Gödel, Escher, Bach

An Eternal Golden Braid

Author: Douglas R. Hofstadter

Publisher: Penguin Group(CA)

ISBN: 9780140289206

Category: Art and music

Page: 832

View: 5819

'What is a self and how can a self come out of inanimate matter?' This is the riddle that drove Douglas Hofstadter to write this extraordinary book. In order to impart his original and personal view on the core mystery of human existence - our intangible sensation of 'I'-ness - Hofstadter defines the playful yet seemingly paradoxical notion of 'strange loop', and explicates this idea using analogies from many disciplines.
Posted in Art and music

I Am a Strange Loop

Author: Douglas R. Hofstadter

Publisher: Basic Books

ISBN: 0465030785

Category: Philosophy

Page: 412

View: 6050

An original, endlessly thought-provoking, and controversial look at the nature of consciousness and identity argues that the key to understanding selves and consciousness is the "strange loop," a special kind of abstract feedback loop inhabiting our brains.
Posted in Philosophy

Metamagical Themas

Questing For The Essence Of Mind And Pattern

Author: Douglas Hofstadter

Publisher: Basic Books

ISBN: 0786723866

Category: Psychology

Page: 880

View: 4256

Hofstadter’s collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.
Posted in Psychology

Surfaces and Essences

Analogy as the Fuel and Fire of Thinking

Author: Douglas Hofstadter,Emmanuel Sander

Publisher: Basic Books

ISBN: 0465018475

Category: Philosophy

Page: 592

View: 6101

Shows how analogy-making pervades human thought at all levels, influencing the choice of words and phrases in speech, providing guidance in unfamiliar situations, and giving rise to great acts of imagination.
Posted in Philosophy

Godel's Proof

Author: Ernest Nagel,James R. Newman

Publisher: NYU Press

ISBN: 0814758010

Category: Mathematics

Page: 160

View: 1825

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. Marking the 50th anniversary of the original publication of Gödel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
Posted in Mathematics

The Mind's I

Fantasies and Reflections on Self and Soul

Author: Douglas R. Hofstadter,Daniel Clement Dennett

Publisher: Bantam Dell Publishing Group

ISBN: 9780553345841

Category: Philosophy

Page: 501

View: 1985

Brilliant, shattering, mind-jolting, "The Mind's I" is a searching, probing nook--a cosmic journey of the mind--that goes deeply into the problem of self and self-consciousness as anything written in our time. From verbalizing chimpanzees to scientific speculations involving machines with souls, from the mesmerizing, maze-like fiction of Borges to the tantalizing, dreamlike fiction of Lem and Princess Ineffable, her circuits glowing read and gold, "The Mind's I " opens the mind to the Black Box of fantasy, to the windfalls of reflection, to new dimensions of exciting possibilities.
Posted in Philosophy

The Unimaginable Mathematics of Borges' Library of Babel

Author: William Goldbloom Bloch

Publisher: Oxford University Press

ISBN: 9780199715169

Category: Mathematics

Page: 224

View: 8548

"The Library of Babel" is arguably Jorge Luis Borges' best known story--memorialized along with Borges on an Argentine postage stamp. Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hidden within one of the classic works of modern literature. Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning G?del, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, information theory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literally unimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books. Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.
Posted in Mathematics

Le Ton Beau de Marot

In Praise of the Music of Language

Author: Douglas R. Hofstadter

Publisher: Basic Books (AZ)

ISBN: 9780465086450

Category: Language Arts & Disciplines

Page: 632

View: 3652

Analyzes the various translations of an obscure French poem to show the endless complexity of humans and their languages
Posted in Language Arts & Disciplines

The Colossal Book of Mathematics

Classic Puzzles, Paradoxes, and Problems : Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics

Author: Martin Gardner

Publisher: W. W. Norton & Company

ISBN: 9780393020236

Category: Games

Page: 724

View: 2435

The author presents a selection of pieces from his Scientific American "Mathematical Games" column, presenting puzzles and concepts that range from arithmetic and geometrical games to the meaning of M.C. Escher's artwork.
Posted in Games

Fluid Concepts and Creative Analogies

Computer Models of the Fundamental Mechanisms of Thought

Author: Douglas R. Hofstadter

Publisher: N.A

ISBN: 9780140258356

Category: Analogy

Page: 518

View: 4361

Hosftadter and his colleagues at The Fluid Analogies Research Group have developed computer models that help describe and explain human discovery, creation and analogical thought. The key issue of perception is investigated through the exploration of playful anagrams, number puzzles, word play and fanciful alphabetical styles, and the result is a survey of cognitive processes. This text presents the results.
Posted in Analogy

The Annotated Turing

A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine

Author: Charles Petzold

Publisher: John Wiley & Sons

ISBN: 0470229055

Category: Computers

Page: 372

View: 7907

Provides an expansion of Turing's original paper, a brief look at his life, and information on the Turing machine and computability topics.
Posted in Computers

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Author: Kurt Gödel

Publisher: Courier Corporation

ISBN: 0486158403

Category: Mathematics

Page: 80

View: 1246

First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Posted in Mathematics

The Emperor's New Mind

Concerning Computers, Minds, and the Laws of Physics

Author: Roger Penrose

Publisher: Oxford University Press

ISBN: 0198784929

Category: Computers

Page: 602

View: 6903

For many decades, the proponents of `artificial intelligence' have maintained that computers will soon be able to do everything that a human can do. In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating tour through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine. Oxford Landmark Science books are 'must-read' classics of modern science writing which have crystallized big ideas, and shaped the way we think.
Posted in Computers

Understanding Comics

Author: Scott McCloud

Publisher: Harper Collins

ISBN: 006097625X

Category: Comics & Graphic Novels

Page: 224

View: 4773

Praised throughout the cartoon industry by such luminaries as Art Spiegelman, Matt Groening, and Will Eisner, this innovative comic book provides a detailed look at the history, meaning, and art of comics and cartooning.
Posted in Comics & Graphic Novels

Semantics and Cognition

Author: Ray Jackendoff,Ray S. Jackendoff

Publisher: MIT Press

ISBN: 9780262600132

Category: Language Arts & Disciplines

Page: 283

View: 6700

This book emphasizes the role of semantics as a bridge between the theory of language and the theories of other cognitive capacities such as visual perception and motor control. It develops the position that the study of semantics of natural language is the study of the structure of thought, and that grammatical structure offers a much more important source of evidence for the theory of cognition than is often supposed by linguists, philosophers, psychologists, or computer scientists.Ray Jackendoff is Professor of Linguistics and Chairman of the Linguistics and Cognitive Science Program at Brandeis University. His most recent book, coauthored with Fred Lerdahl, is A Generative Theory of Tonal Music (MIT Press paperback). Semantics and Cognition is included in the series, Current Studies in Linguistics.
Posted in Language Arts & Disciplines

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: 1323

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.
Posted in Mathematics

Mind and Mechanism

Author: Drew V. McDermott

Publisher: MIT Press

ISBN: 9780262133920

Category: Computers

Page: 262

View: 7881

An exploration of the mind-body problem from the perspective of artificial intelligence.
Posted in Computers