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Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles. The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us.

This is a rare and much-needed book: a concise but comprehensive account of quantum mechanics for popular science readers written by a respected physicist. Sam Treiman--internationally renowned for his work in particle physics--makes quantum mechanics accessible to nonspecialists. Combining mastery of the material with clear, elegant prose and infectious enthusiasm, he conveys the substance, methods, and profound oddities of the field. Treiman begins with an overview of quantum mechanics. He sketches the early development of the field by Einstein, Bohr, Heisenberg, Schrodinger, and others, and he makes clear how the quantum outlook flies in the face of common sense. As he explains, the quantum world is intrinsically probabilistic. For example, a particle is not in general in some particular place at a given instant, nor does it have a definite momentum. According to the Heisenberg uncertainty principle, there is a limit to how well both location and momentum can be specified simultaneously. In addition, particles can move through barriers and otherwise move in regions of space that are forbidden by classical mechanics. If a particle has a choice of different paths, it pursues all of them at once. Particles display wave-like characteristics and waves show particle-like characteristics. Treiman pays special attention to the more fundamental wave outlook and its expression in quantum field theory. He deals here with the remarkable fact that all the particles of a given species are strictly identical, and with the unnerving fact that particles can be created and destroyed. As Treiman introduces us to these and other wonders, he also touches--without resolution--on some of the deep philosophical problems of quantum mechanics, notably how probabilities become facts. Weaving together impeccable and up-to-date science, engaging writing, and a talent for clear explanation honed over Treiman's distinguished career as a physicist and teacher, The Odd Quantum is a remarkable survey of a field that changed the course of modern scientific and philosophical thought.

John Tyler Bonner, one of our most distinguished and creative biologists, here offers a completely new perspective on the role of size in biology. In his hallmark friendly style, he explores the universal impact of being the right size. By examining stories ranging from Alice in Wonderland to Gulliver's Travels, he shows that humans have always been fascinated by things big and small. Why then does size always reside on the fringes of science and never on the center stage? Why do biologists and others ponder size only when studying something else-running speed, life span, or metabolism?Why Size Matters, a pioneering book of big ideas in a compact size, gives size its due by presenting a profound yet lucid overview of what we know about its role in the living world. Bonner argues that size really does matter-that it is the supreme and universal determinant of what any organism can be and do. For example, because tiny creatures are subject primarily to forces of cohesion and larger beasts to gravity, a fly can easily walk up a wall, something we humans cannot even begin to imagine doing.Bonner introduces us to size through the giants and dwarfs of human, animal, and plant history and then explores questions including the physics of size as it affects biology, the evolution of size over geological time, and the role of size in the function and longevity of living things.As this elegantly written book shows, size affects life in its every aspect. It is a universal frame from which nothing escapes.

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

Some 250 million years ago, the Earth suffered the greatest biological crisis in its history. Extinction is a paleontological mystery story that provides a fascinating overview of the evidence for and against a whole host of hypotheses concerning this cataclysmic event that unfolded at the end of the Permian--and set the stage for the development of life as we know it today.

In the 1990s Richard B. Alley and his colleagues made headlines with the discovery that the last ice age came to an abrupt end over a period of only three years. In The Two-Mile Time Machine, Alley tells the fascinating history of global climate changes as revealed by reading the annual rings of ice from cores drilled in Greenland. He explains that humans have experienced an unusually temperate climate compared to the wild fluctuations that characterized most of prehistory. He warns that our comfortable environment could come to an end in a matter of years and tells us what we need to know in order to understand and perhaps overcome climate changes in the future.In a new preface, the author weighs in on whether our understanding of global climate change has altered in the years since the book was first published, what the latest research tells us, and what he is working on next.

"Featuring a new preface by the author."

