Information Randomness Incompleteness Papers On Algorithmic Information Theory

Download Information Randomness Incompleteness Papers On Algorithmic Information Theory full books in PDF, epub, and Kindle. Read online Information Randomness Incompleteness Papers On Algorithmic Information Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Information, Randomness & Incompleteness

Author : Gregory J. Chaitin
Publisher : World Scientific
ISBN 13 : 9789810201715
Total Pages : 332 pages
Book Rating : 4.2/5 (17 download)

DOWNLOAD NOW!

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

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 Gdel 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, Randomness & Incompleteness

Author : Gregory J. Chaitin
Publisher : World Scientific
ISBN 13 : 9789971504809
Total Pages : 292 pages
Book Rating : 4.5/5 (48 download)

DOWNLOAD NOW!

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

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 Gdel'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.

Algorithmic Information Theory

Author : Gregory. J. Chaitin
Publisher : Cambridge University Press
ISBN 13 : 9780521616041
Total Pages : 192 pages
Book Rating : 4.6/5 (16 download)

DOWNLOAD NOW!

Book Synopsis Algorithmic Information Theory by : Gregory. J. Chaitin

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.

Information and Randomness

Author : Cristian Calude
Publisher : Springer Science & Business Media
ISBN 13 : 3662030497
Total Pages : 252 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!

Book Synopsis Information and Randomness by : Cristian Calude

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.

Information-theoretic Incompleteness

Author : Gregory J Chaitin
Publisher : World Scientific
ISBN 13 : 9814505102
Total Pages : 242 pages
Book Rating : 4.8/5 (145 download)

DOWNLOAD NOW!

Book Synopsis Information-theoretic Incompleteness by : Gregory J Chaitin

Download or read book Information-theoretic Incompleteness written by Gregory J Chaitin and published by World Scientific. This book was released on 1992-08-24 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 Gšdel'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.

Exploring RANDOMNESS

Author : Gregory J. Chaitin
Publisher : Springer Science & Business Media
ISBN 13 : 1447103076
Total Pages : 164 pages
Book Rating : 4.4/5 (471 download)

DOWNLOAD NOW!

Book Synopsis Exploring RANDOMNESS by : Gregory J. Chaitin

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.'

Thinking about Gdel and Turing

Author : Gregory J. Chaitin
Publisher : World Scientific
ISBN 13 : 9812708952
Total Pages : 368 pages
Book Rating : 4.8/5 (127 download)

DOWNLOAD NOW!

Book Synopsis Thinking about Gdel and Turing by : Gregory J. Chaitin

Download or read book Thinking about Gdel 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 Gdel 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 Gdel 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.

Information and Randomness

Author : Cristian S. Calude
Publisher : Springer Science & Business Media
ISBN 13 : 3662049783
Total Pages : 481 pages
Book Rating : 4.6/5 (62 download)

DOWNLOAD NOW!

Book Synopsis Information and Randomness by : Cristian S. Calude

Download or read book Information and Randomness written by Cristian S. Calude and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.

Ontological Information: Information In The Physical World

Author : Roman Krzanowski
Publisher : World Scientific
ISBN 13 : 9811248834
Total Pages : 276 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Ontological Information: Information In The Physical World by : Roman Krzanowski

Download or read book Ontological Information: Information In The Physical World written by Roman Krzanowski and published by World Scientific. This book was released on 2022-04-22 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the nature of information. It touches on many core issues of philosophy of the mind, ontology, and epistemology, and draws in several domain-specific concepts from physics, mathematics, thermodynamics, computer science, and biology. The terms used in this book, such as the mind, a conscious agent, meaning, and knowledge are used with very precise meanings because they can be easily misinterpreted. A proper understanding of these terms can be gained from the referenced literature. But more specifically, this book is about the concept of information as physical phenomenon.The book is a unique exposition of the concept of information as physical phenomenon. It provides the detailed analysis and synthesis of the current conceptualizations of information demonstrating the lack of common definition and their incompleteness. The detailed argument is provided why information may be defined as a physical phenomenon and why this type of information may be seen as fundamental to our understanding of this concept.

Mind Out of Matter

Author : G.R. Mulhauser
Publisher : Springer Science & Business Media
ISBN 13 : 9401151040
Total Pages : 401 pages
Book Rating : 4.4/5 (11 download)

DOWNLOAD NOW!

Book Synopsis Mind Out of Matter by : G.R. Mulhauser

Download or read book Mind Out of Matter written by G.R. Mulhauser and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mind Out of Matter aims to transform the way we think about consciousness and the physical world. Unlike many contemporary volumes, it develops a robust and philosophically satisfying account of the mind/body relationship without doing violence to fundamental physics. It expunges popular but ludicrous assumptions about the `in principle' capabilities of cognizers and, with the help of tools from mathematics and scientific fields, supplants flawed notions of representation, function, and mental state with objective and physically grounded alternatives. It debunks quantum theories of consciousness, constructs a simple zombie recipe, and evaluates recent research on chaotic analogue networks. This book is indispensable for readers in philosophy of mind, cognitive science, and artificial intelligence, and for mathematicians applying complexity theory or information theory to biological cognition. Audience: General academic/university libraries, plus university departmental libraries in philosophy, artificial intelligence, cognitive science, and computer science. Researchers and specialists in philosophy of mind, cognitive science, artificial intelligence, artificial life, complexity theory, and information theory. Researchers in the telecommunications industry.

