Download and read online Are Numbers Real in PDF and EPUB Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real? Brian Clegg explores the way that maths has become more and more detached from reality, yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader's eyes to the hidden reality of the strange yet familiar world of numbers.
Download and read online Mathematics and the Physical World in PDF and EPUB Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Download and read online Calculating the Cosmos in PDF and EPUB Ian Stewart's up-to-the-minute guide to the cosmos moves from the formation of the Earth and its Moon to the planets and asteroids of the solar system and from there out into the galaxy and the universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it will end. He considers parallel universes, what forms extra-terrestrial life might take, and the likelihood of Earth being hit by an asteroid. Mathematics, Professor Stewart shows, has been the driving force in astronomy and cosmology since the ancient Babylonians. He describes how Kepler's work on planetary orbits led Newton to formulate his theory of gravity, and how two centuries later irregularities in the motion of Mars inspired Einstein's theory of general relativity. In crystal-clear terms he explains the fundamentals of gravity, spacetime, relativity and quantum theory, and shows how they all relate to each other. Eighty years ago the discovery that the universe is expanding led to the Big Bang theory of its origins. This in turn led cosmologists to posit features such as dark matter and dark energy. But does dark matter exist? Could another scientific revolution be on the way to challenge current scientific orthodoxy? These are among the questions Ian Stewart raises in his quest through the realms of astronomy and cosmology.
Download and read online Mathematical Treks in PDF and EPUB Collected articles on mathematics from the popular Math treks column; extra web support available.
Download and read online A Brief History of Mathematical Thought in PDF and EPUB Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, "no mathematical knowledge required." Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --
Download and read online Void in PDF and EPUB The rising star author of "The Physics of Wall Street" explores why nothing may hold the key to the next era of theoretical physics"
Download and read online Do We Really Understand Quantum Mechanics in PDF and EPUB Quantum mechanics is a very successful theory that has impacted on many areas of physics, from pure theory to applications. However, it is difficult to interpret, and philosophical contradictions and counterintuitive results are apparent at a fundamental level. In this book, Laloë presents our current understanding of the theory. The book explores the basic questions and difficulties that arise with the theory of quantum mechanics. It examines the various interpretations that have been proposed, describing and comparing them and discussing their success and difficulties. The book is ideal for researchers in physics and mathematics who want to know more about the problems faced in quantum mechanics but who do not have specialist knowledge in the subject. It will also interest philosophers of science, as well as all scientists who are curious about quantum physics and its peculiarities.
Download and read online Why Time Flies in PDF and EPUB “[Why Time Flies] captures us. Because it opens up a well of fascinating queries and gives us a glimpse of what has become an ever more deepening mystery for humans: the nature of time.” —The New York Review of Books “Erudite and informative, a joy with many small treasures.” —Science “Time” is the most commonly used noun in the English language; it’s always on our minds and it advances through every living moment. But what is time, exactly? Do children experience it the same way adults do? Why does it seem to slow down when we’re bored and speed by as we get older? How and why does time fly? In this witty and meditative exploration, award-winning author and New Yorker staff writer Alan Burdick takes readers on a personal quest to understand how time gets in us and why we perceive it the way we do. In the company of scientists, he visits the most accurate clock in the world (which exists only on paper); discovers that “now” actually happened a split-second ago; finds a twenty-fifth hour in the day; lives in the Arctic to lose all sense of time; and, for one fleeting moment in a neuroscientist’s lab, even makes time go backward. Why Time Flies is an instant classic, a vivid and intimate examination of the clocks that tick inside us all.
Download and read online Now The Physics of Time in PDF and EPUB “Now” is a simple yet elusive concept. You are reading the word “now” right now. But what does that mean? What makes the ephemeral moment “now” so special? Its enigmatic character has bedeviled philosophers, priests, and modern-day physicists from Augustine to Einstein and beyond. Einstein showed that the flow of time is affected by both velocity and gravity, yet he despaired at his failure to explain the meaning of “now.” Equally puzzling: why does time flow? Some physicists have given up trying to understand, and call the flow of time an illusion, but the eminent experimentalist physicist Richard A. Muller protests. He says physics should explain reality, not deny it. In Now, Muller does more than poke holes in past ideas; he crafts his own revolutionary theory, one that makes testable predictions. He begins by laying out—with the refreshing clarity that made Physics for Future Presidents so successful—a firm and remarkably clear explanation of the physics building blocks of his theory: relativity, entropy, entanglement, antimatter, and the Big Bang. With the stage then set, he reveals a startling way forward. Muller points out that the standard Big Bang theory explains the ongoing expansion of the universe as the continuous creation of new space. He argues that time is also expanding and that the leading edge of the new time is what we experience as “now.” This thought-provoking vision has remarkable implications for some of our biggest questions, not only in physics but also in philosophy—including the ongoing debate about the reality of free will. Moreover, his theory is testable. Muller’s monumental work will spark major debate about the most fundamental assumptions of our universe, and may crack one of physics’s longest-standing enigmas.
Download and read online Street Fighting Mathematics in PDF and EPUB In problem solving, as in street fighting, rules are for fools: do whatever works -- don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge -- from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool -- the general principle -- from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Download and read online Is God a Mathematician in PDF and EPUB 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.
Download and read online Gravity in PDF and EPUB An accessible study on gravity's role in everyday life and influence on other areas of science illuminates Einstein's explanation of how gravity works, discussing its four components, current studies in anti-gravity and more. By the author of Armageddon Science.
Download and read online Infinity in PDF and EPUB This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.
Download and read online Animal Creativity and Innovation in PDF and EPUB Animal Creativity and Innovation explores theories and research on animal innovation and creativity, comparing and contrasting it with theory and research on human creativity and innovation. In doing so, it encompasses findings from psychology, biology, neuroscience, engineering, business, ecology, and education. The book includes examples of animal innovation in parrots, dogs, marine mammals, insects, and primates, exploring parallels from creative play in children. The book defines creativity, differentiating it from play, and looks at evolutionary models and neurological constructs. The book further explores applied aspects of animal innovation and creativity including tool use and group dynamics, as well as barriers to creativity. The final chapters look into how creative behavior may be taught or trained. Each chapter is followed by a commentary for integration of thoughts and ideas between animal and human research, behavioral and cognitive research, and theory and observation in real life. Compares theory and research on animal and human creativity Defines and differentiates creativity from play Reviews applied creativity in tool use and social dynamics Includes examples of animal creativity in multiple species
Download and read online Physics in PDF and EPUB How does the physics we know today - a highly professionalised enterprise, inextricably linked to government and industry - link back to its origins as a liberal art in Ancient Greece? What is the path that leads from the old philosophy of nature and its concern with humankind's place in the universe to modern massive international projects that hunt down fundamental particles and industrial laboratories that manufacture marvels? J. L. Heilbron's fascinating history of physics introduces us to Islamic astronomers and mathematicians, calculating the size of the earth whilst their caliphs conquered much of it; to medieval scholar-theologians investigating light; to Galileo, Copernicus, Kepler, and Newton, measuring, and trying to explain, the universe. We visit the 'House of Wisdom' in 9th-century Baghdad; Europe's first universities; the courts of the Renaissance; the Scientific Revolution and the academies of the 18th century; the increasingly specialised world of 20th and 21st century science. Highlighting the shifting relationship between physics, philosophy, mathematics, and technology -- and the implications for humankind's self-understanding -- Heilbron explores the changing place and purpose of physics in the cultures and societies that have nurtured it over the centuries.