Randomness And Complexity, From Leibniz To Chaitin PDF Download
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Author: Cristian S Calude
Publisher: World Scientific
ISBN: 9814474398
Category : Computers
Languages : en
Pages : 466
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Book Description
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.
Author: Cristian S Calude
Publisher: World Scientific
ISBN: 9814474398
Category : Computers
Languages : en
Pages : 466
Get Book Here
Book Description
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.
Author: Cristian Calude
Publisher: World Scientific
ISBN: 9812770828
Category : Science
Languages : en
Pages : 466
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Book Description
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.
Author: Cristian S. Calude
Publisher: World Scientific
ISBN: 9812770836
Category : Computers
Languages : en
Pages : 466
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Book Description
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.
Author: Gregory J. Chaitin
Publisher: World Scientific
ISBN: 9812708952
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: Francisco Antônio Doria
Publisher: World Scientific
ISBN: 9811200076
Category : Computational complexity
Languages : en
Pages : 445
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Book Description
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
Author: Albrecht von Müller
Publisher: Springer
ISBN: 3319897764
Category : Science
Languages : en
Pages : 235
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Book Description
This volume offers a fundamentally different way of conceptualizing time and reality. Today, we see time predominantly as the linear-sequential order of events, and reality accordingly as consisting of facts that can be ordered along sequential time. But what if this conceptualization has us mistaking the “exhausts” for the “real thing”, i.e. if we miss the best, the actual taking place of reality as it occurs in a very differently structured, primordial form of time, the time-space of the present? In this new conceptual framework, both the sequential aspect of time and the factual aspect of reality are emergent phenomena that come into being only after reality has actually taken place. In the new view, facts are just the “traces” that the actual taking place of reality leaves behind on the co-emergent “canvas’’ of local spacetime. Local spacetime itself emerges only as facts come into being – and only facts can be adequately localized in it. But, how does reality then actually occur? It is conceived as a “constellatory self-unfolding”, characterized by strong self-referentiality, and taking place in the primordial form of time, the not yet sequentially structured “time-space of the present”. Time is seen here as an ontophainetic platform, i.e. as the stage on which reality can first occur. This view of time (and, thus, also space) seems to be very much in accordance with what we encounter in quantum physics before the so-called collapse of the wave function. In parallel, classical and relativistic physics largely operate within the factual portrait of reality, and the sequential aspect of time, respectively. Only singularities constitute an important exemption: here the canvas of local spacetime – that emerged together with factization – melts down again. In the novel framework quantum reduction and singularities can be seen and addressed as inverse transitions: In quantum physical state reduction reality “gains” the chrono-ontological format of facticity, and the sequential aspect of time becomes applicable. In singularities, by contrast, the inverse happens: Reality loses its local spacetime formation and reverts back into its primordial, pre-local shape – making in this way the use of causality relations, Boolean logic and the dichotomization of subject and object obsolete. For our understanding of the relation between quantum and relativistic physics this new view opens up fundamentally new perspectives: Both are legitimate views of time and reality, they just address very different chrono-ontological portraits, and thus should not lead us to erroneously subjugating one view under the other. The task of the book is to provide a formal framework in which this radically different view of time and reality can be addressed properly. The mathematical approach is based on the logical and topological features of the Borromean Rings. It draws upon concepts and methods of algebraic and geometric topology – especially the theory of sheaves and links, group theory, logic and information theory, in relation to the standard constructions employed in quantum mechanics and general relativity, shedding new light on the pestilential problems of their compatibility. The intended audience includes physicists, mathematicians and philosophers with an interest in the conceptual and mathematical foundations of modern physics.
Author: Cristian S Calude
Publisher: World Scientific
ISBN: 9811232296
Category : Computers
Languages : en
Pages : 332
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Book Description
This is a book about the 'Halting Problem', arguably the most (in)famous computer-related problem: can an algorithm decide in finite time whether an arbitrary computer program eventually stops? This seems a dull, petty question: after all, you run the program and wait till it stops. However, what if the program does not stop in a reasonable time, a week, a year, or a decade? Can you infer that it will never stop? The answer is negative. Does this raise your interest? If not, consider these questions: Can mathematics be done by computers only? Can software testing be fully automated? Can you write an anti-virus program which never needs any updates? Can we make the Internet perfectly secure? Your guess is correct: the answer to each question is negative. The Halting Problem is 'hidden' in many subjects, from logic (is mathematics free of contradictions?), physics (is quantum randomness perfect?), to philosophy (do humans have free will, or do our brains generate our thoughts and decisions in a deterministic way?) and quantum computing (why we don't have a quantum Halting Problem?) — this book will visit each of them.Written in an informal and thought-provoking language, supported with suggestive illustrations and applications and almost free of arcane mathematics (formal arguments are relegated to particular parts dedicated to the mathematically-oriented reader), the book will stimulate the curiosity and participation of the reader interested in the consequences of the limits of computing and in various attempts to cope with them.
Author: Mark Burgin
Publisher: World Scientific
ISBN: 9813109041
Category : Computers
Languages : en
Pages : 410
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Book Description
The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity.The research in information theory, the theory of complexity and their interrelations is very active. The book will expand knowledge on information, complexity and their relations representing the most recent and advanced studies and achievements in this area.The goal of the book is to present the topic from different perspectives — mathematical, informational, philosophical, methodological, etc.
Author: Ugo Pagallo
Publisher: Springer Science & Business Media
ISBN: 9400765649
Category : Law
Languages : en
Pages : 222
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Book Description
This book explores how the design, construction, and use of robotics technology may affect today’s legal systems and, more particularly, matters of responsibility and agency in criminal law, contractual obligations, and torts. By distinguishing between the behaviour of robots as tools of human interaction, and robots as proper agents in the legal arena, jurists will have to address a new generation of “hard cases.” General disagreement may concern immunity in criminal law (e.g., the employment of robot soldiers in battle), personal accountability for certain robots in contracts (e.g., robo-traders), much as clauses of strict liability and negligence-based responsibility in extra-contractual obligations (e.g., service robots in tort law). Since robots are here to stay, the aim of the law should be to wisely govern our mutual relationships.
Author: Borislav G. Dimitrov
Publisher: Borislav Dimitrov
ISBN: 1370071213
Category : Philosophy
Languages : en
Pages : 520
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Book Description
The aim of this book is to critically examine whether it is methodologically possible to combine mathematical rigor – topology with a systematic dialectical methodology in Hegel, and if so, to provide as result of my interpretation the outline of Hegel’s Analysis Situs, also with the proposed models (build on the topological manifold, cobordism, topological data analysis, persistent homology, simplicial complexes and graph theory, to provide an indication of how the merger of Hegel’s dialectical logic and topology may be instrumental to a systematic logician and of how a systematic dialectical logic perspective may help mathematical model builders.