An Introduction to Kolmogorov Complexity and Its Applications

Author : Ming Li
Publisher : Springer Science & Business Media
ISBN 13 : 1475726066
Total Pages : 655 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li

Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

The Foundational Debate

Author : Werner DePauli-Schimanovich
Publisher : Springer Science & Business Media
ISBN 13 : 9401733279
Total Pages : 359 pages
Book Rating : 4.4/5 (17 download)

DOWNLOAD NOW!

Book Synopsis The Foundational Debate by : Werner DePauli-Schimanovich

Download or read book The Foundational Debate written by Werner DePauli-Schimanovich and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.

In the World of Signs

Author :
Publisher : BRILL
ISBN 13 : 9004457623
Total Pages : 496 pages
Book Rating : 4.0/5 (44 download)

DOWNLOAD NOW!

Book Synopsis In the World of Signs by :

Download or read book In the World of Signs written by and published by BRILL. This book was released on 2022-04-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers almost the whole range of semiotics: the conceptions of meaning, the appearance of meaning units in semiosis, the dichotomy analyticity/syntheticity, the formal condition of good translation, the metaphorical change in fine arts, the figurativeness in modern literary theories, the metaphor in computer translation, the conditionals with egocentric predicates, the evolution of the notion of cause, the temporal relation in conditionals, the structure of passive voice, the semantics of to think, the reasoning and rationality, the non-formalized reasoning, the operation of acceptance, the principle of non-contradiction, the relation semiotics/logic/philosophy, the interdisciplinarity and exactness, the notion of imprecision, the interpretation of some semiotic notions (i.a. semantic field of terms) in terms of mathematics, the description of categorial grammars in terms of model theory, the human knowledge as moral problem, the conceptualization of the development of knowledge by means of the notion of meme, the cultural relations between some European countries, the typology of scientists, the semiotic studies of some Spanish, Irish, Czech, Polish and Norwegian works of literature, the semiotic aspects of music, television and the whole sphere of artifacts, the history of semiotics (Plato, Gonsung Long, Descartes, Fu Yen, Peirce, Brwal, Lotman, Langer).

Thinking About Godel And Turing: Essays On Complexity, 1970–2007

Author : Gregory J Chaitin
Publisher : World Scientific
ISBN 13 : 9814474703
Total Pages : 368 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Thinking About Godel And Turing: Essays On Complexity, 1970–2007 by : Gregory J Chaitin

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.

Consciousness as Complex Event

Author : Craig Delancey
Publisher : Taylor & Francis
ISBN 13 : 1000649741
Total Pages : 152 pages
Book Rating : 4.0/5 (6 download)

DOWNLOAD NOW!

Book Synopsis Consciousness as Complex Event by : Craig Delancey

Download or read book Consciousness as Complex Event written by Craig Delancey and published by Taylor & Francis. This book was released on 2022-09-09 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consciousness as Complex Event: Towards a New Physicalism provides a new approach to the study of consciousness. The author argues that what makes phenomenal experiences mysterious is that these experiences are extremely complex brain events. The text provides an accessible introduction to descriptive complexity (also known as Kolmogorov Complexity) and then applies this to show that the most influential arguments against physicalism about consciousness are unsound. The text also offers an accessible review of the current debates about consciousness and introduces a rigorous new conception of physicalism. It concludes with a positive program for the future study of phenomenal experience. It is readable and compact and will be of interest to philosophers and cognitive scientists, and of value to advanced students of philosophy. Key Features Provides a new approach to the study of consciousness, using information theory. Offers a valuable discussion of physicalism, of use in other disciplines. Contains an introduction to the main literature and arguments in the debate about consciousness. Includes an accessible overview of how to apply descriptive complexity to philosophical problems.

Mathematical Constants

Author : Steven R. Finch
Publisher : Cambridge University Press
ISBN 13 : 9780521818056
Total Pages : 634 pages
Book Rating : 4.8/5 (18 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Constants by : Steven R. Finch

Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Complexity, Entropy And The Physics Of Information

Author : Wojciech H. Zurek
Publisher : CRC Press
ISBN 13 : 0429971435
Total Pages : 545 pages
Book Rating : 4.4/5 (299 download)

DOWNLOAD NOW!

Book Synopsis Complexity, Entropy And The Physics Of Information by : Wojciech H. Zurek

Download or read book Complexity, Entropy And The Physics Of Information written by Wojciech H. Zurek and published by CRC Press. This book was released on 2018-03-08 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.