Gödel, Escher, Bach

Gödel, Escher, Bach PDF 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

I Am a Strange Loop PDF Author: Douglas R. Hofstadter
Publisher: Basic Books (AZ)
ISBN: 0465030785
Category : Science
Languages : en
Pages : 537

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

Metamagical Themas PDF 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

When Einstein Walked with Gödel PDF Author: Jim Holt
Publisher: Farrar, Straus and Giroux
ISBN: 0374717842
Category : Science
Languages : en
Pages : 384

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.

Surfaces and Essences

Surfaces and Essences PDF 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.

New Bach Reader

New Bach Reader PDF Author: Hans T David
Publisher: W. W. Norton & Company
ISBN: 9780393319569
Category : Biography & Autobiography
Languages : en
Pages : 612

Book Description
'The New Bach Reader' contains a collection of documents intended to bring the composer to life.

Incompleteness

Incompleteness PDF 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.

How Mathematicians Think

How Mathematicians Think PDF 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.

Analogy-making as Perception

Analogy-making as Perception PDF Author: Melanie Mitchell
Publisher: Bradford Book
ISBN: 9780262515443
Category : Analogy
Languages : en
Pages : 0

Book Description
The psychologist William James observed that "a native talent for perceiving analogies is... the leading fact in genius of every order." The centrality and the ubiquity of analogy in creative thought have been noted again and again by scientists, artists, and writers, and understanding and modeling analogical thought have emerged as two of the most important challenges for cognitive science.Analogy-Making as Perception is based on the premise that analogy-making is fundamentally a high-level perceptual process in which the interaction of perception and concepts gives rise to "conceptual slippages" which allow analogies to be made. It describes Copycat - a computer model of analogymaking, developed by the author with Douglas Hofstadter, that models the complex, subconscious interaction between perception and concepts that underlies the creation of analogies.In Copycat, both concepts and high-level perception are emergent phenomena, arising from large numbers of low-level, parallel, non-deterministic activities. In the spectrum of cognitive modeling approaches, Copycat occupies a unique intermediate position between symbolic systems and connectionist systems a position that is at present the most useful one for understanding the fluidity of concepts and high-level perception.On one level the work described here is about analogy-making, but on another level it is about cognition in general. It explores such issues as the nature of concepts and perception and the emergence of highly flexible concepts from a lower-level "subcognitive" substrate.Melanie Mitchell, Assistant Professor in the Department of Electrical Engineering and Computer Science at the University of Michigan, is a Fellow of the Michigan Society of Fellows. She is also Director of the Adaptive Computation Program at the Santa Fe Institute.

Gödel's Proof

Gödel's Proof PDF Author: Ernest Nagel
Publisher: Psychology Press
ISBN: 041504040X
Category : Gödel's theorem
Languages : en
Pages : 118

Book Description
In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
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