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 Mind


Author: Rudy Rucker
Publisher: Рипол Классик
ISBN: 5885010897
Category: Philosophy
Page: N.A
View: 6700

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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 the Brain

A Unified Theory of Mind, Matter and God
Author: Glenn Dudley
Publisher: Paragon House
ISBN: N.A
Category: Religion
Page: 384
View: 2455

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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.

Mind Tools

The Five Levels of Mathematical Reality
Author: Rudy Rucker
Publisher: Courier Corporation
ISBN: 0486492281
Category: Mathematics
Page: 328
View: 9510

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Originally published: Boston: Houghton Mifflin, 1987.

Infinity and Me


Author: Kate Hosford
Publisher: Carolrhoda Books
ISBN: 1467737917
Category: Juvenile Fiction
Page: 32
View: 623

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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.

Satan, Cantor, And Infinity And Other Mind-bogglin


Author: Raymond M. Smullyan
Publisher: Knopf
ISBN: 0307819825
Category: Games & Activities
Page: 270
View: 2252

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More than two hundred new and challenging logic puzzles—the simplest brainteaser to the most complex paradoxes in contemporary mathematical thinking—from our topmost puzzlemaster (“the most entertaining logician who ever lived,” Martin Gardner has called him). Our guide to the puzzles is the Sorcerer, who resides on the Island of Knights and Knaves, where knights always tell the truth and knaves always lie, and he introduces us to the amazing magic—logic—that enables to discover which inhabitants are which. Then, in a picaresque adventure in logic, he takes us to the planet Og, to the Island of Partial Silence, and to a land where metallic robots wearing strings of capital letters are noisily duplicating and dismantling themselves and others. The reader’s job is to figure out how it all works. Finally, we accompany the Sorcerer on an alluring tour of Infinity which includes George Cantor’s amazing mathematical insights. The tour (and the book) ends with Satan devising a diabolical puzzle for one of Cantor’s prize students—who outwits him! In sum: a devilish magician’s cornucopia of puzzles—a delight for every age and level of ability.

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: 4337

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

Infinite Processes

Background to Analysis
Author: A. Gardiner
Publisher: Springer Science & Business Media
ISBN: 1461256542
Category: Mathematics
Page: 306
View: 1809

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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.

Master of Space and Time


Author: Rudy Rucker
Publisher: Running Press
ISBN: 0762441380
Category: Fiction
Page: 288
View: 7089

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The real world is unbearable to madcap inventor Harry Gerber, so he uses his genius to twist the laws of science and create his own tailor-made universe. Master of Space and Time combines high physics and high jinks, blurring the line between science and magic. From a voyage to a mirror-image world where sluglike parasites make slaves of humanity, to trees and bushes that grow fries and pork chops, to a rain of fish, author Rudy Rucker—two-time winner of the Philip K. Dick Award—takes readers on the ultimate joyride. But once the gluons at the core of Harry's creation run out ... disaster looms for Harry and his friends.

A Brief History of Infinity

The Quest to Think the Unthinkable
Author: Brian Clegg
Publisher: Robinson
ISBN: 1472107640
Category: Mathematics
Page: 160
View: 8376

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'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Infinity

Beyond the Beyond the Beyond
Author: Lillian R. Lieber
Publisher: Paul Dry Books
ISBN: 1589880366
Category: Mathematics
Page: 262
View: 6496

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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.

In Search of Infinity


Author: N.Ya. Vilenkin
Publisher: Springer Science & Business Media
ISBN: 1461208378
Category: Mathematics
Page: 146
View: 8649

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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.

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: 1666

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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.

Achilles In the Quantum Universe

The Definitive History Of Infinity
Author: Richard Morris
Publisher: Henry Holt and Company
ISBN: 1627797505
Category: Science
Page: 224
View: 8781

