Advertisement
| godel escher and bach: Godel, Escher, Bach Douglas R. Hofstadter, 1979 Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern mathematics to the study of the human mind and the development of artificial intelligence. |
| godel escher and bach: Gödel, Escher, Bach Douglas R. Hofstadter, 1999 A scientist and mathematician explores the mystery and complexity of human thought processes from an interdisciplinary point of view |
| godel escher and bach: Godel, Escher, Bach Douglas R. Hofstadter, 1999 Winner of the Pulitzer Prize A metaphorical fugue on minds and machines in the spirit of Lewis Carroll Douglas Hofstadter's book is concerned directly with the nature of maps or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more. |
| godel escher and bach: Metamagical Themas Douglas R Hofstadter, 2008-08-04 Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think. |
| godel escher and bach: Incomplete Nature: How Mind Emerged from Matter Terrence W. Deacon, 2011-11-21 A radical new explanation of how life and consciousness emerge from physics and chemistry. As physicists work toward completing a theory of the universe and biologists unravel the molecular complexity of life, a glaring incompleteness in this scientific vision becomes apparent. The Theory of Everything that appears to be emerging includes everything but us: the feelings, meanings, consciousness, and purposes that make us (and many of our animal cousins) what we are. These most immediate and incontrovertible phenomena are left unexplained by the natural sciences because they lack the physical properties—such as mass, momentum, charge, and location—that are assumed to be necessary for something to have physical consequences in the world. This is an unacceptable omission. We need a theory of everything that does not leave it absurd that we exist. Incomplete Nature begins by accepting what other theories try to deny: that, although mental contents do indeed lack these material-energetic properties, they are still entirely products of physical processes and have an unprecedented kind of causal power that is unlike anything that physics and chemistry alone have so far explained. Paradoxically, it is the intrinsic incompleteness of these semiotic and teleological phenomena that is the source of their unique form of physical influence in the world. Incomplete Nature meticulously traces the emergence of this special causal capacity from simple thermodynamics to self-organizing dynamics to living and mental dynamics, and it demonstrates how specific absences (or constraints) play the critical causal role in the organization of physical processes that generate these properties. The book's radically challenging conclusion is that we are made of these specific absenses—such stuff as dreams are made on—and that what is not immediately present can be as physically potent as that which is. It offers a figure/background shift that shows how even meanings and values can be understood as legitimate components of the physical world. |
| godel escher and bach: The Psychopath Test Jon Ronson, 2011-05-12 In this madcap journey, a bestselling journalist investigates psychopaths and the industry of doctors, scientists, and everyone else who studies them. The Psychopath Test is a fascinating journey through the minds of madness. Jon Ronson's exploration of a potential hoax being played on the world's top neurologists takes him, unexpectedly, into the heart of the madness industry. An influential psychologist who is convinced that many important CEOs and politicians are, in fact, psychopaths teaches Ronson how to spot these high-flying individuals by looking out for little telltale verbal and nonverbal clues. And so Ronson, armed with his new psychopath-spotting abilities, enters the corridors of power. He spends time with a death-squad leader institutionalized for mortgage fraud in Coxsackie, New York; a legendary CEO whose psychopathy has been speculated about in the press; and a patient in an asylum for the criminally insane who insists he's sane and certainly not a psychopath. Ronson not only solves the mystery of the hoax but also discovers, disturbingly, that sometimes the personalities at the helm of the madness industry are, with their drives and obsessions, as mad in their own way as those they study. And that relatively ordinary people are, more and more, defined by their maddest edges. |
