Gödel, Escher, Bach

Author: Douglas R. Hofstadter
Publisher: Penguin Group(CA)
ISBN: 9780140289206
Category : Art and music
Languages : en
Pages : 832

Book Description
'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.

I Am a Strange Loop

Author: Douglas R. Hofstadter
Publisher: Basic Books (AZ)
ISBN: 0465030785
Category : Philosophy
Languages : en
Pages : 544

Book Description
Argues that the key to understanding ourselves and consciousness is the "strange loop," a special kind of abstract feedback loop that inhabits the brain.

Metamagical Themas

Author: Douglas R Hofstadter
Publisher: Basic Books
ISBN: 0786723866
Category : Psychology
Languages : en
Pages : 622

Book Description
Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

When Einstein Walked with Gödel

Author: Jim Holt
Publisher: Farrar, Straus and Giroux
ISBN: 0374717842
Category : Science
Languages : en
Pages : 385

Book Description
From Jim Holt, the New York Times bestselling author of Why Does the World Exist?, comes an entertaining and accessible guide to the most profound scientific and mathematical ideas of recent centuries in When Einstein Walked with Gödel: Excursions to the Edge of Thought. Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction—and whether the universe truly has a future.

Incompleteness

Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299

Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

Author: Kurt Gödel
Publisher: Courier Corporation
ISBN: 0486158403
Category : Mathematics
Languages : en
Pages : 82

Book Description
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.

Surfaces and Essences

Author: Douglas Hofstadter
Publisher: Basic Books (AZ)
ISBN: 0465018475
Category : Philosophy
Languages : en
Pages : 594

Book Description
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.

Fluid Concepts and Creative Analogies

Author: Douglas R. Hofstadter
Publisher:
ISBN: 9780140258356
Category : Analogy
Languages : en
Pages : 518

Book Description
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.

The Magician King

Author: Lev Grossman
Publisher: Penguin
ISBN: 0452298016
Category : Fiction
Languages : en
Pages : 433

Book Description
Lev Grossman’s new novel THE BRIGHT SWORD will be on sale July 2024 Return to Fillory in the riveting sequel to the New York Times bestseller and literary phenomenon, The Magicians, now an original series on SYFY, from the author of the #1 bestselling The Magician’s Land. Quentin Coldwater should be happy. He escaped a miserable Brooklyn childhood, matriculated at a secret college for magic, and graduated to discover that Fillory—a fictional utopia—was actually real. But even as a Fillorian king, Quentin finds little peace. His old restlessness returns, and he longs for the thrills a heroic quest can bring. Accompanied by his oldest friend, Julia, Quentin sets off—only to somehow wind up back in the real world and not in Fillory, as they’d hoped. As the pair struggle to find their way back to their lost kingdom, Quentin is forced to rely on Julia’s illicitly learned sorcery as they face a sinister threat in a world very far from the beloved fantasy novels of their youth.

How Mathematicians Think

Author: William Byers
Publisher: Princeton University Press
ISBN: 0691145997
Category : Mathematics
Languages : en
Pages : 424

Book Description
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.