xix, 347 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. On the Difficulty of Computations; Information-Theoretic Computational Complexity; Randomness and Mathematical Proof; Godel's Theorem and Information; Randomness in Arithmetic; Paradoxes of Randomness; Complexity and Leibniz; The Limits of Reason; How Real Are Real Numbers?; Is Incompleteness a Serious Problem?; How Much Information Can There Be in a Real Number?; and other papers. Print version record. Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing. This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size co. English. Gödel's theorem. http://id.loc.gov/authorities/subjects/sh85055601 Incompleteness theorems. http://id.loc.gov/authorities/subjects/sh85064795 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Metamathematics. http://id.loc.gov/authorities/subjects/sh85084269 Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Théorème de Gödel. Théorèmes d'incomplétude. Logique symbolique et mathématique. Métamathématique. Complexité de calcul (Informatique) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Computational complexity fast Gödel's theorem fast Incompleteness theorems fast Logic, Symbolic and mathematical fast Metamathematics fast Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Print version: Chaitin, Gregory J. Thinking about Gödel and Turing. Hackensack, N.J. : World Scientific, ©2007 9789812708960 (DLC) 2008270513 (OCoLC)214286093 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=518641 Volltext |
| spellingShingle | Chaitin, Gregory J. Thinking about Gödel and Turing : essays on complexity 1970-2007 / On the Difficulty of Computations; Information-Theoretic Computational Complexity; Randomness and Mathematical Proof; Godel's Theorem and Information; Randomness in Arithmetic; Paradoxes of Randomness; Complexity and Leibniz; The Limits of Reason; How Real Are Real Numbers?; Is Incompleteness a Serious Problem?; How Much Information Can There Be in a Real Number?; and other papers. Gödel's theorem. http://id.loc.gov/authorities/subjects/sh85055601 Incompleteness theorems. http://id.loc.gov/authorities/subjects/sh85064795 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Metamathematics. http://id.loc.gov/authorities/subjects/sh85084269 Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Théorème de Gödel. Théorèmes d'incomplétude. Logique symbolique et mathématique. Métamathématique. Complexité de calcul (Informatique) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Computational complexity fast Gödel's theorem fast Incompleteness theorems fast Logic, Symbolic and mathematical fast Metamathematics fast Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85055601 http://id.loc.gov/authorities/subjects/sh85064795 http://id.loc.gov/authorities/subjects/sh85078115 http://id.loc.gov/authorities/subjects/sh85084269 http://id.loc.gov/authorities/subjects/sh85029473 http://d-nb.info/gnd/4037951-6 |
| title | Thinking about Gödel and Turing : essays on complexity 1970-2007 / |
| title_alt | Gödel and Turing |
| title_auth | Thinking about Gödel and Turing : essays on complexity 1970-2007 / |
| title_exact_search | Thinking about Gödel and Turing : essays on complexity 1970-2007 / |
| title_full | Thinking about Gödel and Turing : essays on complexity 1970-2007 / Gregory J Chaitin ; with a foreword by Paul Davies. |
| title_fullStr | Thinking about Gödel and Turing : essays on complexity 1970-2007 / Gregory J Chaitin ; with a foreword by Paul Davies. |
| title_full_unstemmed | Thinking about Gödel and Turing : essays on complexity 1970-2007 / Gregory J Chaitin ; with a foreword by Paul Davies. |
| title_short | Thinking about Gödel and Turing : |
| title_sort | thinking about godel and turing essays on complexity 1970 2007 |
| title_sub | essays on complexity 1970-2007 / |
| topic | Gödel's theorem. http://id.loc.gov/authorities/subjects/sh85055601 Incompleteness theorems. http://id.loc.gov/authorities/subjects/sh85064795 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Metamathematics. http://id.loc.gov/authorities/subjects/sh85084269 Computational complexity. http://id.loc.gov/authorities/subjects/sh85029473 Théorème de Gödel. Théorèmes d'incomplétude. Logique symbolique et mathématique. Métamathématique. Complexité de calcul (Informatique) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Computational complexity fast Gödel's theorem fast Incompleteness theorems fast Logic, Symbolic and mathematical fast Metamathematics fast Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 |
| topic_facet | Gödel's theorem. Incompleteness theorems. Logic, Symbolic and mathematical. Metamathematics. Computational complexity. Théorème de Gödel. Théorèmes d'incomplétude. Logique symbolique et mathématique. Métamathématique. Complexité de calcul (Informatique) MATHEMATICS Infinity. MATHEMATICS Logic. Computational complexity Gödel's theorem Incompleteness theorems Logic, Symbolic and mathematical Metamathematics Mathematische Logik |
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| work_keys_str_mv | AT chaitingregoryj thinkingaboutgodelandturingessaysoncomplexity19702007 AT chaitingregoryj godelandturing |