Meta Maths!

The Quest for Omega
Author: Gregory J. Chaitin
Publisher: Vintage
ISBN: 1400077974
Category: Mathematics
Page: 220
View: 3842
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One of the world's leading mathematicians explores the enigmas, paradoxes, and random qualities that exist within the field of mathematics and discusses his ground-breaking discovery of the Omega number, a complex representation of unknowability. Reprint. 10,000 first printing.

Proving Darwin

Making Biology Mathematical
Author: Gregory Chaitin
Publisher: Vintage
ISBN: 1400077982
Category: Science
Page: 123
View: 3818
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A metamathematician best known for his discovery of the Omega number explains how Darwin's theory of evolution succeeds on a mathematic level and argues that no one can be certain about evolution without a proven mathematical theory. Original.

Wittgenstein and the Philosophy of Information

Proceedings of the 30th International Ludwig Wittgenstein-Symposium in Kirchberg, 2007
Author: Alois Pichler,Herbert Hrachovec
Publisher: Walter de Gruyter
ISBN: 3110328461
Category: Philosophy
Page: 351
View: 2475
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This is the first of two volumes of the proceedings from the 30th International Wittgenstein Symposium in Kirchberg, August 2007. In addition to several new contributions to Wittgenstein research (by N. Garver, M. Kross, St. Majetschak, K. Neumer, V. Rodych, L. M. Valdés-Villanueva), this volume contains articles with a special focus on digital Wittgenstein research and Wittgenstein's role for the understanding of the digital turn (by L. Bazzocchi, A. Biletzki, J. de Mul, P. Keicher, D. Köhler, K. Mayr, D. G. Stern), as well as discussions - not necessarily from a Wittgensteinian perspective - about issues in the philosophy of information, including computational ontologies (by D. Apollon, G. Chaitin, F. Dretske, L. Floridi, Y. Okamoto, M. Pasin and E. Motta).

New Theories of Everything

The Quest for Ultimate Explanation
Author: John D. Barrow
Publisher: Oxford University Press
ISBN: 019954817X
Category: Science
Page: 260
View: 5401
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Cosmology & the universe.

Exploring RANDOMNESS


Author: Gregory J. Chaitin
Publisher: Springer Science & Business Media
ISBN: 1447103076
Category: Computers
Page: 164
View: 3590
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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.'

The LIMITS of MATHEMATICS

A Course on Information Theory and the Limits of Formal Reasoning
Author: Gregory J. Chaitin
Publisher: Springer
ISBN: 9781447111214
Category: Mathematics
Page: 150
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As a teenager, Greg created independently of Kolmogorov and Solomonoff, what we call today algorithmic information theory, a sub ject of which he is the main architect. His 1965 paper on gedanken experiments on automata, which he wrote when he was in high school, is still of interest today. He was also heavily involved in IBM, where he has worked for almost thirty years, on the development of RISC technology. Greg's results are widely quoted. My favorite portrait of Greg can be found in John Horgan's-a writer for Scientific American-1996 book The End 01 Science. Greg has gotten many honors. He was a guest of distinguished people like Prigogine, the King and Queen of Belgium, and the Crown Prince of Japan. Just to be brief, allow me to paraphrase Bette Davis in All About Eve. She said, "Fasten your seat belts, it's going to be a bumpy talk!" Ladies and Gentlemen, Greg Chaitin! [Laughter & Applause] CRISTIAN CALUDE introducing GREGORY CHAITIN at the DMTCS'96 meeting at the University of Auckland.

Algorithmic Information Theory


Author: Gregory J. Chaitin
Publisher: Cambridge University Press
ISBN: 9780521616041
Category: Computers
Page: 192
View: 1637
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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.

Conversations with a Mathematician

Math, Art, Science and the Limits of Reason
Author: Gregory J. Chaitin
Publisher: Springer Science & Business Media
ISBN: 1447101855
Category: Science
Page: 158
View: 3364
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The author, G. J. Chaitin, shows that God plays dice not only in quantum mechanics but also in the foundations of mathematics. According to Chaitin there exist mathematical facts that are true for no reason. This fascinating and provocative text contains a collection of his most wide-ranging and non-technical lectures and interviews. It will be of interest to anyone concerned with the philosophy of mathematics, the similarities and differences between physics and mathematics, and mathematics as art.

Proofs and Refutations

The Logic of Mathematical Discovery
Author: Imre Lakatos
Publisher: Cambridge University Press
ISBN: 1316425339
Category: Science
Page: N.A
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Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

Thinking about G”del and Turing

Essays on Complexity, 1970-2007
Author: Gregory J. Chaitin
Publisher: World Scientific
ISBN: 9812708952
Category: Mathematics
Page: 347
View: 7859
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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.

