THE PYTHAGOREAN WORLD WHY MATHEMATICS IS UNREASONABLY EFFECTIVE IN PHYSICS

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Why Mathematics Is Unreasonably Effective In Physics

Author: Jane McDonnell

Publisher: Springer

ISBN: 331940976X

Category: Mathematics

Page: 394

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This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

Author: Peter Bühlmann,Petros Drineas,Michael Kane,Mark van der Laan

Publisher: CRC Press

ISBN: 1482249081

Category: Business & Economics

Page: 464

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Handbook of Big Data provides a state-of-the-art overview of the analysis of large-scale datasets. Featuring contributions from well-known experts in statistics and computer science, this handbook presents a carefully curated collection of techniques from both industry and academia. Thus, the text instills a working understanding of key statistical and computing ideas that can be readily applied in research and practice. Offering balanced coverage of methodology, theory, and applications, this handbook: Describes modern, scalable approaches for analyzing increasingly large datasets Defines the underlying concepts of the available analytical tools and techniques Details intercommunity advances in computational statistics and machine learning Handbook of Big Data also identifies areas in need of further development, encouraging greater communication and collaboration between researchers in big data sub-specialties such as genomics, computational biology, and finance.

Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction (albeit an extremely useful fiction). On this view, the claims of our ordinary mathematical theories are more closely analogous to utterances made in the context of storytelling than to utterances whose aim is to assert literal truths.

The Mysterious Connection Between Physics and Mathematics

Author: Anthony Aguirre,Brendan Foster,Zeeya Merali

Publisher: Springer

ISBN: 3319274953

Category: Science

Page: 250

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The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition “Trick or Truth”, which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores teh leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.

Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. --Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. --Marcus du Sautoy, Oxford University, author of The Music of the Primes and Symmetry: A Journey into the Patterns of Nature Mathematics is thriving. Not only have long-standing problems, such as the Poincare conjecture, been solved, but mathematics is an important element of many modern conveniences, such as cell phones, CDs, and secure transactions over the Internet. For good or for bad, it is also the engine that drives modern investment strategies. Fortunately for the general public, mathematics and its modern applications can be intelligible to the non-specialist, as George Szpiro shows in A Mathematical Medley. In stories of a few pages each, Szpiro describes in layman's terms mathematical problems that have recently been solved (or thought to have been solved), research that was published in scientific journals, and mathematical observations about contemporary life. Anecdotal stories about the lives of mathematicians and stories about famous old problems are interspersed among other vignettes.

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 2012 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 Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford 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.

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

Author: William Byers

Publisher: Princeton University Press

ISBN: 9780691145990

Category: Mathematics

Page: 424

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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.

Expands the search for the origins of the universe beyond God and the Big Bang theory, exploring more bizarre possibilities inspired by physicists, theologians, mathematicians, and even novelists.

Do you ever get the feeling that something went wrong? What with credit crunches, the war on terror, and unemployment, it is natural to hark back to less complicated times. In this witty and inspiring book, Mark Vernon does just that. However, he doesn’t just look back to the 1980s – try 400BC! Filled with timeless insight into life, relationships, work and partying, Plato's Podcasts takes a sideways glance at modern living and presents the would-be thoughts of Ancient Philosophers on various topics central to our 21st century existence. With a zany cast of characters – from the Gymnosophists (the naked philosophers) to Diogenes, who lived in a barrel – this is a humorous but enlightening manual to living well today (and two thousand years ago). Mark Vernon is a writer, journalist, broadcaster, academic, and former priest. Author of numerous books including Wellbeing and What Not to Say, he is an Honorary Research Fellow at Birkbeck College, University of London, UK, and a frequent contributor for BBC radio and the BBC webportal.

A Surprising Excursion Through the Astonishing World of Math

Author: Alex Bellos

Publisher: Simon and Schuster

ISBN: 1416596348

Category: Mathematics

Page: 336

View: 3824

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Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.

The book answers long-standing questions on scientific modeling and inference across multiple perspectives and disciplines, including logic, mathematics, physics and medicine. The different chapters cover a variety of issues, such as the role models play in scientific practice; the way science shapes our concept of models; ways of modeling the pursuit of scientific knowledge; the relationship between our concept of models and our concept of science. The book also discusses models and scientific explanations; models in the semantic view of theories; the applicability of mathematical models to the real world and their effectiveness; the links between models and inferences; and models as a means for acquiring new knowledge. It analyzes different examples of models in physics, biology, mathematics and engineering. Written for researchers and graduate students, it provides a cross-disciplinary reference guide to the notion and the use of models and inferences in science.

A masterful commentary on the history of science from the Greeks to modern times, by Nobel Prize-winning physicist Steven Weinberg—a thought-provoking and important book by one of the most distinguished scientists and intellectuals of our time. In this rich, irreverent, and compelling history, Nobel Prize-winning physicist Steven Weinberg takes us across centuries from ancient Miletus to medieval Baghdad and Oxford, from Plato’s Academy and the Museum of Alexandria to the cathedral school of Chartres and the Royal Society of London. He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy. An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.

Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. This book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain.

This book focuses on the origin of the Gielis curves, surfaces and transformations in the plant sciences. It is shown how these transformations, as a generalization of the Pythagorean Theorem, play an essential role in plant morphology and development. New insights show how plants can be understood as developing mathematical equations, which opens the possibility of directly solving analytically any boundary value problems (stress, diffusion, vibration...) . The book illustrates how form, development and evolution of plants unveil as a musical symphony. The reader will gain insight in how the methods are applicable in many divers scientific and technological fields.