goedel s way exploits into an undecidable world

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Goedel S Way

Author : Gregory Chaitin
ISBN : 9780415690850
Genre : Mathematics
File Size : 55. 2 MB
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Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Goedel S Way

Author : Gregory Chaitin
ISBN : 1136587632
Genre : Mathematics
File Size : 48. 7 MB
Format : PDF, Kindle
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Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Space Time And The Limits Of Human Understanding

Author : Shyam Wuppuluri
ISBN : 9783319444185
Genre : Science
File Size : 47. 63 MB
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In this compendium of essays, some of the world’s leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers etc., all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time? Chapter [15] of this book is available open access under a CC BY 4.0 license.

The Island Of Knowledge

Author : Marcelo Gleiser
ISBN : 9780465080731
Genre : Science
File Size : 51. 62 MB
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Why discovering the limits to science may be the most powerful discovery of all How much can we know about the world? In this book, physicist Marcelo Gleiser traces our search for answers to the most fundamental questions of existence, the origin of the universe, the nature of reality, and the limits of knowledge. In so doing, he reaches a provocative conclusion: science, like religion, is fundamentally limited as a tool for understanding the world. As science and its philosophical interpretations advance, we face the unsettling recognition of how much we don't know. Gleiser shows that by abandoning the dualistic model that divides reality into the known and the unknown, we can embark on a third way based on the acceptance of our limitations. Only then, he argues, will we be truly able to experience freedom; for to be free in an age of science we cannot turn science into a god. Gleiser ultimately offers an uplifting exploration of humanity's longing to conquer the unknown, and of science's power to transform and inspire.

Undecidable Theories

Author : Alfred Tarski
ISBN : 9780444533784
Genre : Decidability (Mathematical logic)
File Size : 73. 77 MB
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G Del Escher Bach

Author : Douglas R. Hofstadter
ISBN : 0140179976
Genre : Artificial intelligence
File Size : 64. 94 MB
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Forever Undecided

Author : Raymond M. Smullyan
ISBN : 9780307962461
Genre : Mathematics
File Size : 40. 46 MB
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Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!

Proving Darwin

Author : Gregory J. Chaitin
ISBN : 9780375423147
Genre : Mathematics
File Size : 86. 6 MB
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Explains how evolution works on a mathematical level, arguing that mathematical theory is an essential part of evolution while highlighting mathematical principles in the biological world.

A Madman Dreams Of Turing Machines

Author : Janna Levin
ISBN : 9780307538031
Genre : Fiction
File Size : 86. 28 MB
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Kurt Gödel’s Incompleteness Theorems sent shivers through Vienna’s intellectual circles and directly challenged Ludwig Wittgenstein’s dominant philosophy. Alan Turing’s mathematical genius helped him break the Nazi Enigma Code during WWII. Though they never met, their lives strangely mirrored one another—both were brilliant, and both met with tragic ends. Here, a mysterious narrator intertwines these parallel lives into a double helix of genius and anguish, wonderfully capturing not only two radiant, fragile minds but also the zeitgeist of the era. From the Trade Paperback edition.

Godel S Proof

Author : Ernest Nagel
ISBN : 9780814758373
Genre : Mathematics
File Size : 33. 37 MB
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“Come to me, all you that labor and are heavy laden, and I will give you rest.”Mathew 11:28 (AKJV) In the early 1990s, a grassroots coalition of churches in Baltimore, Maryland helped launch what would become a national movement. Joining forces with labor and low-wage worker organizations, they passed the first municipal living wage ordinance. Since then, over 144 municipalities and counties as well as numerous universities and local businesses in the United States have enacted such ordinances. Although religious persons and organizations have been important both in the origins of the living wage movement and in its continuing success, they are often ignored or under analyzed. Drawing on participant observation in multiple cities, All You That Labor analyzes and evaluates the contributions of religious activists to the movement. The book explores the ways religious organizations do this work in concert with low-wage workers, the challenges religious activists face, and how people of faith might better nurture moral agency in relation to the political economy. Ultimately, C. Melissa Snarr provides clarity on how to continue to cultivate, renew, and expand religious resources dedicated to the moral agency of low-wage workers and their allies.

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