| godel escher and bach: Surfaces and Essences Douglas R Hofstadter, Emmanuel Sander, 2013-04-23 Analogy is the core of all thinking. This is the simple but unorthodox premise that Pulitzer Prize -- winning author Douglas Hofstadter and French psychologist Emmanuel Sander defend in their new work. Hofstadter has been grappling with the mysteries of human thought for over thirty years. Now, with his trademark wit and special talent for making complex ideas vivid, he has partnered with Sander to put forth a highly novel perspective on cognition. We are constantly faced with a swirling and intermingling multitude of ill-defined situations. Our brain's job is to try to make sense of this unpredictable, swarming chaos of stimuli. How does it do so? The ceaseless hail of input triggers analogies galore, helping us to pinpoint the essence of what is going on. Often this means the spontaneous evocation of words, sometimes idioms, sometimes the triggering of nameless, long-buried memories. Why did two-year-old Camille proudly exclaim, I undressed the banana!? Why do people who hear a story often blurt out, Exactly the same thing happened to me! when it was a completely different event? How do we recognize an aggressive driver from a split-second glance in our rearview mirror? What in a friend's remark triggers the offhand reply, That's just sour grapes? What did Albert Einstein see that made him suspect that light consists of particles when a century of research had driven the final nail in the coffin of that long-dead idea? The answer to all these questions, of course, is analogy-making -- the meat and potatoes, the heart and soul, the fuel and fire, the gist and the crux, the lifeblood and the wellsprings of thought. Analogy-making, far from happening at rare intervals, occurs at all moments, defining thinking from top to toe, from the tiniest and most fleeting thoughts to the most creative scientific insights. Like Gö, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core -- the incessant, unconscious quest for strong analogical links to past experiences -- this book puts forth a radical and deeply surprising new vision of the act of thinking. |
| godel escher and bach: New Bach Reader Hans T David, 1999-10-26 'The New Bach Reader' contains a collection of documents intended to bring the composer to life. |
| godel escher and bach: On Formally Undecidable Propositions of Principia Mathematica and Related Systems Kurt Gödel, 1992-01-01 In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite. |
| godel escher and bach: Blood Crazy Simon Clark, 2014-10-28 It is a quiet, uneventful Saturday in Doncaster. Nick Aten, and his best friend Steve Price – troubled seventeen year olds – spend it as usual hanging around the sleepy town, eating fast food and planning their revenge on Tug Slatter, a local bully and their arch-enemy. But by Sunday, Tug Slatter becomes the last of their worries because somehow overnight civilization is in ruins. Adults have become murderously insane – literally. They're infected with an uncontrollable urge to kill the young. Including their own children. As Nick and Steve try to escape the deadly town covered with the mutilated bodies of kids, a group of blood-thirsty adults ambushes them. Just a day before they were caring parents and concerned teachers, today they are savages destroying the future generation. Will Nick and Steve manage to escape? Is their hope that outside the Doncaster borders the world is 'normal' just a childish dream? Blood Crazy, first published in 1995, is a gripping, apocalyptic horror from Simon Clark. |
| godel escher and bach: Doing AI Richard Heimann, 2021-12-14 Artificial intelligence (AI) has captured our imaginations—and become a distraction. Too many leaders embrace the oversized narratives of artificial minds outpacing human intelligence and lose sight of the original problems they were meant to solve. When businesses try to “do AI,” they place an abstract solution before problems and customers without fully considering whether it is wise, whether the hype is true, or how AI will impact their organization in the long term. Often absent is sound reasoning for why they should go down this path in the first place. Doing AI explores AI for what it actually is—and what it is not— and the problems it can truly solve. In these pages, author Richard Heimann unravels the tricky relationship between problems and high-tech solutions, exploring the pitfalls in solution-centric thinking and explaining how businesses should rethink AI in a way that aligns with their cultures, goals, and values. As the Chief AI Officer at Cybraics Inc., Richard Heimann knows from experience that AI-specific strategies are often bad for business. Doing AI is his comprehensive guide that will help readers understand AI, avoid common pitfalls, and identify beneficial applications for their companies. This book is a must-read for anyone looking for clarity and practical guidance for identifying problems and effectively solving them, rather than getting sidetracked by a shiny new “solution” that doesn’t solve anything. |
| godel escher and bach: How Mathematicians Think William Byers, 2010-05-02 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. |
| godel escher and bach: A World Without Time Palle Yourgrau, 2009-03-04 It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together. |
| godel escher and bach: The 100 Best Nonfiction Books of All Time Robert McCrum, 2018 Beginning in 1611 with the King James Bible and ending in 2014 with Elizabeth Kolbert's 'The Sixth Extinction', this extraordinary voyage through the written treasures of our culture examines universally-acclaimed classics such as Pepys' 'Diaries', Charles Darwin's 'The Origin of Species', Stephen Hawking's 'A Brief History of Time' and a whole host of additional works -- |
