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Information, Randomness & Incompleteness

1987 Mathematics
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Release : 1987
Genre : Mathematics
Kind : eBook
Book Rating : 809/5 ( reviews)

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Book Synopsis Information, Randomness & Incompleteness by : Gregory J. Chaitin

Download or read book Information, Randomness & Incompleteness written by Gregory J. Chaitin. This book was released on 1987. 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.

Information, Randomness & Incompleteness

1990-01-01 Mathematics
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Release : 1990-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 715/5 ( reviews)

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Book Synopsis Information, Randomness & Incompleteness by : Gregory J. Chaitin

Download or read book Information, Randomness & Incompleteness written by Gregory J. Chaitin. This book was released on 1990-01-01. 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.

Information-Theoretic Incompleteness

1992 Computers
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Release : 1992
Genre : Computers
Kind : eBook
Book Rating : 953/5 ( reviews)

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Book Synopsis Information-Theoretic Incompleteness by : Gregory J. Chaitin

Download or read book Information-Theoretic Incompleteness written by Gregory J. Chaitin. This book was released on 1992. 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.

Randomness and Complexity

2007 Computers
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Release : 2007
Genre : Computers
Kind : eBook
Book Rating : 836/5 ( reviews)

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Book Synopsis Randomness and Complexity by : Cristian S. Calude

Download or read book Randomness and Complexity written by Cristian S. Calude. This book was released on 2007. 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.

Information and Randomness

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 497/5 ( reviews)

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Book Synopsis Information and Randomness by : Cristian Calude

Download or read book Information and Randomness written by Cristian Calude. This book was released on 2013-03-09. 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.

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