Information Randomness Amp Incompleteness

Author : Gregory J. Chaitin
Publisher : World Scientific
ISBN 13 : 9789810201715
Total Pages : 332 pages
Book Rating : 4.10/5 ( download)

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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.

Author : Gregory J. Chaitin
Publisher : World Scientific
ISBN 13 : 9812708952
Total Pages : 368 pages
Book Rating : 4.53/5 ( download)

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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.

Author : Anthony Aguirre
Publisher : Springer Nature
ISBN 13 : 3030703541
Total Pages : 181 pages
Book Rating : 4.47/5 ( download)

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Download or read book Undecidability, Uncomputability, and Unpredictability written by Anthony Aguirre and published by Springer Nature. This book was released on 2021-08-20 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.​

Author : Niels Henrik Gregersen
Publisher : Oxford University Press on Demand
ISBN 13 : 0195150708
Total Pages : 256 pages
Book Rating : 4.04/5 ( download)

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Download or read book From Complexity to Life written by Niels Henrik Gregersen and published by Oxford University Press on Demand. This book was released on 2003 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. Contributors1. Introduction: Towards an Emergentist Worldview, Paul DaviesPART I. DEFINING COMPLEXITY2. Randomness and Mathematical Proof, Gregory J. Chaitin3. How to Define Complexity in Physics, and Why, Charles H. BennettPART II. THE CONCEPT OF INFORMATION IN PHYSICS AND BIOLOGY4. The Emergence of Autonomous Agents, Stuart Kauffman5. Complexity and the Arrow of Time, Paul Davies6. Can Evolutionary Algorithms Generate Specified Complexity?, William A. Dembski7. The Second Law of Gravutucs and the Fourth Law of Thermodynamics, Ian Stewart8. Two Arros from a Mighty Bow, Werner R. LoewensteinPART III. PHILOSOPHICAL AND RELIGIOUS PERSPECTIVES9. Emergence of Transcendence, Harold J. Morowitz10. Complexity, Emergence, and Divine Creativity, Arthur Peacocke11. From Anthropic Design to Self-Organized Complexity, Niels Henrik GregersenIndex.

Author : Gregory J Chaitin
Publisher : World Scientific
ISBN 13 : 9814474703
Total Pages : 368 pages
Book Rating : 4.02/5 ( download)

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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.

Author : A. Shen
Publisher : American Mathematical Society
ISBN 13 : 1470470640
Total Pages : 511 pages
Book Rating : 4.47/5 ( download)

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Download or read book Kolmogorov Complexity and Algorithmic Randomness written by A. Shen and published by American Mathematical Society. This book was released on 2022-05-18 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

Author : Daniel M. Greenberger
Publisher :
ISBN 13 :
Total Pages : 946 pages
Book Rating : 4.34/5 ( download)

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Download or read book Fundamental Problems in Quantum Theory written by Daniel M. Greenberger and published by . This book was released on 1995 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ed. Daniel Greenberger, 750pp May 1995 164.95

Author :
Publisher :
ISBN 13 :
Total Pages : 1114 pages
Book Rating : 4.38/5 ( download)

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Download or read book Arizona Law Review written by and published by . This book was released on 1990 with total page 1114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Mo Jamshidi
Publisher : CRC Press
ISBN 13 : 1420065890
Total Pages : 480 pages
Book Rating : 4.93/5 ( download)

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Download or read book Systems of Systems Engineering written by Mo Jamshidi and published by CRC Press. This book was released on 2017-12-19 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: As technology presses forward, scientific projects are becoming increasingly complex. The international space station, for example, includes over 100 major components, carried aloft during 88 spaces flights which were organized by over 16 nations. The need for improved system integration between the elements of an overall larger technological system has sparked further development of systems of systems (SoS) as a solution for achieving interoperability and superior coordination between heterogeneous systems. Systems of Systems Engineering: Principles and Applications provides engineers with a definitive reference on this newly emerging technology, which is being embraced by such engineering giants as Boeing, Lockheed Martin, and Raytheon. The book covers the complete range of fundamental SoS topics, including modeling, simulation, architecture, control, communication, optimization, and applications. Containing the contributions of pioneers at the forefront of SoS development, the book also offers insight into applications in national security, transportation, energy, and defense as well as healthcare, the service industry, and information technology. System of systems (SoS) is still a relatively new concept, and in time numerous problems and open-ended issues must be addressed to realize its great potential. THis book offers a first look at this rapidly developing technology so that engineers are better equipped to face such challenges.

Author : Karl Svozil
Publisher : World Scientific
ISBN 13 : 9789810208097
Total Pages : 314 pages
Book Rating : 4.9X/5 ( download)

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Download or read book Randomness & Undecidability in Physics written by Karl Svozil and published by World Scientific. This book was released on 1993 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an ?inner description?, a ?virtual physics? of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as ?randomness? in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the ?distant future?. In other words: no ?speedup? or ?computational shortcut? is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.