Infinity and the Mind

The Science and Philosophy of the Infinite

Author: Rudy Rucker

Publisher: Princeton University Press

ISBN: 1400849047

Category: Mathematics

Page: 368

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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.

Infinity and the Brain

A Unified Theory of Mind, Matter and God

Author: Glenn Dudley

Publisher: Paragon House

ISBN: N.A

Category: Religion

Page: 384

View: 428

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Infinity and the Brain offers a unique and logical solution to the mind-body problem. The book proposes that the relationship between mind and body is understandable only to the measure that we and our brains are unceasingly dependent upon the immanence of God. Part I explains why this is true based on how all physical structure tends to dissipate, thus moving toward its own nonexistence-a process that links the stability of all organized matter, including the brain, to the infinitude of God. The book explains why, were it not for the expectable wholeness of an image and a concomitant restraint of the Second Law of Thermodynamics, matter itself would be impossible. Part II theorizes that we have necessarily been made "in the image" of God if we are to explain the brain's homuncular design, a design by which the release of structurally-bound energy-in the incipient absence of an image-parallels an accelerating movement toward infinitude. The only requirement is that the universe must be fundamentally God-centered and personal-so personal that perception is literally equivalent to the efficiency by which an organism expects and habituates to its own finitude as contrasted with the infinitude of God.

Infinity and the Mind

Author: Rudy Rucker

Publisher: Рипол Классик

ISBN: 5885010897

Category: Philosophy

Page: N.A

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The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."

Infinity and Me

Author: Kate Hosford

Publisher: Carolrhoda Books

ISBN: 1467737917

Category: Juvenile Fiction

Page: 32

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When I looked up, I shivered. How many stars were in the sky? A million? A billion? Maybe the number was as big as infinity. I started to feel very, very small. How could I even think about something as big as infinity? Uma can't help feeling small when she peers up at the night sky. She begins to wonder about infinity. Is infinity a number that grows forever? Is it an endless racetrack? Could infinity be in an ice cream cone? Uma soon finds that the ways to think about this big idea may just be . . . infinite.

Mind Tools

The Five Levels of Mathematical Reality

Author: Rudy Rucker

Publisher: Courier Corporation

ISBN: 0486492281

Category: Mathematics

Page: 328

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Originally published: Boston: Houghton Mifflin, 1987.

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: 8941

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Looks at the competition between French and Russian mathematicians over the nature of infinity during the twentieth century.

Satan, Cantor & Infinity

Mind-boggling Puzzles

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 0486470369

Category: Games

Page: 270

View: 300

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Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions.

Infinite Processes

Background to Analysis

Author: A. Gardiner

Publisher: Springer Science & Business Media

ISBN: 1461256542

Category: Mathematics

Page: 306

View: 3224

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What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this including teachers, teachers in training, students in their last year at school, and others interested in mathematics.

Infinite Mind

Science of the Human Vibrations of Consciousness

Author: Valerie V. Hunt

Publisher: Malibu Publishing

ISBN: 9780964398818

Category: Philosophy

Page: 364

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Roads to Infinity

The Mathematics of Truth and Proof

Author: John C. Stillwell

Publisher: CRC Press

ISBN: 1439865507

Category: Mathematics

Page: 250

View: 2753

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Winner of a CHOICE Outstanding Academic Title Award for 2011! This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developments in mathematics. A particular aim of the book is to acknowledge some important but neglected figures in the history of infinity, such as Post and Gentzen, alongside the recognized giants Cantor and Gödel.

In Search of Infinity

Author: N.Ya. Vilenkin

Publisher: Springer Science & Business Media

ISBN: 1461208378

Category: Mathematics

Page: 146

View: 2792

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The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.

Infinity

Beyond the Beyond the Beyond

Author: Lillian R. Lieber

Publisher: Paul Dry Books

ISBN: 1589880366

Category: Mathematics

Page: 262

View: 8445

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This book offers an entertaining, yet thorough, explanation of the concept of, yes, infinity. Accessible to non-mathematicians, this book also cleverly connects mathematical reasoning to larger issues in society.

The Mystery of the Aleph

Mathematics, the Kabbalah, and the Search for Infinity

Author: Amir D. Aczel

Publisher: Simon and Schuster

ISBN: 0743422996

Category: Biography & Autobiography

Page: 272

View: 1129

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Journeys into the work of Georg Cantor, a Russian-born German mathematician, who developed set theory and the concept of infinite numbers, but was condemned by his peers and spent many years in an asylum.

Everything and More: A Compact History of Infinity

Author: David Foster Wallace,Neal Stephenson

Publisher: W. W. Norton & Company

ISBN: 0393339289

Category: Mathematics

Page: 344

View: 6251

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The bestselling author of "Infinite Jest" takes on the 2,000 year-old quest to understand infinity. Wallace brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.

Shadows of the Mind

A Search for the Missing Science of Consciousness

Author: Roger Penrose

Publisher: Oxford University Press, USA

ISBN: 9780195106466

Category: Computers

Page: 457

View: 3017

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Presenting a look at the human mind's capacity while criticizing artificial intelligence, the author makes suggestions about classical and quantum physics and the role of microtubules

Big Numbers

A Mind Expanding Trip to Infinity and Back

Author: John Gribben,Mary Gribben

Publisher: Ibooks

ISBN: 9780743497671

Category: Education

Page: 192

View: 6816

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A fascinating odyssey through the complex world of mathematics, physics, and other scientific fields provides a look at the comparative scale of phenomena, from the infinitely vast to the infinitesmally small, covering such topics as fractals, codes, subatomic particles, galaxies, nanotechnology, and more. Original.

Emblems of the Mind

Author: Edward Rothstein

Publisher: Harper Perennial

ISBN: 9780380727476

Category: Mathematics

Page: 263

View: 1754

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Unravels the mystery of the relationship between music and mathematics, discussing their differences and their surprising similarities--including their origins and historical links

The Beginning of Infinity

Explanations that Transform the World

Author: David Deutsch

Publisher: Penguin UK

ISBN: 0140278168

Category: Explanation

Page: 487

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'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world . . . I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman 'Bold . . . profound . . . provocative and persuasive' Economist 'Science has never had an advocate quite like David Deutsch . . . A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent

Java 9 Modularity

Patterns and Practices for Developing Maintainable Applications

Author: Sander Mak,Paul Bakker

Publisher: "O'Reilly Media, Inc."

ISBN: 1491954132

Category: Computers

Page: 300

View: 3760

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The upcoming Java 9 module system will affect existing applications and offer new ways of creating modular and maintainable applications. With this hands-on book, Java developers will learn not only about the joys of modularity, but also about the patterns needed to create truly modular and reliable applications. Authors Sander Mak and Paul Bakker teach you the concepts behind the Java 9 module system, along with the new tools it offers. You’ll also gain learn how to modularize existing code and how to build new Java applications in a modular way. Understand Java 9 module system concepts Master the patterns and practices for building truly modular applications Migrate existing applications and libraries to Java 9 modules Use JDK 9 tools for modular development and migration

Beyond Infinity

An expedition to the outer limits of the mathematical universe

Author: Eugenia Cheng

Publisher: Profile Books

ISBN: 1782830812

Category: Mathematics

Page: 204

View: 8944

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SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.