| godel escher and bach: Analogy-making as Perception Melanie Mitchell, 1993 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. |
| godel escher and bach: Am I Too Loud? Gerald Moore, 1962 Famous British accompanist recalls his association with singers, violinists, and others. Includes many anecdotes, praise where it is due, and some remarks on artistic temperament. |
| godel escher and bach: Fluid Concepts and Creative Analogies Douglas R. Hofstadter, 1998 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. |
| godel escher and bach: Le Ton Beau De Marot Douglas R. Hofstadter, 1998-05-23 Lost in an art—the art of translation. Thus, in an elegant anagram (translation = lost in an art), Pulitzer Prize-winning author and pioneering cognitive scientist Douglas Hofstadter hints at what led him to pen a deep personal homage to the witty sixteenth-century French poet Clément Marot.”Le ton beau de Marot” literally means ”The sweet tone of Marot”, but to a French ear it suggests ”Le tombeau de Marot”—that is, ”The tomb of Marot”. That double entendre foreshadows the linguistic exuberance of this book, which was sparked a decade ago when Hofstadter, under the spell of an exquisite French miniature by Marot, got hooked on the challenge of recreating both its sweet message and its tight rhymes in English—jumping through two tough hoops at once.In the next few years, he not only did many of his own translations of Marot's poem, but also enlisted friends, students, colleagues, family, noted poets, and translators—even three state-of-the-art translation programs!—to try their hand at this subtle challenge.The rich harvest is represented here by 88 wildly diverse variations on Marot's little theme. Yet this barely scratches the surface of Le Ton beau de Marot, for small groups of these poems alternate with chapters that run all over the map of language and thought.Not merely a set of translations of one poem, Le Ton beau de Marot is an autobiographical essay, a love letter to the French language, a series of musings on life, loss, and death, a sweet bouquet of stirring poetry—but most of all, it celebrates the limitless creativity fired by a passion for the music of words.Dozens of literary themes and creations are woven into the picture, including Pushkin's Eugene Onegin, Dante's Inferno, Salinger's Catcher in the Rye, Villon's Ballades, Nabokov's essays, Georges Perec's La Disparition, Vikram Seth's Golden Gate, Horace's odes, and more.Rife with stunning form-content interplay, crammed with creative linguistic experiments yet always crystal-clear, this book is meant not only for lovers of literature, but also for people who wish to be brought into contact with current ideas about how creativity works, and who wish to see how today's computational models of language and thought stack up next to the human mind.Le Ton beau de Marot is a sparkling, personal, and poetic exploration aimed at both the literary and the scientific world, and is sure to provoke great excitement and heated controversy among poets and translators, critics and writers, and those involved in the study of creativity and its elusive wellsprings. |
| godel escher and bach: The Death of Philosophy Isabelle Thomas-Fogiel, 2011-05-24 Philosophers debate the death of philosophy as much as they debate the death of God. Kant claimed responsibility for both philosophy's beginning and end, while Heidegger argued it concluded with Nietzsche. In the twentieth century, figures as diverse as John Austin and Richard Rorty have proclaimed philosophy's end, with some even calling for the advent of postphilosophy. In an effort to make sense of these conflicting positions which often say as much about the philosopher as his subject Isabelle Thomas-Fogiel undertakes the first systematic treatment of the end of philosophy, while also recasting the history of western thought itself. Thomas-Fogiel begins with postphilosophical claims such as scientism, which she reveals to be self-refuting, for they subsume philosophy into the branches of the natural sciences. She discovers similar issues in Rorty's skepticism and strands of continental thought. Revisiting the work of late-nineteenth and early-twentieth-century philosophers, when the split between analytical and continental philosophy began, Thomas-Fogiel finds both traditions followed the same path the road of reference which ultimately led to self-contradiction. This phenomenon, whether valorized or condemned, has been understood as the death of philosophy. Tracing this pattern from Quine to Rorty, from Heidegger to Levinas and Habermas, Thomas-Fogiel reveals the self-contradiction at the core of their claims while also carving an alternative path through self-reference. Trained under the French philosopher Bernard Bourgeois, she remakes philosophy in exciting new ways for the twenty-first century. |
