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.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    In The Perfect Bet, mathematician and award-winning writer Adam Kucharski tells the astonishing story of how the experts have succeeded, revolutionizing mathematics and science in the process. The house can seem unbeatable. Kucharski shows us just why it isn't. Even better, he demonstrates how the search for the perfect bet has been crucial for the scientific pursuit of a better world.

    This book reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    An extremely clever account.--The New Yorker.

    There are updates throughout the book as well. These take into account important advances in cognitive psychology and the science of design while confirming and extending the book's basic thesis: that a physical symbol system has the necessary and sufficient means for intelligent action. The chapter "Economic Reality" has also been revised to reflect a change in emphasis in Simon's thinking about the respective roles of organizations and markets in economic systems."People sometimes ask me what they should read to find out about artificial intelligence. Herbert Simon's book The Sciences of the Artificial is always on the list I give them. Every page issues a challenge to conventional thinking, and the layman who digests it well will certainly understand what the field of artificial intelligence hopes to accomplish. I recommend it in the same spirit that I recommend Freud to people who ask about psychoanalysis, or Piaget to those who ask about child psychology: If you want to learn about a subject, start by reading its founding fathers." -- George A. Miller

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    Written by two of the world’s foremost authorities on space history, Hubble: Imaging Space and Time illuminates the solar system’s workings, the expansion of the universe, the birth and death of stars, the formation of planetary nebulae, the dynamics of galaxies, and the mysterious force known as "dark energy." The potential impact of this book cannot be overstressed: The 2008 servicing mission to install new high-powered scientific instruments is especially high profile because the cancellation of the previous mission, in 2004, caused widespread controversy. The authors reveal the inside story of Hubble’s beginnings, its controversial early days, the drama of its first servicing missions, and the creation of the dynamic images that reach into the deepest regions of visible space, close to the time when the universe began. A wealth of astonishing images leads us to the very edge of known space, setting the stage for the new James Webb Space Telescope, scheduled to launch in 2013. Find the stunning panoramic of Carina Nebula, detailing star birth as never before; a jet from a black hole in one galaxy striking a neighboring galaxy; a jewel-like collection of galaxies from the early years of the universe; and a giant galaxy cannibalizing a smaller galaxy. Timed for the 2008 shuttle launch and coinciding with the 400th anniversary of Galileo’s first telescope, Hubble: Imaging Space and Time accompanies a high-profile exhibit at the National Air and Space Museum and will be featured on the popular NASM website.

    This work offers accesible coverage of the fundamentals of electrodynamics, enhanced with with discussion points, examples and exercises.

    Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.

    Raised on Baffin Island, Nunavut, he grew up in one of the only non-Inuit families in a tiny native settlement amid the ice fields, floes, and frigid seas of Northern Canada. At an age when most children are playing hide-and-seek, he was learning life-and-death lessons of survival: how to read the weather, find shelter in a frozen snowscape, or live off the land as his Inuit neighbors had done for centuries.Today Nicklen is a naturalist and wildlife photographer uniquely qualified to portray the impact of climate change on the polar regions and their inhabitants, human and animal alike. In a wise and wonderful intertwining of art and science, his bold expeditions plunge him into freezing seas to capture unprecedented, up-close documentation of the lives of leopard seals, whales, walruses, polar bears, bearded seals, and narwhals. Bathed in polar light, his images, inspiring and amazing, break new ground in photography and provide a vivid, timely portrait of two extraordinary, endangered ecosystems.

    Captioned cartoon drawings offering an overview of universal order as they deal with various phenomena are combined with scientific commentary

    How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic.