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
Category: Religion
Page: 384
View: 5647

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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.

Of Time and Infinity

To Touch the Mind of God
Author: Leon Arceneaux
Publisher: iUniverse
ISBN: 0595810985
Category: Religion
Page: 50
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We live in a universe that in many respects is a mystery that we are trying to understand. Join the author on a voyage-a voyage past time into infinity. Walk with the author as he discusses the tiniest particles of matter, and then reach out into our indescribable universe-to Black Holes and Quasars. Wonder about other dimensions and other beings. Question how microbes and trees communicate. Launch your voyage from the beginning of creation and hang on for the ride. The purpose of, Of Time and Infinity, is to open the door of the "cage" where we have been taught to imprison our mind, and let it fly free-to look beyond the four dimensions that we are familiar with-beyond time into infinity. In doing so, we may touch the mind of God.

To Infinity and Beyond

A Cultural History of the Infinite
Author: Eli Maor
Publisher: Princeton University Press
ISBN: 9780691025117
Category: Mathematics
Page: 284
View: 8709

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Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

Satan, Cantor, And Infinity And Other Mind-bogglin

Author: Raymond M. Smullyan
Publisher: Knopf
ISBN: 0307819825
Category: Games & Activities
Page: 270
View: 3131

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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.

Infinite Minds

A Philosophical Cosmology
Author: John Leslie
Publisher: Oxford University Press
ISBN: 9780199248933
Category: Philosophy
Page: 234
View: 6141

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John Leslie unfolds his view of the nature of the universe in this book - a view which is unusual yet rich in philosophical inspiration and suggestion. Over the last three decades he has been developing his theory in a series of publications, and with this title he brings it to its definitive conclusion.


New Research Frontiers
Author: Michael Heller,W. Hugh Woodin
Publisher: Cambridge University Press
ISBN: 1139495569
Category: Mathematics
Page: N.A
View: 1419

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This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.

Mechanism, Mentalism and Metamathematics

An Essay on Finitism
Author: J. Webb
Publisher: Springer Science & Business Media
ISBN: 940157653X
Category: Philosophy
Page: 285
View: 1082

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This book grew out of a graduate student paper [261] in which I set down some criticisms of J. R. Lucas' attempt to refute mechanism by means of G6del's theorem. I had made several such abortive attempts myself and had become familiar with their pitfalls, and especially with the double edged nature of incompleteness arguments. My original idea was to model the refutation of mechanism on the almost universally accepted G6delian refutation of Hilbert's formalism, but I kept getting stuck on questions of mathematical philosophy which I found myself having to beg. A thorough study of the foundational works of Hilbert and Bernays finally convinced me that I had all too naively and uncritically bought this refutation of formalism. I did indeed discover points of surprisingly close contact between formalism and mechanism, but also that it was possible to under mine certain strong arguments against these positions precisely by invok ing G6del's and related work. I also began to realize that the Church Turing thesis itself is the principal bastion protecting mechanism, and that G6del's work was perhaps the best thing that ever happened to both mechanism and formalism. I pushed these lines of argument in my dis sertation with the patient help of my readers, Raymond Nelson and Howard Stein. I would especially like to thank the latter for many valuable criticisms of my dissertation as well as some helpful suggestions for reor ganizing it in the direction of the present book.

Georg Cantor

der Jahrhundertmathematiker und die Entdeckung des Unendlichen
Author: David Foster Wallace
Publisher: N.A
ISBN: 9783492048262
Page: 407
View: 7769

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Space and the Self in Hume's Treatise

Author: Marina Frasca-Spada
Publisher: Cambridge University Press
ISBN: 9780521891622
Category: Philosophy
Page: 236
View: 5826

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A rich and original examination of Hume's discussion of the idea of space.

Philosophy Classics

British and European Philosophers (Includes 20 Titles)
Author:, Limited,Various
ISBN: 1458795527
Category: Philosophy
Page: N.A
View: 4412

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This title contains, Pragmatism and Other Writings by William James, The Fair Haven by Samuel Butler, The Querist Part Three by George Berkeley, Erewhon Revisited by Samuel Butler, Philosophical Enquiry into the Sublime and the Beautiful by The Right Honourable Edmund Burke, A Treatise Concerning the Principles of Human Knowledge by George Berkeley, An Essay Concerning Human Understanding by John Locke, Three Dialogues between Hylas and Philonous by George Berkeley, Autobiography by John Stuart Mill, Essays of Francis Bacon by Sir Francis Bacon, Utopia by Sir Thomas More, Pannomial Fragments by Jeremy Bentham, Utilitarianism by John Stuart Mill, Thoughts on Man, His Nature, Productions and Discoveries by William Godwin, The Analects of Confucius by Confucius, The Social Contract by Jean-Jacques Rousseau, Discourse on the Method by Rene Descartes, Meditations of First Philosophy by Rene Descartes, Man a Machine by Julien Offray de La Mettrie, A Discourse on Method by Rene Descartes, A Discourse Upon the Origin of Inequality by Jean-Jacques Rousseau, A Treatise on the Anger of God by Lucius Caecilius Firmianus Lactantius, Politics by Aristotle, The Birth of Tragedy by Friedrich Wilhelm Nietzsche, Human, All Too Human by Friedrich Wilhelm Nietzsche, The Almanac of Love by Chikamatsu Monzaemon, Hagakure: Selections by Yamamoto Tsunetomo, The Book of Tea by Kakuzo Okakura, On the Significance of Science and Art by Leo Nikoleyevich Tolstoy, Ethics by Benedict de Spinoza,


Author: Marvin Lee Minsky
Publisher: N.A
ISBN: 9783608931174
Page: 342
View: 711

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Computing Methodologies -- Artificial Intelligence.

Orthodox Christianity

Overview and Bibliography
Author: Carl S. Tyneh
Publisher: Nova Publishers
ISBN: 9781590334669
Category: Religion
Page: 347
View: 1713

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The Orthodox Church is one of the three major branches of Christianity. There are over 300 million adherents throughout the world. The Orthodox Church is a fellowship of independent churches, which split form the Roman Church over the question of papal supremacy in 1054. The Orthodox adherents include people in: Greece, Georgia, Russia, and Serbia. There are an estimated one million members in the United States. This Advanced book explains the basic principles of Orthodox Christianity and describes in detail the holidays observed by the Orthodox Church. In addition, relevant book literature is presented in bibliographic form with easy access provided by title, subject and author indexes.

Eine kleine Geschichte der Unendlichkeit

Author: Brian Clegg
Publisher: Rowohlt Verlag GmbH
ISBN: 364404371X
Category: Fiction
Page: 352
View: 8909

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Philosophen und Mathematiker hat das Nachsinnen über das Wesen des Unendlichen buchstäblich den Verstand geraubt – und dennoch ist es ein Konzept, das immer wieder unser Leben bestimmt. In diesem mit Anekdoten und Geschichten gespickten Buch nimmt uns Brian Clegg mit auf eine Reise durch das Grenzland zwischen dem extrem Großen und dem Ultimativen, von Archimedes, der die Zahl der Sandkörner bestimmte, die das Universum füllen würden, bis zu den neuesten Theorien über die physikalische Realität des Unendlichen.