To Infinity and Beyond

A Cultural History of the Infinite

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 9780691025117

Category: Mathematics

Page: 284

View: 1746

Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

A Brief History of Infinity

The Quest to Think the Unthinkable

Author: Brian Clegg

Publisher: Robinson

ISBN: 1472107640

Category: Mathematics

Page: 160

View: 5175

'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Beautiful Geometry

Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

View: 1951

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.


Beyond the Beyond the Beyond

Author: Lillian R. Lieber

Publisher: Paul Dry Books

ISBN: 1589880366

Category: Mathematics

Page: 262

View: 1231

This book offers an entertaining, yet thorough, explanation of the concept of, yes, infinity. Accessible to non-mathematicians, this book also cleverly connects mathematical reasoning to larger issues in society.

Naming Infinity

A True Story of Religious Mysticism and Mathematical Creativity

Author: Loren Graham,Jean-Michel Kantor

Publisher: Harvard University Press

ISBN: 0674032934

Category: History

Page: 239

View: 3585

Looks at the competition between French and Russian mathematicians over the nature of infinity during the twentieth century.

Zeno's Paradox

Unraveling the Ancient Mystery Behind the Science of Space and Time

Author: Joseph Mazur

Publisher: Penguin

ISBN: 9780452289178

Category: Science

Page: 262

View: 3550

Traces the epic history of ancient Greek philosopher Zeno's yet-unsolved paradox of motion, citing the contributions of such top minds as Aristotle, Newton, and Hawking to furthering the scientific community's understanding of the elusive basic structure of time and space. Originally published as The Motion Paradox. Reprint.

The Mystery of the Aleph

Mathematics, the Kabbalah, and the Search for Infinity

Author: Amir D. Aczel

Publisher: Simon and Schuster

ISBN: 0743422996

Category: Biography & Autobiography

Page: 272

View: 6118

Journeys into the work of Georg Cantor, a Russian-born German mathematician, who developed set theory and the concept of infinite numbers, but was condemned by his peers and spent many years in an asylum.

The Pythagorean Theorem

A 4,000-Year History

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 0691148236

Category: Mathematics

Page: 280

View: 375

The author presents a complex history of the Pythagorean Theorem, examining the earliest evidence of knowledge of the theorem to Einstein's theory of relativity.

The Beginning of Infinity

Explanations that Transform The World

Author: David Deutsch

Publisher: Penguin UK

ISBN: 0141969695

Category: Science

Page: 496

View: 895

A bold and all-embracing exploration of the nature and progress of knowledge from one of today's great thinkers. Throughout history, mankind has struggled to understand life's mysteries, from the mundane to the seemingly miraculous. In this important new book, David Deutsch, an award-winning pioneer in the field of quantum computation, argues that explanations have a fundamental place in the universe. They have unlimited scope and power to cause change, and the quest to improve them is the basic regulating principle not only of science but of all successful human endeavor. This stream of ever improving explanations has infinite reach, according to Deutsch: we are subject only to the laws of physics, and they impose no upper boundary to what we can eventually understand, control, and achieve. In his previous book, The Fabric of Reality, Deutsch describe the four deepest strands of existing knowledge-the theories of evolution, quantum physics, knowledge, and computation-arguing jointly they reveal a unified fabric of reality. In this new book, he applies that worldview to a wide range of issues and unsolved problems, from creativity and free will to the origin and future of the human species. Filled with startling new conclusions about human choice, optimism, scientific explanation, and the evolution of culture, The Beginning of Infinity is a groundbreaking book that will become a classic of its kind.

Ideas at the Intersection of Mathematics, Philosophy, and Theology

Author: Carlos R. Bovell

Publisher: Wipf and Stock Publishers

ISBN: 1608999734

Category: Religion

Page: 142

View: 9865

How do mathematics, philosophy, and theology intersect? In Ideas at the Intersection of Mathematics, Philosophy, and Theology, Carlos Bovell proposes a wide range of possibilities. In a series of eleven thought-provoking essays, the author explores such topics as the place of mathematics in the work of Husserl and Heidegger, the importance of infinity for the Christian conception of God, and the impact of Gšdel's Theorem on the Westminster Confession of Faith. This book will appeal to readers with backgrounds in mathematics, philosophy, and theology and can be used in core, interdisciplinary modules that contain a math component.


