Thinking About Godel And Turing: Essays On Complexity, 1970–2007 PDF Download
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Author: Gregory J Chaitin
Publisher: World Scientific
ISBN: 9814474703
Category : Computers
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 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 of Gödel 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: Gregory J Chaitin
Publisher: World Scientific
ISBN: 9814474703
Category : Computers
Languages : en
Pages : 368
Get Book Here
Book Description
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 of Gödel 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: Gregory J. Chaitin
Publisher: World Scientific
ISBN: 9812708979
Category : Computers
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 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."
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: Jakub Dziadkowiec
Publisher: Cambridge Scholars Publishing
ISBN: 1527540081
Category : Science
Languages : en
Pages : 179
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Book Description
The relationship of mind to matter, and the very understanding of mind and matter still eludes understanding, even after millennia of philosophical work and centuries of scientific reflection. The present volume shows how process philosophy helps us in conceptualizing such problems. The reader will find twelve chapters—written by prominent specialists of various specializations—discussing the relation between a processual school of thinking and natural and psychological scientific research, with a focus on the problems of mind and experience. The three successive sections of the book scrutinise in increasing detail the human mind, to give the full overview of the role that process philosophy might play in providing a consistent, unified language for the description of physical and mental reality.
Author: Gianfranco Minati
Publisher: World Scientific
ISBN: 9814383325
Category : Computers
Languages : en
Pages : 725
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Book Description
The book contains the Proceedings of the 2010 Conference of the Italian Systems Society. Papers deal with the interdisciplinary study of processes of changing related to a wide variety of specific disciplinary aspects. Classical attempts to deal with them, based on generalising approaches used to study the movement of bodies and environmental influence, have included ineffective reductionistic simplifications. Indeed changing also relates, for instance, to processes of acquisition and varying properties such as for software; growing and aging biological systems; learning/cognitive systems; and socio-economic systems growing and developing through innovations. Some approaches to modelling such processes are based on considering changes in structure, e.g., phase-transitions. Other approaches are based on considering (1) periodic changes in structure as for processes of self-organisation; (2) non-periodic but coherent changes in structure, as for processes of emergence; (3) the quantum level of description. Papers in the book study the problem considering its transdisciplinary nature, i.e., systemic properties studied per se and not within specific disciplinary contexts. The aim of these studies is to outline a transdisciplinary theory of change in systemic properties. Such a theory should have simultaneous, corresponding and eventually hierarchical disciplinary aspects as expected for a general theory of emergence. Within this transdisciplinary context, specific disciplinary research activities and results are assumed to be mutually represented as within a philosophical and conceptual framework based on the theoretical centrality of the observer and conceptual non-separability of context and observer, related to logically open systems and Quantum Entanglement. Contributions deal with such issues in interdisciplinary ways considering theoretical aspects and applications from Physics, Cognitive Science, Biology, Artificial Intelligence, Economics, Architecture, Philosophy, Music and Social Systems.
Author: Byron K. Jennings
Publisher: Byron Jennings
ISBN: 0994058926
Category : Science
Languages : en
Pages : 236
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Book Description
This book is a series of short, perceptive and witty essays about science and how it works. The author, a long-time theoretical physicist and science administrator, shares his hard-won insights about science gained from years of working in the trenches. The approach is eclectic with examples and quotes from a wide variety of sources. However, a unified view of science is presented, namely that science is simply the straightforward application of model building and testing against observation. The technique is applicable to all walks of life, hence the title of the book.