| godel escher and bach: I is a Strange Loop Marcus du Sautoy, Victoria Gould, 2021-06-03 Alone in a cube that's glowing in the darkness, X is content within its little universe of infinite thought. This solitude is disturbed by the appearance of Y, who insists on exposing X to the richness of the physical world. Each begins to long for what the other has, luring them into a strange loop. In this play for two variables, Marcus du Sautoy and Victoria Gould use mathematics and theatre to navigate the furthest reaches of our world. Through a series of surreal episodes, X and Y tackle some of life's greatest questions: where did the universe come from, does time have an end, do we have free will? I is a Strange Loop was first performed by the authors at the Barbican Pit, London, in March 2019. ' I is a Strange Loop is a play that plays... with ideas, concepts, abstractions and relationships that are, usually, hidden from the sight of ordinary mortals, articulating the ineffable, incarnating the incorporeal, revealing the inconceivable... it makes us feel we know a great deal more than we do.... and is also very funny, utterly compelling and marvellously human.' Simon McBurney |
| godel escher and bach: The Emperor's New Mind Roger Penrose, 1999-03-04 Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever approach the intricacy of the human mind. 144 illustrations. |
| godel escher and bach: I Have the Right to Culture Alain Serres, 2021-10-01 From the author and illustrator duo who created the award-winning I Have the Right to Be a Child and I Have the Right to Save My Planet comes this beautifully illustrated third book in the series. I Have the Right to Culture explores a child’s right to be curious and to experience all of humanity’s shared knowledge, including music, art, dance and much more. When a child is born, they learn the language of their parents, they sing the songs of their grandparents and they eat the delicious food that their family prepares. They also start to wonder about the lives of other children who live far away. What languages do they speak? What songs do they sing? And what games do they play? Every child has the right to learn about the world they live in, including its history and its inventions. Every child has the right to learn about artists, about writers, about potters and photographers and architects, about musicians and dancers and poets. All of humanity’s treasures are for sharing, and every child has the right to know about what has come before them! Children have the right to partake in culture as proclaimed in the United Nations Convention on the Rights of the Child. Told from the perspective of a child, this colorful and vibrant book explores what it means to be a child who has the right to find beauty in their world. Key Text Features further reading Correlates to the Common Core State Standards in English Language Arts: CCSS.ELA-LITERACY.RI.K.1 With prompting and support, ask and answer questions about key details in a text. CCSS.ELA-LITERACY.RI.K.6 Name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text. CCSS.ELA-LITERACY.RI.K.7 With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts). CCSS.ELA-LITERACY.RI.1.8 Identify the reasons an author gives to support points in a text. |
| godel escher and bach: The Beginning of Infinity David Deutsch, 2011-07-21 The New York Times bestseller: A provocative, imaginative exploration of the nature and progress of knowledge “Dazzling.” – Steven Pinker, The Guardian In this groundbreaking book, award-winning physicist David Deutsch argues that explanations have a fundamental place in the universe—and that improving them is the basic regulating principle of all successful human endeavor. Taking us on a journey through every fundamental field of science, as well as the history of civilization, art, moral values, and the theory of political institutions, Deutsch tracks how we form new explanations and drop bad ones, explaining the conditions under which progress—which he argues is potentially boundless—can and cannot happen. Hugely ambitious and highly original, The Beginning of Infinity explores and establishes deep connections between the laws of nature, the human condition, knowledge, and the possibility for progress. |
| godel escher and bach: Diagonalization and Self-reference Raymond M. Smullyan, 1994 The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The firstchapters are of an introductory nature and consist mainly of exercises with solutions given to most of them. |
| godel escher and bach: The Mind's I Douglas R. Hofstadter, Daniel Clement Dennett, 1981 |
| godel escher and bach: The Grand Biocentric Design Robert Lanza, Matej Pavsic, Bob Berman, 2020-11-17 What if life isn't just a part of the universe . . . what if it determines the very structure of the universe itself? The theory that blew your mind in Biocentrism and Beyond Biocentrism is back, with brand-new research revealing the startling truth about our existence. What is consciousness? Why are we here? Where did it all come from—the laws of nature, the stars, the universe? Humans have been asking these questions forever, but science hasn't succeeded in providing many answers—until now. In The Grand Biocentric Design, Robert Lanza, one of Time Magazine's 100 Most Influential People, is joined by theoretical physicist Matej Pavšic and astronomer Bob Berman to shed light on the big picture that has long eluded