Toward a New Paradigm for Cognitive Science

Author: John Stewart,John Robert Stewart,Olivier Gapenne,Ezequiel A. Di Paolo

Publisher: MIT Press

ISBN: 0262014602

Category: Philosophy

Page: 463

View: 8061

"Based on an International CNRS Summer School organized by the Association pour la Recherche Cognitive (ARC), held from 29 May to 03 June 2006, Ile d'Oleron, France"--Text.

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

ISBN: 0195132440

Category: Drama

Page: 275

View: 9622

The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

Music by the Numbers

From Pythagoras to Schoenberg

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 1400889898

Category: Mathematics

Page: 176

View: 9686

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

Clash of Symbols

A ride through the riches of glyphs

Author: Stephen Webb

Publisher: Springer

ISBN: 3319713507

Category: Science

Page: 245

View: 1299

From the ampersat and amerpsand, via smileys and runes to the ubiquitous presence of mathematical and other symbols in sciences and technology: both old and modern documents abound with many familiar as well as lesser known characters, symbols and other glyphs. Yet, who would be readily able to answer any question like: ‘who chose π to represent the ratio of a circle’s diameter to its circumference?’ or ‘what’s the reasoning behind having a ⌘ key on my computer keyboard?’ This book is precisely for those who have always asked themselves this sort of questions. So, here are the stories behind one hundred glyphs, the book being evenly divided into five parts, with each featuring 20 symbols. Part 1, called Character sketches, looks at some of the glyphs we use in writing. Part 2, called Signs of the times, discusses some glyphs used in politics, religion, and other areas of everyday life. Some of these symbols are common; others are used only rarely. Some are modern inventions; others, which seem contemporary, can be traced back many hundreds of years. Part 3, called Signs and wonders, explores some of the symbols people have developed for use in describing the heavens. These are some of the most visually striking glyphs in the book, and many of them date back to ancient times. Nevertheless their use — at least in professional arenas — is diminishing. Part 4, called It’s Greek to me, examines some symbols used in various branches of science. A number of these symbols are employed routinely by professional scientists and are also familiar to the general public; others are no longer applied in a serious fashion by anyone — but the reader might still meet them, from time to time, in older works. The final part of the book, Meaningless marks on paper, looks at some of the characters used in mathematics, the history of which one can easily appreciate with only a basic knowledge of mathematics. There are obviously countless others symbols. In recent years the computing industry has developed Unicode and it currently contains more than 135 000 entries. This book would like to encourage the curious reader to take a stroll through Unicode, to meet many characters that will delight the eye and, researching their history, to gain some fascinating insights. ​

Game, Set and Math

Enigmas and Conundrums

Author: Ian Stewart

Publisher: Courier Corporation

ISBN: 0486150968

Category: Mathematics

Page: 208

View: 8173

Twelve essays take a playful approach to mathematics, investigating the topology of a blanket, the odds of beating a superior tennis player, and how to distinguish between fact and fallacy.

Keys to Infinity

Author: Clifford A. Pickover

Publisher: Wiley

ISBN: 9780471193340

Category: Science

Page: 360

View: 5493

"An original and exciting exploration of how utterly weird, and utterly beautiful, the infinite can be."-Ian Stewart, author of Does God Play Dice? What can we know about numbers too large to compute or even imagine? Do the tiny bubbles in the froth of a milkshake actually form an infinite fractal pattern? What are apocalyptic numbers and recursive worlds? These and dozens of equally beguiling mathematical mysteries, problems, and paradoxes fill this mind-bending new book. In each chapter, acclaimed author Clifford Pickover poses a delightful brain-teasing challenge that reveals the scope and splendor of the world of infinity. Try scaling the ladders to heaven, playing a game of infinite chess, or escaping from the land of Fractalia. Along the way you will encounter a myriad of intriguing topics from vampire numbers, to abduction algebra, to the infinity worms of Callisto. Every problem and puzzle is presented in a remarkably accessible style requiring no specialized mathematical knowledge. Over one hundred illustrations enhance the text and help to explain the mathematical concepts, and stunning color images created by the author reveal the breathtaking beauty of the patterns of infinity. A variety of computer programs offer additional ways to penetrate the enigma of infinity. For anyone who has ever wondered just how big infinity really is, or just how small, this book will provide an endless source of insight, creativity, and fun. Advance praise for KEYS TO INFINITY "In this the latest of Dr. Pickover's marvelous books, he breaks all finite chains to soar into the transcendental, mind-boggling regions of mathematical infinity. Written in the author's informal, clear style, it is a treasure trove of recreational problems, many published here for the first time, with special emphasis on computer programs and riveting graphics. As you soar, fasten your seat belt."-Martin Gardner, author of The Magic Numbers of Dr. Matrix "Inventive, quirky, fun! Pickover presents an engaging, inspiring romp in the realm of number and mathematical thought."-Ivars Peterson, author of The Mathematical Tourist "Join Pickover on his wonderful merry-go-round of ideas, and reach for the infinite. Keys to Infinity is an engaging book. . .a must for those wishing to explore the infinite in all its manifestations."-Theoni Pappas, author of The Joy of Mathematics "Keys to Infinity contains a near infinity of absorbing themes: from stepladders to the moon and spiral earths, to worm worlds, random chords, and self-similar curlicues. Fascinating!"-Manfred Schroeder, author of Fractals, Chaos, Power Laws "What could be more appropriate to the subject of infinity than a book like this one, so dense with wonderful puzzles, anecdotes, images, and computer programs that you could pore over it forever? In Keys to Infinity, Pickover has once again assembled a mathematical feast."-Carl Zimmer, Senior Editor Discover "Cliff Pickover has produced yet another book of mathematical puzzles, weird facts, computer art, and simple programs to challenge our minds and enthrall us with the beauty of the infinite mathematical world in which we live."-Dr. Julien C. Sprott, author of Strange Attractors