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Centuries ago, when the ancient philosopher Zeno proposedhis famous paradox involving Achilles and the Tortoise, he struck at the heart of one of science's most enduring and intractable problems: How do we define the infinite? From then on, our greatest natural philosophers, logicians, mathematicians, and scientists, from Aristotle to Stephen Hawking, have been stymied-and driven-by infinity. Acclaimed Science writer Richard Morris guides us on a fascinating, literate and entertaining tour of the efforts made throughout history to make sense of the mind-bending concept of the infinite. In tracing this quest, Morris shows us how each new encounter with infinity drove the advancement of physics and mathematics. Along the way, we encounter such luminaries as Galileo and Newton, Tycho Brahe and Giordano Bruno, and the giants of modern physics: Planck, Einstein, Bohr, Feynmann, Hawking, and numerous others. Beginning with simple logical puzzles and progressing to the latest cosmological theories, Morris shows how these same infinity problems helped spawn such groundbreaking scientific developments as relativity and quantum mechanics. Though in many ways, the infinite is just as baffling today as it was in antiquity, contemporary scientists are probing ever deeper into the nature of our universe and catching fleeting glimpses of the infinite in ways the ancients could never have imagined. Ultimately, we see that hidden within the theoretical possibility of an infinite number of universes may lie the answers to some of humankind's most fundamental questions: Why is there something rather than nothing? Why are we here?

The Beginning of Infinity

Explanations that Transform The World
Author: David Deutsch
Publisher: Penguin UK
ISBN: 0141969695
Category: Science
Page: 496
View: 4644

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A bold and all-embracing exploration of the nature and progress of knowledge from one of today's great thinkers. Throughout history, mankind has struggled to understand life's mysteries, from the mundane to the seemingly miraculous. In this important new book, David Deutsch, an award-winning pioneer in the field of quantum computation, argues that explanations have a fundamental place in the universe. They have unlimited scope and power to cause change, and the quest to improve them is the basic regulating principle not only of science but of all successful human endeavor. This stream of ever improving explanations has infinite reach, according to Deutsch: we are subject only to the laws of physics, and they impose no upper boundary to what we can eventually understand, control, and achieve. In his previous book, The Fabric of Reality, Deutsch describe the four deepest strands of existing knowledge-the theories of evolution, quantum physics, knowledge, and computation-arguing jointly they reveal a unified fabric of reality. In this new book, he applies that worldview to a wide range of issues and unsolved problems, from creativity and free will to the origin and future of the human species. Filled with startling new conclusions about human choice, optimism, scientific explanation, and the evolution of culture, The Beginning of Infinity is a groundbreaking book that will become a classic of its kind.

Everything and More: A Compact History of Infinity


Author: David Foster Wallace
Publisher: W. W. Norton & Company
ISBN: 0393241998
Category: Mathematics
Page: 384
View: 6590

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"A gripping guide to the modern taming of the infinite."—The New York Times. With a new introduction by Neal Stephenson. Is infinity a valid mathematical property or a meaningless abstraction? David Foster Wallace brings his intellectual ambition and characteristic bravura style to the story of how mathematicians have struggled to understand the infinite, from the ancient Greeks to the nineteenth-century mathematical genius Georg Cantor's counterintuitive discovery that there was more than one kind of infinity. Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

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: 1507

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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.

Roads to Infinity

The Mathematics of Truth and Proof
Author: John C. Stillwell
Publisher: CRC Press
ISBN: 1439865507
Category: Mathematics
Page: 250
View: 8085

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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.

Geometry, Relativity and the Fourth Dimension


Author: Rudolf Rucker
Publisher: Courier Corporation
ISBN: 0486140334
Category: Science
Page: 160
View: 3960

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Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

Rabindranath Tagore

A Mind Staring Into Infinity
Author: Chhanda Chatterjee
Publisher: Primus Books
ISBN: 9789384082826
Category: Biography & Autobiography
Page: 166
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Rabindranath Tagore: A Mind Staring into Infinity explores the multifaceted genius of Rabindranath Tagore in rescuing the stagnant cultural life of Bengal from its many inhibitions. He was an ardent supporter of women's participation in dance and drama. He was a precursor of Indian abstract art. In education, he was heavily influenced by the New School Movement, teaching young children to live in harmony with nature. His works often explore the relationship between human experience, and the landscape and atmosphere and he mobilized the energy of dedicated children (bratibalakas and bratibalikas) for rural resuscitation. He acted as a fountainhead of inspiration behind the missionary zeal of C.F. Andrews and Mahatma Gandhi for radical social changes. He was a great innovator and set many new trends in poetics, breathing new life into old Vaisnava themes. A bitter critic of the aggressive nationalism of the West, he acted as a cultural mascot for the 'submerged nationalities' of war-ravaged East Europe. In this collection of essays, our contributors explore the works and legacy of a man much ahead of his time.