Biological evolution is a fact--but the many conflicting theories of evolution remain controversial even today. In 1966, simple Darwinism, which holds that evolution functions primarily at the level of the individual organism, was threatened by opposing concepts such as group selection, a popular idea stating that evolution acts to select entire species rather than individuals. George Williams's famous argument in favor of the Darwinists struck a powerful blow to those in opposing camps. His Adaptation and Natural Selection, now a classic of science literature, is a thorough and convincing essay in defense of Darwinism; its suggestions for developing effective principles for dealing with the evolution debate and its relevance to many fields outside biology ensure the timelessness of this critical work.

Every day, we use our computers to perform remarkable feats. A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "e;tricks"e; behind nine types of computer algorithms, including artificial intelligence (where we learn about the "e;nearest neighbor trick"e; and "e;twenty questions trick"e;), Google's famous PageRank algorithm (which uses the "e;random surfer trick"e;), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

The impact on climate from 200 years of industrial development is an everyday fact of life, but did humankind's active involvement in climate change really begin with the industrial revolution, as commonly believed? Plows, Plagues, and Petroleum has sparked lively scientific debate since it was first published--arguing that humans have actually been changing the climate for some 8,000 years--as a result of the earlier discovery of agriculture.The "e;Ruddiman Hypothesis"e; will spark intense debate. We learn that the impact of farming on greenhouse-gas levels, thousands of years before the industrial revolution, kept our planet notably warmer than if natural climate cycles had prevailed--quite possibly forestalling a new ice age.Plows, Plagues, and Petroleum is the first book to trace the full historical sweep of human interaction with Earth's climate. Ruddiman takes us through three broad stages of human history: when nature was in control; when humans began to take control, discovering agriculture and affecting climate through carbon dioxide and methane emissions; and, finally, the more recent human impact on climate change. Along the way he raises the fascinating possibility that plagues, by depleting human populations, also affected reforestation and thus climate--as suggested by dips in greenhouse gases when major pandemics have occurred. While our massive usage of fossil fuels has certainly contributed to modern climate change, Ruddiman shows that industrial growth is only part of the picture. The book concludes by looking to the future and critiquing the impact of special interest money on the global warming debate. In the afterword, Ruddiman explores the main challenges posed to his hypothesis, and shows how recent investigations and findings ultimately strengthen the book's original claims.

The history of civilization is, in many ways, the history of wine. This book is the first comprehensive and up-to-date account of the earliest stages of vinicultural history and prehistory, which extends back into the Neolithic period and beyond. Elegantly written and richly illustrated, Ancient Wine opens up whole new chapters in the fascinating story of wine and the vine by drawing upon recent archaeological discoveries, molecular and DNA sleuthing, and the texts and art of long-forgotten peoples. Patrick McGovern takes us on a personal odyssey back to the beginnings of this consequential beverage when early hominids probably enjoyed a wild grape wine. We follow the course of human ingenuity in domesticating the Eurasian vine and learning how to make and preserve wine some 7,000 years ago. Early winemakers must have marveled at the seemingly miraculous process of fermentation. From success to success, viniculture stretched out its tentacles and entwined itself with one culture after another (whether Egyptian, Iranian, Israelite, or Greek) and laid the foundation for civilization itself. As medicine, social lubricant, mind-altering substance, and highly valued commodity, wine became the focus of religious cults, pharmacopoeias, cuisines, economies, and society. As an evocative symbol of blood, it was used in temple ceremonies and occupies the heart of the Eucharist. Kings celebrated their victories with wine and made certain that they had plenty for the afterlife. (Among the colorful examples in the book is McGovern's famous chemical reconstruction of the funerary feast--and mixed beverage--of "e;King Midas."e;) Some peoples truly became "e;wine cultures.? When we sip a glass of wine today, we recapitulate this dynamic history in which a single grape species was harnessed to yield an almost infinite range of tastes and bouquets. Ancient Wine is a book that wine lovers and archaeological sleuths alike will raise their glasses to.

