Circularity

A Common Secret to Paradoxes, Scientific Revolutions and Humor
Author: Ron Aharoni
Publisher: World Scientific
ISBN: 9814723703
Category: Mathematics
Page: 180
View: 382

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"Circularity" is the story of a Janus-faced conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question "What is humor". The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct. See Press Release: Vicious circles -- confusing, instructive, amusing? Contents:The Dark Side — Paradoxes:MagicFree WillThe Mind–Body ProblemThe Illuminated Side — Scientific Breakthroughs:Large Infinities and Still Larger OnesGödel's Incompleteness TheoremTuring Invents the ComputerFor the Experienced Hikers Readership: Researchers in mathematics, philosophy and general public.

The Best Writing on Mathematics 2017


Author: Mircea Pitici
Publisher: Princeton University Press
ISBN: 1400888557
Category: Mathematics
Page: 248
View: 6675

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The year's finest mathematics writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Evelyn Lamb describes the excitement of searching for incomprehensibly large prime numbers, Jeremy Gray speculates about who would have won math’s highest prize—the Fields Medal—in the nineteenth century, and Philip Davis looks at mathematical results and artifacts from a business and marketing viewpoint. In other essays, Noson Yanofsky explores the inherent limits of knowledge in mathematical thinking, Jo Boaler and Lang Chen reveal why finger-counting enhances children’s receptivity to mathematical ideas, and Carlo Séquin and Raymond Shiau attempt to discover how the Renaissance painter Fra Luca Pacioli managed to convincingly depict his famous rhombicuboctahedron, a twenty-six-sided Archimedean solid. And there’s much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Mathematics, Poetry and Beauty


Author: Ron Aharoni
Publisher: World Scientific
ISBN: 9814602965
Category: Mathematics
Page: 272
View: 9542

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What does mathematics have to do with poetry? Seemingly, nothing. Mathematics deals with abstractions while poetry with emotions. And yet, the two share something essential: Beauty. “Euclid alone has looked on beauty bare,” says the title of a poem by Edna St. Vincent Millay. “Mathematics, Poetry and Beauty” tries to solve the secret of the similarity between the two domains. It tries to explain how a mathematical argument and a poem can move us in the same way. Mathematical and poetic techniques are compared, with the aim of showing how they evoke the same sense of beauty. The reader may find that, as Bertrand Russell said, “Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty hold and austere, like that of sculpture … sublimely pure, and capable of a stern perfection such as only the greatest art can show.” Contents:Order:The Curious Case of the Ants on the PoleHidden OrderTo Discover or to InventOrder and BeautyMathematical HarmoniesWhy √2 is Not a Rational NumberThe Real NumbersThe Miracle of OrderSimple Conjectures, Complex ProofsIndependent EventsHow Mathematicians and Poets Think:Poetic Image, Mathematical ImageThe Power of the ObliqueCompressionMathematical Ping-PongThe Book in HeavenPoetical Ping-PongLaws of ConservationAn Idea from Somewhere ElseThree Types of MathematicsTopologyMatchmakingImaginationA Magic NumberReality or ImaginationUnexpected CombinationsWhat is Mathematics?Deep TautologiesSymmetryImpossibilityInfinitely LargeCantor's StoryThe Most Beautiful Proof?Paradoxes and OxymoronsSelf-Reference and Gödel's TheoremHalfway to Infinity: Large NumbersInfinitely SmallInfinitely Many Numbers Having a Finite SumTwistsTwo Levels of Perception:Knowing without KnowingContent and HuskChangeEstrangementAn Endless EncounterAppendix A: Mathematical FieldsAppendix B: Sets of NumbersAppendix C: Poetical Mechanisms Mentioned in the Book Readership: Those interested in Mathematics, those interested in poetry, and the general public. Key Features:It presents laymen and mathematicians alike with beautiful pieces of mathematics, and studies techniques of both poetry and mathematics that contribute to beautyKeywords:Mathematics;Poetry;Aesthetics;Beauty;Popular Mathematics;Paradoxes;Psychology of BeautyReviews: “The book is well-illustrated with diagrams and small photographs. The style is discursive and lively, but the central ideas are clearly communicated. It is not always easy to portray the attraction of mathematics to friends or relatives, or to get across that the essence of mathematics is imagination and creativity rather than routine calculation or the mere manipulation of symbols. By highlighting parallels with poetry, the book may help break down such communication barriers. It may also provide youngsters, so often disillusioned by a prescriptive curriculum, with an insight into the true nature of mathematics.” London Mathematical Society Newsletter

Art of Doing Science and Engineering

Learning to Learn
Author: Richard R. Hamming
Publisher: CRC Press
ISBN: 1482283190
Category: Technology & Engineering
Page: 376
View: 8938

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Highly effective thinking is an art that engineers and scientists can be taught to develop. By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

A Brief History of the Paradox

Philosophy and the Labyrinths of the Mind
Author: Roy Sorensen
Publisher: Oxford University Press
ISBN: 9780199728572
Category: Philosophy
Page: 416
View: 4299

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Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor.

