The Unknowable

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Author: Gregory J. Chaitin

Publisher: Springer Science & Business Media

ISBN: 9789814021722

Category: Mathematics

Page: 124

View: 3386

This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER

The Art of Artificial Evolution

A Handbook on Evolutionary Art and Music

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Author: Juan J. Romero,Penousal Machado

Publisher: Springer Science & Business Media

ISBN: 3540728775

Category: Computers

Page: 459

View: 1303

This comprehensive book gives an up-to-date survey of the relevant bioinspired computing research fields – such as evolutionary computation, artificial life, swarm intelligence and ant colony algorithms – and examines applications in art, music and design. The editors and contributors are researchers and artists with deep experience of the related science, tools and applications, and the book includes overviews of historical developments and future perspectives.

Distributed Networked Operations

The Foundations of Network Centric Warfare

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Author: Jeff Cares

Publisher: iUniverse

ISBN: 0595378005

Category: Technology & Engineering

Page: 220

View: 9014

Distributed Networked Operations describes a refinement of what popularly has been called "network centric operations."Distributed networked operations envision combat conducted by large numbers of diverse, small units-rather than by small numbers of generally homogenous, large units. In theory and to a significant extent in practice in Afghanistan and Iraq, distributed networked operations involve a mixed bag of naval, ground and air units, none of which is individually as powerful as a fleet, air wing or armored division.Author Jeff Cares discusses distributed networked operations from the perspective of adaptive control theory and details implications for force structure, hardware employment, and networked competition. Jeff presents a formal model of Information Age combat and explores the civilian business applications of the theory.

Aspects of Kolmogorov Complexity the Physics of Information

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Author: Bradley S. Tice

Publisher: River Publishers

ISBN: 8792329268

Category: Computers

Page: 174

View: 8338

The research presented in Aspects of Kolmogorov Complexity addresses the fundamental standard of defining randomness as measured by a Martin-Lof level of randomness as found in random sequential binary strings. A classical study of statistics that addresses both a fundamental standard of statistics as well as an applied measure for statistical communication theory. The research points to compression levels in a random state that are greater than is found in current literature. A historical overview of the field of Kolmogorov Complexity and Algorithmic Information Theory, a subfield of Information Theory, is given as well as examples using a radix 3, radix 4, and radix 5 base numbers for both random and non-random sequential strings. The text also examines monochromatic and chromatic symbols and both theoretical and applied aspects of data compression as they relate to the transmission and storage of information. The appendix contains papers on the subject given at conferences and the references are current.

Exploring RANDOMNESS

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Author: Gregory J. Chaitin

Publisher: Springer Science & Business Media

ISBN: 1447103076

Category: Computers

Page: 164

View: 5913

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.'

International Mathematical News

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9901

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.

Thinking about Godel and Turing

Essays on Complexity, 1970-2007L

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Author: Gregory J. Chaitin

Publisher: World Scientific

ISBN: 9812708979

Category: Computational complexity

Page: 368

View: 8639

Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O 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 GAdel 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 GAdel 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."

Theories of Everything

The Quest for Ultimate Explanation

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Author: John D. Barrow

Publisher: Ballantine Books

ISBN: N.A

Category: Philosophy

Page: 302

View: 3016

A new account of the search for the definitive theory of the physical world examines changing ideas about the existence, from creation myths to Einstein to the most recent trends in physics