Download or read book Information Theoretic Incompleteness written by Gregory J. Chaitin and published by World Scientific. This book was released on 1992 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this mathematical autobiography, Gregory Chaitin presents a technical survey of his work and a nontechnical discussion of its significance. The volume is an essential companion to the earlier collection of Chaitin's papers Information, Randomness and Incompleteness, also published by World Scientific.The technical survey contains many new results, including a detailed discussion of LISP program size and new versions of Chaitin's most fundamental information-theoretic incompleteness theorems. The nontechnical part includes the lecture given by Chaitin in G?del's classroom at the University of Vienna, a transcript of a BBC TV interview, and articles from New Scientist, La Recherche, and the Mathematical Intelligencer.

Download or read book Information Randomness Incompleteness written by Gregory J. Chaitin and published by World Scientific. This book was released on 1987 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers gathered in this book were published over a period of more than twenty years in widely scattered journals. They led to the discovery of randomness in arithmetic which was presented in the recently published monograph on ?Algorithmic Information Theory? by the author. There the strongest possible version of G”del's incompleteness theorem, using an information-theoretic approach based on the size of computer programs, was discussed. The present book is intended as a companion volume to the monograph and it will serve as a stimulus for work on complexity, randomness and unpredictability, in physics and biology as well as in metamathematics.

Download or read book Algorithmic Information Theory written by Gregory. J. Chaitin and published by Cambridge University Press. This book was released on 2004-12-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

Download or read book Algorithmic Information Theory written by Gregory. J. Chaitin and published by Cambridge University Press. This book was released on 2004-12-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation.

Download or read book Thinking about G del and Turing written by Gregory J. Chaitin and published by World Scientific. This book was released on 2007 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable ê 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 G”del 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 complexity or algorithmic information content in order to shed further light on the fundamental work of G”del and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.

Download or read book Randomness and Complexity written by Cristian Calude and published by World Scientific. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.

Download or read book Information theoretic Incompleteness written by G. J. Chaitin and published by . This book was released on 1992 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Exploring RANDOMNESS written by Gregory J. Chaitin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'

Download or read book Randomness and Complexity written by Cristian S. Calude and published by World Scientific. This book was released on 2007 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin''s 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. Sample Chapter(s). Chapter 1: On Random and Hard-to-Describe Numbers (902 KB). Contents: On Random and Hard-to-Describe Numbers (C H Bennett); The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies); What is a Computation? (M Davis); A Berry-Type Paradox (G Lolli); The Secret Number. An Exposition of Chaitin''s Theory (G Rozenberg & A Salomaa); Omega and the Time Evolution of the n-Body Problem (K Svozil); God''s Number: Where Can We Find the Secret of the Universe? In a Single Number! (M Chown); Omega Numbers (J-P Delahaye); Some Modern Perspectives on the Quest for Ultimate Knowledge (S Wolfram); An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding (D Zeilberger); and other papers. Readership: Computer scientists and philosophers, both in academia and industry.

Download or read book Unravelling Complexity written by Francisco Antônio Doria and published by World Scientific. This book was released on 2020 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revolutions that Gregory Chaitin brought within the fields of science are well known. From his discovery of algorithmic information complexity to his work on Gödel's theorem, he has contributed deeply and expansively to such diverse fields. This book attempts to bring together a collection of articles written by his colleagues, collaborators and friends to celebrate his work in a festschrift. It encompasses various aspects of the scientific work that Chaitin has accomplished over the years. Topics range from philosophy to biology, from foundations of mathematics to physics, from logic to computer science, and all other areas Chaitin has worked on. It also includes sketches of his personality with the help of biographical accounts in some unconventional articles that will provide a rare glimpse into the personal life and nature of Chaitin. Compared to the other books that exist along a similar vein, this book stands out primarily due to its highly interdisciplinary nature and its scope that will attract readers into Chaitin's world

Download or read book Information Randomness Incompleteness written by Gregory J. Chaitin and published by World Scientific. This book was released on 1990-01-01 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of G”del and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.

Download or read book Incompleteness written by Rebecca Goldstein and published by W. W. Norton & Company. This book was released on 2006-01-31 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Download or read book Information and Randomness written by Cristian Calude and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously", says G.J. Chaitin, one of the fathers of this theory of complexity and randomness, which is also known as Kolmogorov complexity. It is relevant for logic (new light is shed on Gödel's incompleteness results), physics (chaotic motion), biology (how likely is life to appear and evolve?), and metaphysics (how ordered is the universe?). This book, benefiting from the author's research and teaching experience in Algorithmic Information Theory (AIT), should help to make the detailed mathematical techniques of AIT accessible to a much wider audience.

Download or read book The Limits of Mathematics written by Gregory J. Chaitin and published by Springer. This book was released on 1998 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Godel is much more widespread and serious than hitherto suspected.

Download or read book The Incompleteness Phenomenon written by Martin Goldstern and published by CRC Press. This book was released on 2018-10-08 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the foundations and limitations of modern mathematics.

Download or read book Thinking About Godel And Turing Essays On Complexity 1970 2007 written by Gregory J Chaitin and published by World Scientific. This book was released on 2007-08-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable Ω 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 complexity or algorithmic information content in order to shed further light on the fundamental work of Gödel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.

Download or read book Meta Math written by Gregory Chaitin and published by Vintage. This book was released on 2006-11-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory. Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.