Infinity and the Mind

The Science and Philosophy of the Infinite
Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 1400849047
Category: Mathematics
Page: 368
View: 9826

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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: 7728

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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: 5671

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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.

To Infinity and Beyond

A Cultural History of the Infinite
Author: Eli Maor
Publisher: Princeton University Press
ISBN: 9780691025117
Category: Mathematics
Page: 284
View: 3934

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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: 4927

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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: 679

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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.

Georg Cantor

der Jahrhundertmathematiker und die Entdeckung des Unendlichen
Author: David Foster Wallace
Publisher: N.A
ISBN: 9783492048262
Category:
Page: 407
View: 5615

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Weißes Licht

Roman
Author: Rudy Rucker
Publisher: Heyne Verlag
ISBN: 3641151759
Category: Fiction
Page: N.A
View: 2612

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Am Ende der Unendlichkeit Felix Rayman lebt im Staat New York und hat den langweiligsten Beruf der Welt: Er ist Mathematiklehrer in einer Provinzstadt. Seine Familie ist zerrüttet, seine Karriere stritt schon seit Jahren auf der Stelle – Was hat Felix also zu verlieren? Er bringt sich selbst das luzide Träumen bei, um komplexe mathematische Probleme zu lösen, und macht so außerkörperliche Erfahrungen. Bei einer davon trifft er auf den Teufel, dem er mit knapper Not entkommt. Sein Retter ist niemand geringeres als Jesus, der ihn um einen Gefallen bittet: Rayman soll Kathy, einer jungen Frau, die im Wochenbett gestorben ist, nach Cimön bringen. Doch wie gelangt man in ein Land, das unendlich weit entfernt ist? Wie besteigt man dort einen Berg, der unendlich hoch ist? Und gibt es das absolut Unendliche eigentlich?

Meilensteine der Mathematik


Author: Ian Stewart
Publisher: Spektrum Akademischer Verlag
ISBN: 9783827423009
Category: Science
Page: 288
View: 9183

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Wer hat die Null erfunden? Wie können imaginäre Zahlen helfen, dass reale Wolkenkratzer nicht umfallen? Wo treffen sich parallele Linien? Und wann haben Sie heute zuletzt abstrakte Algebra genutzt? (Doch, Sie haben.) Wie die Mathematik die moderne Welt erschaffen hat – eine illustrierte Geschichte der Mathematik für ein breites Publikum, von den Ursprüngen im Zweistromland bis zur Gegenwart Ian Stewarts spannende Geschichte der Mathematik führt uns von der frühen Hochkultur der Babylonier bis zu den letzten ungelösten Rätseln dieser Disziplin. In typisch Stewart'scher Manier, also unterhaltsam und zugleich fundiert, schildert und erklärt er die großen Meilensteine der Mathematik – von den ersten Zahlensystemen bis zur Chaostheorie – und geht der Frage nach, welche Auswirkungen sie auf die Gesellschaft hatten und wie sie den Alltag auf alle Zeit veränderten. Er bringt uns dabei auch die Geistesgrößen der Mathematik näher, von den Naturforschern und Denkern Babyloniens, Griechenlands und Ägyptens über Newton und Descartes bis zu Fermat, Babbage und Gödel. Ohne den Leser mit komplizierten Formeln zu erschrecken, macht er die Schlüsselkonzepte der Mathematik verständlich. Als anregender historischer Streifzug für den interessierten Laien steckt Meilensteine der Mathematik voller faszinierender Details und kurioser Anekdoten. Hundert Abbildungen und Diagramme beleuchten und erhellen ein Gebiet, das von vielen Menschen gefürchtet wird, das aber unsere heutige Welt entscheidend geprägt hat.

Eine kleine Geschichte der Unendlichkeit


Author: Brian Clegg
Publisher: Rowohlt Verlag GmbH
ISBN: 364404371X
Category: Fiction
Page: 352
View: 2896

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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.

Hohlwelt

Roman
Author: Rudy Rucker
Publisher: Heyne Verlag
ISBN: 3641151767
Category: Fiction
Page: N.A
View: 9381

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Abstieg ins Innere der Erde Im Jahre 1839 muss der fünfzehnjährige Mason Algiers Reynolds die Farm seiner Eltern in Virginia verlassen, weil man ihn für einen Mörder hält. Dabei war der Tod seines Doppelgängers nichts weiter als ein dummer Unfall! Er flüchtet sich nach Richmond zu seinem Helden, dem trinkfreudigen Edgar Allan Poe, der ihm eine Stelle als Druckerlehrling anbietet. Poe trägt sich mit einem verrückten Gedanken: Er will das Schreiben aufgeben und zum Südpol reisen, wo er durch einen Vulkan ins Innere der Erde absteigen will. Dort, so sagt er, befinde sich die gigantische Hohlwelt, in der die Menschen in Blumen wohnen, seltsame Tiere leben und Raum und Zeit sich einander rätselhaft durchdringen ....

Infinity

New Research Frontiers
Author: Michael Heller,W. Hugh Woodin
Publisher: Cambridge University Press
ISBN: 1139495569
Category: Mathematics
Page: N.A
View: 3385

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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.

Of Time and Infinity

To Touch the Mind of God
Author: Leon Arceneaux
Publisher: iUniverse
ISBN: 0595810985
Category: Religion
Page: 50
View: 3749

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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.

The Large, the Small and the Human Mind


Author: Roger Penrose,Abner Shimony,Malcolm Longair,Nancy Cartwright,Stephen Hawking
Publisher: Cambridge University Press
ISBN: 9780521785723
Category: Computers
Page: 201
View: 7403

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Accessible and stimulating introduction to Roger Penrose's vision of theoretical physics for the twenty-first century.

Mechanism, Mentalism and Metamathematics

An Essay on Finitism
Author: J. Webb
Publisher: Springer Science & Business Media
ISBN: 940157653X
Category: Philosophy
Page: 285
View: 6218

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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.

A Brief History of Infinity

The Quest to Think the Unthinkable
Author: Brian Clegg
Publisher: Hachette UK
ISBN: 1472107640
Category: Mathematics
Page: 160
View: 6942

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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.