Author: George Gilder
Publisher: Simon and Schuster
ISBN: 1621576132
Category : Business & Economics
Languages : en
Pages : 337
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Book Description
A FINANCIAL TIMES BOOK OF THE MONTH FROM THE WALL STREET JOURNAL: "Nothing Mr. Gilder says or writes is ever delivered at anything less than the fullest philosophical decibel... Mr. Gilder sounds less like a tech guru than a poet, and his words tumble out in a romantic cascade." “Google’s algorithms assume the world’s future is nothing more than the next moment in a random process. George Gilder shows how deep this assumption goes, what motivates people to make it, and why it’s wrong: the future depends on human action.” — Peter Thiel, founder of PayPal and Palantir Technologies and author of Zero to One: Notes on Startups, or How to Build the Future The Age of Google, built on big data and machine intelligence, has been an awesome era. But it’s coming to an end. In Life after Google, George Gilder—the peerless visionary of technology and culture—explains why Silicon Valley is suffering a nervous breakdown and what to expect as the post-Google age dawns. Google’s astonishing ability to “search and sort” attracts the entire world to its search engine and countless other goodies—videos, maps, email, calendars….And everything it offers is free, or so it seems. Instead of paying directly, users submit to advertising. The system of “aggregate and advertise” works—for a while—if you control an empire of data centers, but a market without prices strangles entrepreneurship and turns the Internet into a wasteland of ads. The crisis is not just economic. Even as advances in artificial intelligence induce delusions of omnipotence and transcendence, Silicon Valley has pretty much given up on security. The Internet firewalls supposedly protecting all those passwords and personal information have proved hopelessly permeable. The crisis cannot be solved within the current computer and network architecture. The future lies with the “cryptocosm”—the new architecture of the blockchain and its derivatives. Enabling cryptocurrencies such as bitcoin and ether, NEO and Hashgraph, it will provide the Internet a secure global payments system, ending the aggregate-and-advertise Age of Google. Silicon Valley, long dominated by a few giants, faces a “great unbundling,” which will disperse computer power and commerce and transform the economy and the Internet. Life after Google is almost here. For fans of "Wealth and Poverty," "Knowledge and Power," and "The Scandal of Money."
Author: Ian Sample
Publisher: Basic Books
ISBN: 0465031692
Category : Science
Languages : en
Pages : 274
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Book Description
The biggest science story of our time, Massive spans four decades, weaving together the personal narratives and international rivalries behind the search for the "God" particle, or Higgs boson. A story of grand ambition, intense competition, clashing egos, and occasionally spectacular failures, Massive is the first book that reveals the science, culture, and politics behind the biggest unanswered question in modern physics -- what gives things mass? Drawing upon his unprecedented access to Peter Higgs, after whom the particle is named, award-winning science writer Ian Sample chronicles the multinational and multibillion-dollar quest to solve the mystery of mass. For scientists, to find the God particle is to finally understand the origin of mass, and until now, the story of their search has never been told.
Author: Danko D. Georgiev
Publisher: CRC Press
ISBN: 1351401777
Category : Science
Languages : en
Pages : 265
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Book Description
"I loved the book! This book is not just interesting, it is exciting. I have probably read every significant book in the field, and this is the strongest and most convincing one yet. It is also one of the most comprehensive in its explanations. I shall most certainly recommend the book to colleagues." –Richard G. Petty, MD "a very good introduction to the basic theory of quantum systems.... Dr. Georgiev’s book aptly prepares the reader to confront whatever might be in store later." –from the Foreword by Prof. James F. Glazebrook, Eastern Illinois University This book addresses the fascinating cross-disciplinary field of quantum information theory applied to the study of brain function. It offers a self-study guide to probe the problems of consciousness, including a concise but rigorous introduction to classical and quantum information theory, theoretical neuroscience, and philosophy of the mind. It aims to address long-standing problems related to consciousness within the framework of modern theoretical physics in a comprehensible manner that elucidates the nature of the mind-body relationship. The reader also gains an overview of methods for constructing and testing quantum informational theories of consciousness.
Author: Zondervan,
Publisher: Zondervan Academic
ISBN: 0310106923
Category : Religion
Languages : en
Pages : 254
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Book Description
A Fresh Look at the Holy Spirit. Recent decades have recognized pneumatology—the theology of the Holy Spirit—as a critical component in Christian thought, worthy of increased attention. While scholarly discussion about the Spirit is both creative and lively, it does sometimes occur in outlying areas of doctrine and practice rather than within its context of the doctrine of God. The Third Person of the Trinity represents the proceedings of the 2020 Los Angeles Theology Conference, which examined pneumatology as a core component of the doctrine of the Trinity, offering constructive proposals for understanding the doctrine of the Holy Spirit with theological and historical depth, ecumenical scope, and analytic clarity. The twelve diverse essays in this collection include discussions on: Understanding the Holy Spirit’s presence in creation. The mystery of the Trinity and the procession of the Spirit. An exploration of a Black American pneumatology of freedom. Exploring pneumatology alongside sorrow and suffering. Each of the essays collected in this volume engage with Scripture as well as with others in the field—theologians both past and present, from different confessions—in order to provide constructive resources for contemporary systematic theology and to forge a theology for the future.
