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Thinking about Gdel and Turing
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...
Randomness and Complexity
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.
Phenomenology or Deconstruction?
Phenomenology or Deconstruction? challenges traditional understandings of the relationship between phenomenology and deconstruction through new readings of the work of Maurice Merleau-Ponty, Paul Ricur and Jean-Luc Nancy. A constant dialogue with Jacques Derrida's engagement with phenomenological themes provides the impetus to establishing a new understanding of 'being' and 'presence' that exposes significant blindspots inherent in traditional readings of both phenomenology and deconstruction. In reproducing neither a stock phenomenological reaction to deconstruction nor the routine deconstructive reading of phenomenology, Christopher Watkin provides a fresh assessment of the possibilities f...
The Temporal Mechanics of the Fourth Gospel
By redefining narrative temporality in light of modern physics, this book advances a unique and innovative approach to the deep-seated temporalities within the Gospel of Johna "and challenges the implicit assumptions of textual brokenness that run throughout Johannine scholarship.
Conversations with a Mathematician
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.
Thinking About Godel And Turing: Essays On Complexity, 1970–2007
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...
Exploring RANDOMNESS
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.'
Unconventional Models of Computation, UMC’2K
This book contains papers presented at the 2nd International Conference on Unconventional Models of Computation (UMCK'2K), which was held at Solvay Institutes, Brussels, Belgium, in December 2000. Computers as we know them may be getting better and cheaper, and doing more for us, but they are still unable to cope with many tasks of practical interest. Nature, though, has been 'computing' with molecules and cells for billions of years, and these natural processes form the main motivation for the construction of radically new models of computation, the core theme of the papers in this volume. Unconventional Models of Computation, UMCK'2K covers all major areas of unconventional computation, including quantum computing, DNA-based computation, membrane computing and evolutionary algorithms.
Perspective, Projections and Design
The essays selected for this book, presented in chronological order, discuss various aspects of image-making technologies, geometrical knowledge and tools for architectural design, focusing in particular on two historical periods marked by comparable patterns of technological and cultural change. The first is the Renaissance; characterized by the rediscovery of linear perspectives and the simultaneous rise of new formats for architectural drawing and design on paper; the second, the contemporary rise of digital technologies and the simultaneous rise of virtual reality and computer-based design and manufacturing. Many of the contributing authors explore the parallel between the invention of the perspectival paradigm in early-modern Europe and the recent development of digitized virtual reality. This issue in turn bears on the specific purposes of architectural design, where various representational tools and devices are used to visualize bi-dimensional aspects of objects that must be measured and eventually built in three-dimensional space.
Greek Thought
In more than 60 essays by an international team of scholars, this volume explores the full breadth and reach of Greek thought, investigating what the Greeks knew as well as what they thought they knew, and what they believed, invented, and understood about the possibilities of knowing. 65 color illustrations. Maps.
