Proving Darwin

Author: Gregory Chaitin
Editor: Vintage
ISBN: 1400077982
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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.

Proving Darwin

Author: Gregory J. Chaitin
Editor: Pantheon
ISBN: 0375423141
Size: 19,44 MB
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Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world.

Proving Darwin

Author: Gregory Chaitin
Editor: Vintage
ISBN: 0307907465
Size: 11,56 MB
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Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level. For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has even attempted to answer it until now. In this illuminating and provocative book, Gregory Chaitin argues that we can’t be sure evolution makes sense without a mathematical theory. He elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Chaitin presents an accessible introduction to metabiology, a new way of thinking about biological science that highlights the mathematical structures underpinning the biological world. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.

Meta Maths

Author: Gregory J. Chaitin
Editor: Vintage Books USA
ISBN: 1400077974
Size: 12,15 MB
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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.

Introduction To Evolutionary Informatics

Author: Marks Ii Robert J
Editor: World Scientific
ISBN: 9813142162
Size: 13,59 MB
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Science has made great strides in modeling space, time, mass and energy. Yet little attention has been paid to the precise representation of the information ubiquitous in nature. Introduction to Evolutionary Informatics fuses results from complexity modeling and information theory that allow both meaning and design difficulty in nature to be measured in bits. Built on the foundation of a series of peer-reviewed papers published by the authors, the book is written at a level easily understandable to readers with knowledge of rudimentary high school math. Those seeking a quick first read or those not interested in mathematical detail can skip marked sections in the monograph and still experience the impact of this new and exciting model of nature's information. This book is written for enthusiasts in science, engineering and mathematics interested in understanding the essential role of information in closely examined evolution theory.

Algorithmic Information Theory

Author: Gregory J. Chaitin
Editor: Cambridge University Press
ISBN: 9780521616041
Size: 11,74 MB
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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.

The Limits Of Mathematics

Author: Gregory J. Chaitin
Editor: Springer
ISBN: 1852336684
Size: 18,24 MB
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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.

Computation And Its Limits

Author: W. Paul Cockshott
Editor: Oxford University Press
ISBN: 0199640327
Size: 15,27 MB
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Although we are entirely unaware of it, computation is central to all aspects of our existences. Every day we solve, or try to solve, a myriad of problems, from the utterly trivial to the bafflingly complex. This book explains why it is possible to do computation and what the ultimate limits of it are, as understood by modern science.

Exploring Randomness

Author: Gregory J. Chaitin
Editor: Springer Science & Business Media
ISBN: 1447103076
Size: 18,59 MB
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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.'

Thinking About G Del And Turing

Author: Gregory J. Chaitin
Editor: World Scientific
ISBN: 9812708952
Size: 20,50 MB
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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.