Infinity and the Mind

The Science and Philosophy of the Infinite

Author: Rudy Rucker

Publisher: Princeton University Press

ISBN: 1400849047

Category: Mathematics

Page: 368

View: 1643

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

The Meaning of the Library

A Cultural History

Author: Alice Crawford

Publisher: Princeton University Press

ISBN: 0691175748

Category: Business & Economics

Page: 336

View: 1030

"Tracing what the library has meant since its beginning, examining how its significance has shifted, and pondering its importance in the twenty-first century, significant contributors--including the librarian of the Congress and the former executive director of the HathiTrust--present a cultural history of the library"--Dust jacket flap.

Freedom Sounds

Civil Rights Call out to Jazz and Africa

Author: Ingrid Monson

Publisher: Oxford University Press

ISBN: 9780198029403

Category: Social Science

Page: 416

View: 5561

An insightful examination of the impact of the Civil Rights Movement and African Independence on jazz in the 1950s and 60s, Freedom Sounds traces the complex relationships among music, politics, aesthetics, and activism through the lens of the hot button racial and economic issues of the time. Ingrid Monson illustrates how the contentious and soul-searching debates in the Civil Rights, African Independence, and Black Power movements shaped aesthetic debates and exerted a moral pressure on musicians to take action. Throughout, her arguments show how jazz musicians' quest for self-determination as artists and human beings also led to fascinating and far reaching musical explorations and a lasting ethos of social critique and transcendence. Across a broad body of issues of cultural and political relevance, Freedom Sounds considers the discursive, structural, and practical aspects of life in the jazz world in the 1950s and 1960s. In domestic politics, Monson explores the desegregation of the American Federation of Musicians, the politics of playing to segregated performance venues in the 1950s, the participation of jazz musicians in benefit concerts, and strategies of economic empowerment. Issues of transatlantic importance such as the effects of anti-colonialism and African nationalism on the politics and aesthetics of the music are also examined, from Paul Robeson's interest in Africa, to the State Department jazz tours, to the interaction of jazz musicians such Art Blakey and Randy Weston with African and African diasporic aesthetics. Monson deftly explores musicians' aesthetic agency in synthesizing influential forms of musical expression from a multiplicity of stylistic and cultural influences--African American music, popular song, classical music, African diasporic aesthetics, and other world musics--through examples from cool jazz, hard bop, modal jazz, and the avant-garde. By considering the differences between aesthetic and socio-economic mobility, she presents a fresh interpretation of debates over cultural ownership, racism, reverse racism, and authenticity. Freedom Sounds will be avidly read by students and academics in musicology, ethnomusicology, anthropology, popular music, African American Studies, and African diasporic studies, as well as fans of jazz, hip hop, and African American music.

Infinite Potential

The Life and Times of David Bohm

Author: F. David Peat

Publisher: Perseus Books


Category: Science

Page: 353

View: 740

Recounts the life of the physicist, psychologist, and philosopher David Bohm, including his friendship with J. Robert Oppenheimer and his protest against Senator Joseph McCarthy, and explains his landmark scientific discoveries and his work with Eastern philosophy.