Among the many constants that appear in mathematics, I , e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues I and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, the author reveals the full story of this ubiquitous geometric theorem. It shows that the theorem, although attributed to Pythagoras, was known to the Babylonians more than a thousand years earlier.

Trigonometry has always been the black sheep of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.Maor, whose previous books have demystified the concept of infinity and the unusual number "e;e,"e; begins by examining the "e;proto-trigonometry"e; of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles.Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor--but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "e;the witch of Agnesi."e; The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.

Since the publication of the first edition in 1966, Eye and Brain has established itself worldwide as an essential introduction to the basic phenomena of visual perception. Richard Gregory offers clear explanations of how we see brightness, movement, color, and objects, and he explores the phenomena of visual illusions to establish principles about how perception normally works and why it sometimes fails.Illusion continues to be a major theme in the book, which provides a comprehensive classification system. There are also sections on what babies see and how they learn to see, on motion perception, the relationship between vision and consciousness, and on the impact of new brain imaging techniques.

Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations-as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

After his famous visit to the Galapagos Islands, Darwin speculated that "e;one might fancy that, from an original paucity of birds in this archipelago, one species had been taken and modified for different ends."e; This book is the classic account of how much we have since learned about the evolution of these remarkable birds. Based upon over a decade's research, Grant shows how interspecific competition and natural selection act strongly enough on contemporary populations to produce observable and measurable evolutionary change. In this new edition, Grant outlines new discoveries made in the thirteen years since the book's publication. Ecology and Evolution of Darwin's Finches is an extraordinary account of evolution in action.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Design pervades our lives. Everything from drafting a PowerPoint presentation to planning a state-of-the-art bridge embodies this universal human activity. But what makes a great design? In this compelling and wide-ranging look at the essence of invention, distinguished engineer and author Henry Petroski argues that, time and again, we have built success on the back of failure--not through easy imitation of success. Success through Failure shows us that making something better--by carefully anticipating and thus averting failure--is what invention and design are all about. Petroski explores the nature of invention and the character of the inventor through an unprecedented range of both everyday and extraordinary examples--illustrated lectures, child-resistant packaging for drugs, national constitutions, medical devices, the world's tallest skyscrapers, long-span bridges, and more. Stressing throughout that there is no surer road to eventual failure than modeling designs solely on past successes, he sheds new light on spectacular failures, from the destruction of the Tacoma Narrows Bridge in 1940 and the space shuttle disasters of recent decades, to the collapse of the World Trade Center in 2001. Petroski also looks at the prehistoric and ancient roots of many modern designs. The historical record, especially as embodied in failures, reveals patterns of human social behavior that have implications for large structures like bridges and vast organizations like NASA. Success through Failure--which will fascinate anyone intrigued by design, including engineers, architects, and designers themselves--concludes by speculating on when we can expect the next major bridge failure to occur, and the kind of bridge most likely to be involved.

Australopithecines, dinosaurs, trilobites--such fossils conjure up images of lost worlds filled with vanished organisms. But in the full history of life, ancient animals, even the trilobites, form only the half-billion-year tip of a nearly four-billion-year iceberg. Andrew Knoll explores the deep history of life from its origins on a young planet to the incredible Cambrian explosion, presenting a compelling new explanation for the emergence of biological novelty. The very latest discoveries in paleontology--many of them made by the author and his students--are integrated with emerging insights from molecular biology and earth system science to forge a broad understanding of how the biological diversity that surrounds us came to be. Moving from Siberia to Namibia to the Bahamas, Knoll shows how life and environment have evolved together through Earth's history. Innovations in biology have helped shape our air and oceans, and, just as surely, environmental change has influenced the course of evolution, repeatedly closing off opportunities for some species while opening avenues for others. Readers go into the field to confront fossils, enter the lab to discern the inner workings of cells, and alight on Mars to ask how our terrestrial experience can guide exploration for life beyond our planet. Along the way, Knoll brings us up-to-date on some of science's hottest questions, from the oldest fossils and claims of life beyond the Earth to the hypothesis of global glaciation and Knoll's own unifying concept of ''permissive ecology.'' In laying bare Earth's deepest biological roots, Life on a Young Planet helps us understand our own place in the universe--and our responsibility as stewards of a world four billion years in the making.In a new preface, Knoll describes how the field has broadened and deepened in the decade since the book's original publication.