The Hedgehog, the Fox, and the Magister's Pox


Author: Stephen Jay Gould
Publisher: Harvard University Press
ISBN: 0674061667
Category: History
Page: 273
View: 3533

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In his final book, Gould offers a surprising and nuanced study of the complex relationship between our two great ways of knowing: science and the humanities, twin realms of knowledge that have been divided against each other for far too long.

Good and Real

Demystifying Paradoxes from Physics to Ethics
Author: Gary L. Drescher
Publisher: MIT Press
ISBN: 0262042339
Category: Philosophy
Page: 347
View: 948

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Examining a series of provocative paradoxes about consciousness, choice, ethics, andother topics, Good and Real tries to reconcile a purely mechanical view of the universe with keyaspects of our subjective impressions of our own existence.

Beyond Aesthetics

Philosophical Essays
Author: Noël Carroll
Publisher: Cambridge University Press
ISBN: 9780521786560
Category: Art
Page: 450
View: 2281

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Claims authorial intention, art history, and morality play a role in our encounter with art works.

A Glossary of Literary Terms


Author: M.H. Abrams,Geoffrey Harpham
Publisher: Cengage Learning
ISBN: 1285974514
Category: Education
Page: 448
View: 9523

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First published over fifty years ago, A GLOSSARY OF LITERARY TERMS remains an essential text for all serious students of literature. Now fully updated to reflect the latest scholarship on recent and rapidly evolving critical theories, the eleventh edition contains a complete glossary of essential literary terms presented as a series of engaging, beautifully crafted essays that explore the terms, place them in context, and suggest related entries and additional reading. This indispensable, authoritative, and highly affordable reference covers terms useful in discussing literature and literary history, theory, and criticism. Perfect as a core text for introductory literary theory or as a supplement to any literature course, this classic work is an invaluable reference that students can continue to use throughout their academic and professional careers. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

The Interpretation of Cultures


Author: Clifford Geertz
Publisher: Basic Books
ISBN: 0465093566
Category: Social Science
Page: 576
View: 7259

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In The Interpretation of Cultures, the most original anthropologist of his generation moved far beyond the traditional confines of his discipline to develop an important new concept of culture. This groundbreaking book, winner of the 1974 Sorokin Award of the American Sociological Association, helped define for an entire generation of anthropologists what their field is ultimately about.

Male Femaling

A Grounded Theory Approach to Cross-dressing and Sex-changing
Author: Richard Ekins
Publisher: Routledge
ISBN: 1134844735
Category: Social Science
Page: 208
View: 1139

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The glamour of transvestite fashion is the epitome of 90s style, but the significance of cross-dressing and sex-changing goes much deeper than the annals of fashion. Ekins vividly details the innermost desires and the varied practices of males who wear the clothes of women for the pleasure it gives them (cross-dressers), or who wish to change sex and are actively going about it (sex-changers). This unique and fascinating book transforms an area of study previously dominated by clinical models to look instead at cross-dressing and sex-changing as a highly variable social process. Giving precedence to the processual and ermergent nature of much cross-dressing and sex-changing phenomena, the book traces the phased femaling career path of the 'male femaler' from 'beginning femaling' through to 'consolidating femaling'. Based upon seventeen years of fieldwork, life history work, qualitative analysis, archival work and contact with several thousand cross-dressers and sex-changers, the book meticulously and systematically develops a theory of 'male femaling' which has major ramifications for both the field of 'transvestism' and 'transsexualism', and for the analysis of sex and gender more generally. Male-Femaling provides social and cultural theorists with a lively case study for the generation of new theory. Social psychologists and sociologists interested in seeing grounded theory applied to a particular case study will be well rewarded. It will be essential reading for students of gender studies who seek to explore the interrelations between sex, sexuality and gender from the informants' point of view.