philosophers and scientists alike. This engaging, mind-stretching exposition of how the history of physics has led us to Biocentrism—the idea that life creates reality-takes readers on a step-by-step adventure into the great science breakthroughs of the past centuries, from Newton to the weirdness of quantum theory, culminating in recent revelations that will challenge everything you think you know about our role in the universe. This book offers the most complete explanation of the science behind Biocentrism to date, delving into the origins of the memorable principles introduced in previous books in this series, as well as introducing new principles that complete the theory. The authors dive deep into topics including consciousness, time, and the evidence that our observations-or even knowledge in our minds-can affect how physical objects behave. The Grand Biocentric Design is a one-of-a-kind, groundbreaking explanation of how the universe works, and an exploration of the science behind the astounding fact that time, space, and reality itself, all ultimately depend upon us. |
| godel escher and bach: The Mathematics of Life Ian Stewart, 2011-06-07 Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself. |
| godel escher and bach: To Mock a Mockingbird Raymond M. Smullyan, 2000 In this entertaining and challenging collection of logic puzzles, Raymond Smullyan -- author of Forever Undecided -- continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time. In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell the truth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle in which Inspector Craig of Scotland Yard gets involved in a search for the Fountain of Youth on the Island of Knights and Knaves. In the second part of To Mock a Mockingbird, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and -- thanks to Godel's famous theorem -- the final revelation. |
| godel escher and bach: The Mind's I Douglas R. Hofstadter, 1982 Brilliant, shattering, mind-jolting,The Mind's Iis 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. |
| godel escher and bach: Beyond the Rice Fields Naivo, 2017-10-31 The first novel from Madagascar ever to be translated into English, Naivo’s magisterial Beyond the Rice Fields delves into the upheavals of the nation’s precolonial past through the twin narratives of a slave and his master’s daughter. Fara and her father’s slave, Tsito, have shared a tender intimacy since her father bought the young boy who’d been ripped away from his family after their forest village was destroyed. Now in Sahasoa, amongst the cattle and rice fields, everything is new for Tsito, and Fara at last has a companion to play with. But as Tsito looks forward toward the bright promise of freedom and Fara, backward to a twisted, long-denied family history, a rift opens that a rapidly shifting political and social terrain can only widen. As love and innocence fall away, their world becomes defined by what tyranny and superstition both thrive upon: fear. With captivating lyricism and undeniable urgency, Naivo crafts an unsentimental interrogation of the brutal history of nineteenth-century Madagascar as a land newly exposed to the forces of Christianity and modernity, and preparing for a violent reaction against them. Beyond the Rice Fields is a tour de force about the global history of human bondage and the competing narratives that keep us from recognizing ourselves and each other, our pasts and our destinies. |
| godel escher and bach: Godel's Proof Ernest Nagel, James R. Newman, 2012-11-12 The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. |
| godel escher and bach: The Art of Mathematics Béla Bollobás, 2006-09-14 Publisher description |
| godel escher and bach: Dialogues on Mathematics Alfréd Rényi, 1967 |
| godel escher and bach: Mathematics Today Twelve Informal Essays L.A. Steen, 2012-12-06 The objective of the present book of essays is to convey to the intelligent nonmathematician something of the nature, development, and use of mathe matical concepts, particularly those that have found application in current scientific research. The idea of assembling such a volume goes back at least to 1974, when it was discussed by the then-newly-formed Joint Projects Committee for Mathematics (JPCM) of the American Mathematical Soci ety, the Mathematical Association of America, and the Society for Indus trial and Applied Mathematics. Currently, the nine members of the JPCM are Saunders Mac Lane (Chairman) of the University of Chicago, Frederick J. Almgren, Jr. of Princeton University, Richard D. Anderson of Louisiana State University, George E. Carrier of Harvard University, Hirsh G. Cohen ofthe International Business Machines Corporation, Richard C. DiPrima of Rensselaer Polytechnic Institute, Robion C. Kirby of the University of California at Berkeley, William H. Kruskal of the University of Chicago, and George D. Mostow of Yale University. The JPCM decided to make production of this volume its first major proj ect and requested the Conference Board of the Mathematical Sciences (CBMS), of which its three sponsoring societies are all member organiza tions, to approach the National Science Foundation on its behalffor support of the undertaking. A proposal submitted by the C BMS in December 1974 and in revised form in July 1975 was granted by the Foundation in May 1976, and work on assembling the volume got under way. |