In Reinventing Discovery, Michael Nielsen argues that we are living at the dawn of the most dramatic change in science in more than 300 years. This change is being driven by powerful new cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business or the workplace or government. But this is the first book about something much more fundamental: how the internet is transforming the nature of our collective intelligence and how we understand the world. Reinventing Discovery tells the exciting story of an unprecedented new era of networked science. We learn, for example, how mathematicians in the Polymath Project are spontaneously coming together to collaborate online, tackling and rapidly demolishing previously unsolved problems. We learn how 250,000 amateur astronomers are working together in a project called Galaxy Zoo to understand the large-scale structure of the Universe, and how they are making astonishing discoveries, including an entirely new kind of galaxy. These efforts are just a small part of the larger story told in this book--the story of how scientists are using the internet to dramatically expand our problem-solving ability and increase our combined brainpower. This is a book for anyone who wants to understand how the online world is revolutionizing scientific discovery today--and why the revolution is just beginning.

An insider's view on bringing extinct species back to lifeCould extinct species, like mammoths and passenger pigeons, be brought back to life? The science says yes. In How to Clone a Mammoth, Beth Shapiro, evolutionary biologist and pioneer in "e;ancient DNA"e; research, walks readers through the astonishing and controversial process of de-extinction. From deciding which species should be restored, to sequencing their genomes, to anticipating how revived populations might be overseen in the wild, Shapiro vividly explores the extraordinary cutting-edge science that is being used-today-to resurrect the past. Journeying to far-flung Siberian locales in search of ice age bones and delving into her own research-as well as those of fellow experts such as Svante Paabo, George Church, and Craig Venter-Shapiro considers de-extinction's practical benefits and ethical challenges. Would de-extinction change the way we live? Is this really cloning? What are the costs and risks? And what is the ultimate goal?Using DNA collected from remains as a genetic blueprint, scientists aim to engineer extinct traits--traits that evolved by natural selection over thousands of years-into living organisms. But rather than viewing de-extinction as a way to restore one particular species, Shapiro argues that the overarching goal should be the revitalization and stabilization of contemporary ecosystems. For example, elephants with genes modified to express mammoth traits could expand into the Arctic, re-establishing lost productivity to the tundra ecosystem.Looking at the very real and compelling science behind an idea once seen as science fiction, How to Clone a Mammoth demonstrates how de-extinction will redefine conservation's future.

Explores the complex problem of mental life. This book argues that the roots of creativity for lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness.

Are the problems we define and pursue freely chosen according to our conscious interests? Or does the historical process itself determine which phenomena merit examination at any one time? This title discusses these issues in the far-ranging philosophical terms, while illustrating them with specific examples.

JBS Haldane (1892-1964), one of the founders of the science of population genetics, was also one of the greatest practitioners of the art of explaining science to the layperson. This title provides accessible introduction to the genetical basis of evolution by natural selection.

How is our fate linked to the earth's creatures, and the cycle of flourishing and extinction? Does human activity accelerate extinction? And what really causes it? This account of the widespread reduction of the world's wildlife examines humankind's role in the larger life cycles of the earth, composing a provocative general theory of extinction.

There has been an explosive increase in scientists' ability to explain the structure and functioning of the human brain. This title elucidates knowledge of the human brain, taking an interdisciplinary approach and explaining in layman's terms the complex theories and scientific breakthroughs.

More than fifty illustrations highlight a provocative study tracing the origins of culture as man now knows it back to the early biological evolution of animals.

How do scientists look at chance, or randomness, and chaos in physical systems? This book answers this question for a general audience.