"Any reader who aspires to be scientifically literate will find this a good starting place." —Publishers Weekly While we may be familiar with some of science’s greatest equations, we may not know that each and every equation emerged not in "Eureka!" moments but in years of cultural developments and scientific knowledge. With vignettes full of humor, drama, and eccentricity, philosopher and science historian Robert P. Crease shares the stories behind ten of history’s greatest equations, from the "first equation," 1 + 1 = 2, which promises a rational, well-ordered world, to Heisenberg’s uncertainty principle, which reveals the limitations of human knowledge. For every equation, Crease provides a brief account of who discovered it, what dissatisfactions lay behind its discovery, and what the equation says about the nature of our world.
Here are the stories of the ten most popular equations of all time as voted for by readers of Physics World, including - accessibly described here for the first time - the favourite equation of all, Euler's equation. Each is an equation that captures with beautiful simplicity what can only be described clumsily in words. Euler's equation [eip + 1 = 0] was described by respondents as 'the most profound mathematic statement ever written', 'uncanny and sublime', 'filled with cosmic beauty' and 'mind-blowing'. Collectively these equations also amount to the world's most concise and reliable body of knowledge. Many scientists and those with a mathematical bent have a soft spot for equations. This book explains both why these ten equations are so beautiful and significant, and the human stories behind them.
This illuminating history explores the complex relationship between mathematics, religious belief, and Victorian culture. Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece. In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.
Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.
Acclaimed popular-science writer Brian Clegg and popular TV and radio astronomer Rhodri Evans give us a Top Ten list of physicists as the central theme to build an exploration of the most exciting breakthroughs in physics, looking not just at the science, but also the fascinating lives of the scientists themselves. The Top Ten are: 1.Isaac Newton (1642-1727) 2.Niels Bohr (1885-1962) 3.Galileo Galilei (1564-1642) 4.Albert Einstein (1879-1955) 5.James Clerk Maxwell (1831-1879) 6.Michael Faraday (1791-1867) 7.Marie Curie (1867-1934) 8.Richard Feynman (1918-1988) 9.Ernest Rutherford (1871-1937) 10.Paul Dirac (1902-1984) Each of these figures has made a huge contribution to physics. Some are household names, others more of a mystery, but in each case there is an opportunity to combine a better understanding of the way that each of them has advanced our knowledge of the universe with an exploration of their often unusual, always interesting lives. Whether we are with Curie, patiently sorting through tons of pitchblende to isolate radium or feeling Bohr's frustration as once again Einstein attempts to undermine quantum theory, the combination of science and biography humanizes these great figures of history and makes the Physics itself more accessible. In exploring the way the list has been built the authors also put physics in its place amongst the sciences and show how it combines an exploration of the deepest and most profound questions about life and the universe with practical applications that have transformed our lives. The book is structured chronologically, allowing readers to follow the development of scientific knowledge over more than 400 years, showing clearly how this key group of individuals has fundamentally altered our understanding of the world around us.
An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.
Everything around us is made of 'stuff', from planets, to books, to our own bodies. Whatever it is, we call it matter or material substance. It is solid; it has mass. But what is matter, exactly? We are taught in school that matter is not continuous, but discrete. As a few of the philosophers of ancient Greece once speculated, nearly two and a half thousand years ago, matter comes in 'lumps', and science has relentlessly peeled away successive layers of matter to reveal its ultimate constituents. Surely, we can't keep doing this indefinitely. We imagine that we should eventually run up against some kind of ultimately fundamental, indivisible type of stuff, the building blocks from which everything in the Universe is made. The English physicist Paul Dirac called this 'the dream of philosophers'. But science has discovered that the foundations of our Universe are not as solid or as certain and dependable as we might have once imagined. They are instead built from ghosts and phantoms, of a peculiar quantum kind. And, at some point on this exciting journey of scientific discovery, we lost our grip on the reassuringly familiar concept of mass. How did this happen? How did the answers to our questions become so complicated and so difficult to comprehend? In Mass Jim Baggott explains how we come to find ourselves here, confronted by a very different understanding of the nature of matter, the origin of mass, and its implications for our understanding of the material world. Ranging from the Greek philosophers Leucippus and Democritus, and their theories of atoms and void, to the development of quantum field theory and the discovery of a Higgs boson-like particle, he explores our changing understanding of the nature of matter, and the fundamental related concept of mass.
What is life? Where do we come from and how did we evolve? What is the universe and how was it formed? What is the nature of the material world? How does it work? How and why do we think? What does it mean to be human? How do we know? There are many different versions of our creation story. This book tells the version according to modern science. It is a unique account, starting at the Big Bang and travelling right up to the emergence of humans as conscious intelligent beings, 13.8 billion years later. Chapter by chapter, it sets out the current state of scientific knowledge: the origins of space and time; energy, mass, and light; galaxies, stars, and our sun; the habitable earth, and complex life itself. Drawing together the physical and biological sciences, Baggott recounts what we currently know of our history, highlighting the questions science has yet to answer.
Utterly beautiful. Profoundly disconcerting. Quantum theory is quite simply the most successful account of the physical universe ever devised. Its concepts underpin much of the twenty-first century technology that we now take for granted. But at the same time it has completely undermined our ability to make sense of the world at its most fundamental level. Niels Bohr claimed that anybody who is not shocked by the theory has not understood it. The American physicist Richard Feynman went further: he claimed that nobody understands it. The Quantum Story begins in 1900, tracing a century of game-changing science. Popular science writer Jim Baggott first shows how, over the space of three decades, Einstein, Bohr, Heisenberg, and others formulated and refined the theory--and opened the floodgates. Indeed, since then, a torrent of ideas has flowed from the world's leading physicists, as they explore and apply the theory's bizarre implications. To take us from the story's beginning to the present day, Baggott organizes his narrative around forty turning-point moments of discovery. Many of these are inextricably bound up with the characters involved--their rivalries and their collaborations, their arguments and, not least, their excitement as they sense that they are redefining what reality means. Through the mix of story and science, we experience their breathtaking leaps of theory and experiment, as they uncover such undreamed of and mind-boggling phenomenon as black holes, multiple universes, quantum entanglement, the Higgs boson, and much more. Brisk, clear, and compelling, The Quantum Story is science writing at its best. A compelling look at the one-hundred-year history of quantum theory, it illuminates the idea as it reveals how generations of physicists have grappled with this monster ever since.
Is there a secret formula for getting rich? For going viral? For deciding how long to stick with your current job, Netflix series, or even relationship? This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthfully, and see through scaremongering. They are known by only the privileged few - until now. With wit and clarity, mathematician David Sumpter shows that it isn't the technical details that make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn. Empowering and illuminating, The Ten Equations shows how math really can change your life.