| godel escher and bach: Models of Peano Arithmetic Richard W. Kaye, |
| godel escher and bach: Simply Gödel Richard Tieszen, 2017-04-11 Tieszen’s Simply Gödel is a remarkable achievement—a handy guide with the impact of a philosophical tome. It’s all here: elegantly lucid discussions of Kurt Gödel’s epochal discoveries, a sympathetic account of the eccentric genius’s life, focused discussions of his encounters with his astonished peers, and a visionary peek into the future of mathematics, philosophy, and the on-rushing specter of robots with minds. A compact masterpiece, brimming with fresh revelations. —Rudy Rucker, author of Infinity and the Mind Kurt Gödel (1906–1978) was born in Austria-Hungary (now the Czech Republic) and grew up in an ethnic German family. As a student, he excelled in languages and mathematics, mastering university-level math while still in high school. He received his doctorate from the University of Vienna at the age of 24 and, a year later, published the pioneering theorems on which his fame rests. In 1939, with the rise of Nazism, Gödel and his wife settled in the U.S., where he continued his groundbreaking work at the Institute for Advanced Study (IAS) in Princeton and became a close friend of Albert Einstein’s. In Simply Gödel, Richard Tieszen traces Gödel’s life and career, from his early years in tumultuous, culturally rich Vienna to his many brilliant achievements as a member of IAS, as well as his repeated battles with mental illness. In discussing Gödel’s ideas, Tieszen not only provides an accessible explanation of the incompleteness theorems, but explores some of his lesser-known writings, including his thoughts on time travel and his proof of the existence of God. With clarity and sympathy, Simply Gödel brings to life Gödel’s fascinating personal and intellectual journey and conveys the lasting impact of his work on our modern world. |
| godel escher and bach: Swampland Flowers Zonggao, 2006 The translator provides the text and historical context of the writings of the twelfth-century Chinese Zen master Ta Hui Tsung Kao in the Chi Yeuh Lu. Included are letters, sermons, and lectures, which cover a variety of subjects ranging from concern over the illness of a friend's son to the tending of an ox. Ta Hui addresses his remarks mainly to people in lay life and not to his fellow monks, emphasizing ways in which those immersed in worldly occupations can nevertheless learn Zen and achieve the liberation promised by the Buddha. |
| godel escher and bach: The End of the Myth Greg Grandin, 2019-03-05 WINNER OF THE PULITZER PRIZE A new and eye-opening interpretation of the meaning of the frontier, from early westward expansion to Trump’s border wall. Ever since this nation’s inception, the idea of an open and ever-expanding frontier has been central to American identity. Symbolizing a future of endless promise, it was the foundation of the United States’ belief in itself as an exceptional nation – democratic, individualistic, forward-looking. Today, though, America hasa new symbol: the border wall. In The End of the Myth, acclaimed historian Greg Grandin explores the meaning of the frontier throughout the full sweep of U.S. history – from the American Revolution to the War of 1898, the New Deal to the election of 2016. For centuries, he shows, America’s constant expansion – fighting wars and opening markets – served as a “gate of escape,” helping to deflect domestic political and economic conflicts outward. But this deflection meant that the country’s problems, from racism to inequality, were never confronted directly. And now, the combined catastrophe of the 2008 financial meltdown and our unwinnable wars in the Middle East have slammed this gate shut, bringing political passions that had long been directed elsewhere back home. It is this new reality, Grandin says, that explains the rise of reactionary populism and racist nationalism, the extreme anger and polarization that catapulted Trump to the presidency. The border wall may or may not be built, but it will survive as a rallying point, an allegorical tombstone marking the end of American exceptionalism. |
| godel escher and bach: The Logician and the Engineer Paul Nahin, 2017-04-04 Third printing. First paperback printing. Original copyright date: 2013. |
| godel escher and bach: The Cosmic Code Heinz R. Pagels, 2012-02-15 This is one of the most important books on quantum mechanics ever written for lay readers, in which an eminent physicist and successful science writer, Heinz Pagels, discusses and explains the core concepts of physics without resorting to complicated mathematics. Can be read by anyone. I heartily recommend it! -- New York Times Book Review. 1982 edition-- |
Kurt Gödel - Wikipedia
Kurt Friedrich Gödel (/ ˈɡɜːrdəl / GUR-dəl; [2] German: [kʊʁt ˈɡøːdl̩] ⓘ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher.