Historical Ontology


Author: Ian Hacking
Publisher: Harvard University Press
ISBN: 9780674016071
Category: Philosophy
Page: 279
View: 3702

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With the unusual clarity, distinctive and engaging style, and penetrating insight that have drawn such a wide range of readers to his work, Ian Hacking here offers his reflections on the philosophical uses of history. The focus of this volume, which collects both recent and now-classic essays, is the historical emergence of concepts and objects, through new uses of words and sentences in specific settings, and new patterns or styles of reasoning within those sentences. In its lucid and thoroughgoing look at the historical dimension of concepts, the book is at once a systematic formulation of Hacking's approach and its relation to other types of intellectual history, and a valuable contribution to philosophical understanding. Hacking opens the volume with an extended meditation on the philosophical significance of history. The importance of Michel Foucault--for the development of this theme, and for Hacking's own work in intellectual history--emerges in the following chapters, which place Hacking's classic essays on Foucault within the wider context of general reflections on historical methodology. Against this background, Hacking then develops ideas about how language, styles of reasoning, and "psychological" phenomena figure in the articulation of concepts--and in the very prospect of doing philosophy as historical ontology.

The Taming of Chance


Author: Ian Hacking
Publisher: Cambridge University Press
ISBN: 9780521388849
Category: History
Page: 264
View: 8869

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This book combines detailed scientific historical research with characteristic philosophic breadth and verve.

Language, Music, and the Brain

A Mysterious Relationship
Author: Michael A. Arbib
Publisher: MIT Press
ISBN: 0262018101
Category: Language Arts & Disciplines
Page: 662
View: 4541

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A presentation of music and language within an integrative, embodied perspective of brain mechanisms for action, emotion, and social coordination.

A Cultural History of Physics


Author: Károly Simonyi
Publisher: CRC Press
ISBN: 1439865116
Category: Mathematics
Page: 636
View: 7358

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While the physical sciences are a continuously evolving source of technology and of understanding about our world, they have become so specialized and rely on so much prerequisite knowledge that for many people today the divide between the sciences and the humanities seems even greater than it was when C. P. Snow delivered his famous 1959 lecture, "The Two Cultures." In A Cultural History of Physics, Hungarian scientist and educator Károly Simonyi succeeds in bridging this chasm by describing the experimental methods and theoretical interpretations that created scientific knowledge, from ancient times to the present day, within the cultural environment in which it was formed. Unlike any other work of its kind, Simonyi’s seminal opus explores the interplay of science and the humanities to convey the wonder and excitement of scientific development throughout the ages. These pages contain an abundance of excerpts from original resources, a wide array of clear and straightforward explanations, and an astonishing wealth of insight, revealing the historical progress of science and inviting readers into a dialogue with the great scientific minds that shaped our current understanding of physics. Beautifully illustrated, accurate in its scientific content and broad in its historical and cultural perspective, this book will be a valuable reference for scholars and an inspiration to aspiring scientists and humanists who believe that science is an integral part of our culture.

Thought Experiments


Author: Roy A. Sorensen
Publisher: Oxford University Press on Demand
ISBN: 019512913X
Category: Philosophy
Page: 318
View: 1898

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This text analyses a variety of thought experiments, and explores what they are, how they work, and what their positive and negative aspects are. It also sets the theory within an evolutionary framework of advances in experimental psychology.

Arithmetic for Parents

A Book for Grown-ups about Children's Mathematics
Author: Ron Aharoni
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814602891
Category: Education
Page: 200
View: 4593

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This book is the result of a unique experience: a research mathematician teaching in an elementary school. It summarizes this experience and quickly became a bestseller in Israel. It tells about a fascinating discovery made by the author that elementary mathematics has a lot of depth and beauty, and that the secret to its teaching is to understand its deep points. The first part of the book discusses the nature of mathematic and its beauty. The second part tells about the teaching principles the author distilled from his experience. The third part is an excursion through the arithmetic studied in elementary school, accompanied by personal stories, historical anecdotes and teaching suggestions. The appendix relates the fascinating story of modern day politics of mathematical education. This is a unique guide for parents and teachers, describing vividly and informally the principles of teaching mathematics in elementary school. It is written from the perspective of a mathematician, and goes into the delicate mathematical points that are the secrets to teaching well.

Kiss of the Fur Queen


Author: Tomson Highway
Publisher: Anchor Canada
ISBN: 0385674163
Category: Fiction
Page: 320
View: 3050

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Born into a magical Cree world in snowy northern Manitoba, Champion and Ooneemeetoo Okimasis are all too soon torn from their family and thrust into the hostile world of a Catholic residential school. Their language is forbidden, their names are changed to Jeremiah and Gabriel, and both boys are abused by priests. As young men, estranged from their own people and alienated from the culture imposed upon them, the Okimasis brothers fight to survive. Wherever they go, the Fur Queen--a wily, shape-shifting trickster--watches over them with a protective eye. For Jeremiah and Gabriel are destined to be artists. Through music and dance they soar. From the Trade Paperback edition.

The Racial Contract


Author: Charles Wade Mills
Publisher: Cornell University Press
ISBN: 9780801434549
Category: Philosophy
Page: 171
View: 6899

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Argues that racially structured discrimination is the norm by using social contract theory