The Fabric of Reality


Author: David Deutsch
Publisher: Penguin UK
ISBN: 014196961X
Category: Science
Page: 400
View: 1376
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An extraordinary and challenging synthesis of ideas uniting Quantum Theory, and the theories of Computation, Knowledge and Evolution, Deutsch's extraordinary book explores the deep connections between these strands which reveal the fabric of realityin which human actions and ideas play essential roles.

Infinity and the Mind

The Science and Philosophy of the Infinite
Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 1400849047
Category: Mathematics
Page: 368
View: 887
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In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

Naming Infinity

A True Story of Religious Mysticism and Mathematical Creativity
Author: Loren Graham,Jean-Michel Kantor
Publisher: Harvard University Press
ISBN: 0674032934
Category: History
Page: 239
View: 3064
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Looks at the competition between French and Russian mathematicians over the nature of infinity during the twentieth century.

Impossibility

The Limits of Science and the Science of Limits
Author: John D. Barrow
Publisher: Oxford University Press on Demand
ISBN: 0195130820
Category: Science
Page: 279
View: 2882
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Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

El cálculo de la vida


Author: Andrés Moya
Publisher: Universitat de València
ISBN: 8437096219
Category:
Page: 174
View: 2463
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«El cálculo de la vida» versa sobre biología y sus aproximaciones teóricas desde una perspectiva cualitativa. Andrés Moya pretende mostrar que la biología actual está más cerca que nunca de realizar el sueño de Goethe, de la convergencia de las tradiciones analíticas y sintéticas para comprender al organismo vivo en su totalidad.

The Dialectic of Duration


Author: Gaston Bachelard
Publisher: Rowman & Littlefield International
ISBN: 9781786600585
Category: Science
Page: 160
View: 4856
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In The Dialectic of Duration Gaston Bachelard addresses the nature of time in response to the writings of his great contemporary, Henri Bergson. For Bachelard, experienced time is irreducibly fractured and interrupted, as indeed are material events. At stake is an entire conception of the physical world, an entire approach to the philosophy of science. It was in this work that Bachelard first marshalled all the components of his visionary philosophy of science, with its steady insistence on the human context and subtle encompassing of the irrational within the rational.

The Economics of Identity and Creativity

A Cultural Science Approach
Author: Carsten Herrmann-Pillath
Publisher: Transaction Publishers
ISBN: 1412843693
Category: Psychology
Page: 259
View: 7769
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The Economics of Identity and Creativity aims to sythesize naturalistic evolutionary theory while discussing new developments in economics. The author's approach reexamines fundamental assumptions about how a capitalist economy works, from the relation between producers and consumers to the functioning of intellectual property rights. In the creative economy, the author argues, identities merge with the flow of creative action. To explain these changes, he draws upon a range of theories from analytical philosophy to biology, and from economics to sociology. The first part of the book examines the role of language in the naturalistic approach to cultural science. Hermann-Pillath draws on Darwinian evolutionary theory to map a concept of knowledge. Part Two offers a systematic approach to creativity and identity from the naturalistic point of view developed in Part One. Here the author builds a theory of creativity from the ideas of conceptual blending in the cognitive sciences. Herrmann-Pillath presents a theory of identity based on analytical philosophy, and looks at the problems in fixing the boundaries of an individual identity both in biological evolutionary theory and brain sciences. He takes the concept of identity through the current economic approaches, examining the distinction between social and personal identity. This fascinating interdisciplinary work provides a precise argument that the foundations of economics can be found in cultural science, and it has evolved to become the cultural institution at the core of the modern economy.

On Constructive Interpretation of Predictive Mathematics (1990)


Author: Charles Parsons
Publisher: Routledge
ISBN: 1315397056
Category: Philosophy
Page: 342
View: 1142
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First published in 1990, this book consists of a detailed exposition of results of the theory of "interpretation" developed by G. Kreisel — the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work. It contains more complex versions of the information obtained by Kreisel for number theory and clustering around the no-counter-example interpretation, for number-theorectic forumulae provide in ramified analysis. It also proves the omega-consistency of ramified analysis. The author also presents proofs of Schütte’s cut-elimination theorems which are based on his consistency proofs and essentially contain them — these went further than any published work up to that point, helping to squeeze the maximum amount of information from these proofs.

Personal Knowledge


Author: Michael Polanyi
Publisher: Routledge
ISBN: 1134746091
Category: Philosophy
Page: 503
View: 5458
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First published in 2012. Routledge is an imprint of Taylor & Francis, an informa company.

The Unknowable


Author: Gregory J. Chaitin
Publisher: Springer Science & Business Media
ISBN: 9789814021722
Category: Mathematics
Page: 124
View: 3728
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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