Godel Terminal
Gödel Terminal features real-time charting powered by Nasdaq data, providing unlimited historical and intraday charts. It delivers realtime global news from hundreds of news wires and …
Kurt Gödel - Stanford Encyclopedia of Philosophy
Feb 13, 2007 · Kurt Friedrich Gödel (b. 1906, d. 1978) was one of the principal founders of the modern, metamathematical era in mathematical logic.
Kurt Gödel | Austrian Logician, Mathematician & Philosopher ...
Apr 24, 2025 · Kurt Gödel (born April 28, 1906, Brünn, Austria-Hungary [now Brno, Czech Rep.]—died Jan. 14, 1978, Princeton, N.J., U.S.) was an Austrian-born mathematician, …
What is Godel's Theorem? | Scientific American
Jan 25, 1999 · What Godel's theorem says is that there are properly posed questions involving only the arithmetic of integers that Oracle cannot answer. In other words, there are statements …
Kurt Gödel: Life, Work, and Legacy | Institute for Advanced Study
Looking back over that century in the year 2000, TIME magazine included Kurt Gödel (1906–78), the foremost mathematical logician of the twentieth century among its top 100 most influential …
Gödel and the limits of logic | plus.maths.org
Jun 1, 2006 · Gödel proved that the mathematical methods in place since the time of Euclid (around 300 BC) were inadequate for discovering all that is true about the natural numbers.
Kurt Gödel - Wikipedia
Kurt Friedrich Gödel (/ ˈɡɜːrdəl / GUR-dəl; [2] German: [kʊʁt ˈɡøːdl̩] ⓘ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher.
Godel Terminal
Gödel Terminal features real-time charting powered by Nasdaq data, providing unlimited historical and intraday charts. It delivers realtime global news from hundreds of news wires and …
Kurt Gödel - Stanford Encyclopedia of Philosophy
Feb 13, 2007 · Kurt Friedrich Gödel (b. 1906, d. 1978) was one of the principal founders of the modern, metamathematical era in mathematical logic.
Kurt Gödel | Austrian Logician, Mathematician & Philosopher ...
Apr 24, 2025 · Kurt Gödel (born April 28, 1906, Brünn, Austria-Hungary [now Brno, Czech Rep.]—died Jan. 14, 1978, Princeton, N.J., U.S.) was an Austrian-born mathematician, …
What is Godel's Theorem? | Scientific American
Jan 25, 1999 · What Godel's theorem says is that there are properly posed questions involving only the arithmetic of integers that Oracle cannot answer. In other words, there are statements …
Kurt Gödel: Life, Work, and Legacy | Institute for Advanced Study
Looking back over that century in the year 2000, TIME magazine included Kurt Gödel (1906–78), the foremost mathematical logician of the twentieth century among its top 100 most influential …
Gödel and the limits of logic | plus.maths.org
Jun 1, 2006 · Gödel proved that the mathematical methods in place since the time of Euclid (around 300 BC) were inadequate for discovering all that is true about the natural numbers.
