A mathematical sightseeing tour of the natural world from the author of THE MAGICAL MAZE Why do many flowers have five or eight petals, but very few six or seven? Why do snowflakes have sixfold symmetry? Why do tigers have stripes but leopards have spots? Mathematics is to nature as Sherlock Holmes is to evidence. Mathematics can look at a single snowflake and deduce the atomic geometry of its crystals; it can start with a violin string and uncover the existence of radio waves. And mathematics still has the power to open our eyes to new and unsuspected regularities - the secret structure of a cloud or the hidden rhythms of the weather. There are patterns in the world we are now seeing for the first time - patterns at the frontier of science, yet patterns so simple that anybody can see them once they know where to look.
The Mathematical Archetypes of Nature, Art, and Science
Author: Michael S. Schneider
Publisher: Harper Collins
The Universe May Be a Mystery, But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round. Why one and two weren't considered numbers by the ancient Greeks. Why squares show up so often in goddess art and board games. What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster and a cathedral. And much more.
How Order Emerges from Chaos In the Universe, Nature, and Daily Life
Author: Steven H. Strogatz
Publisher: Hachette Books
At the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.
How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organizations
Author: Adrian Bejan,J. Peder Zane
Reveals how recurring patterns in nature are accounted for by a single governing principle of physics, explaining how all designs in the world from biological life to inanimate systems evolve in a sequence of ever-improving designs that facilitate flow.
Mathematical Patterns and Principles from the Natural World
Author: Ian Stewart
Think of a zebra's stripes, the complexities of a spider's web, the uniformity of desert dunes, or the spirals in a sunflower head ... think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth forms the principles of mathematics. Starting with the simplest patterns, each chapter looks at a different kind of patterning system and the mathematics that underlies it. In doing so the book also uncovers some universal patterns, both in nature and man-made, from the basic geometry of ancient Greece to the visually startling fractals that we are familiar with today. Elegantly illustrated, The Beauty of Numbers in Nature is an illuminating and engaging vision of how the apparently cold laws of mathematics find expression in the beauty of nature.
The contemporary discipline of biolinguistics is beginning to have the feel of scientific inquiry. Biolinguistics--especially the work of Noam Chomsky--suggests that the design of language may be "perfect": language is an optimal solution to conditions of sound and meaning. What is the scope of this inquiry? Which aspect of nature does this science investigate? What is its relation to the rest of science? What notions of language and mind are under investigation? This book is a study of such foundational questions. Exploring Chomsky's claims, Nirmalangshu Mukherji argues that the significance of biolinguistic inquiry extends beyond the domain of language. Biolinguistics is primarily concerned with grammars that represent just the computational aspects of the mind/brain. This restriction to grammars, Mukherji argues, opens the possibility that the computational system of human language may be involved in each cognitive system that requires similar computational resources. Deploying analytical argumentation and empirical evidence, Mukherji suggests that a computational system of language consisting of very specific principles and operations is likely to be involved in each articulatory symbol system--such as music--that manifests unboundedness. In that sense, the biolinguistics approach may have identified, after thousands of years of inquiry, a specific structure of the human mind.
Fundamentals of Biogeographyoffers a fresh, uptodate, introduction to biogeography, explaining the ecology, geography and history of animals and plants. The book defines and examines populations, communities and ecosystems - examining where different animals and plants live and how they came to be living there, investigating how populations grow, interact and survive. Stressing the role of ecological, geographical, historical and human factors in fashioning animal and plant distributions, Huggett reveals how life has and is adapting to its biological and physical surroundings. The book includes several sections on human attitudes to Nature differ, and how biogeography can affect conservation practice. As well as explaining key concepts and interactions, Huggett tackles many topical and controversial environmental and ethical concerns including: animal rights, species exploitation, habitat fragmentation, biodiversity, metapopulations, patchy landscapes and chaos. Illustrated throughout with informative diagrams and photos, and including chapter summaries, guides to further reading and an extensive glossary of key terms, Fundamentals of Biogeographypresents an engaging introduction for students.
Team working and learning through reflection are both fundamental to quality healthcare. This book is the first to explore the use of the practices of reflection to develop health care teams that can deliver sustainable, high-quality personalised care. Developing the Reflective Healthcare Team is structured in three parts which are about new views of reflective practice, improving team working, and the use of the TA2LK facilitative reflective process to develop high performing teams.
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.
In the social sciences today, students are taught theory by reading and analyzing the works of Karl Marx, Max Weber, and other foundational figures of the discipline. What they rarely learn, however, is how to actually theorize. The Art of Social Theory is a practical guide to doing just that. In this one-of-a-kind user's manual for social theorists, Richard Swedberg explains how theorizing occurs in what he calls the context of discovery, a process in which the researcher gathers preliminary data and thinks creatively about it using tools such as metaphor, analogy, and typology. He guides readers through each step of the theorist’s art, from observation and naming to concept formation and explanation. To theorize well, you also need a sound knowledge of existing social theory. Swedberg introduces readers to the most important theories and concepts, and discusses how to go about mastering them. If you can think, you can also learn to theorize. This book shows you how. Concise and accessible, The Art of Social Theory features helpful examples throughout, and also provides practical exercises that enable readers to learn through doing.
Creativity: Theory, History, Practice offers important new perspectives on creativity in the light of contemporary critical theory and cultural history. Innovative in approach as well as argument, the book crosses disciplinary boundaries and builds new bridges between the critical and the creative. It is organised in four parts: Why creativity now? offers much-needed alternatives to both the Romantic stereotype of the creator as individual genius and the tendency of the modern creative industries to treat everything as a commodity defining creativity, creating definitions traces the changing meaning of 'create' from religious ideas of divine creation from nothing to advertising notions of concept creation. It also examines the complex history and extraordinary versatility of terms such as imagination, invention, inspiration and originality dreation as myth, story, metaphor begins with modern re-tellings of early African, American and Australian creation myths and – picking up Biblical and evolutionary accounts along the way – works round to scientific visions of the Big Bang, bubble universes and cosmic soup creative practices, cultural processes is a critical anthology of materials, chosen to promote fresh thinking about everything from changing constructions of 'literature' and 'design' to artificial intelligence and genetic engineering. Rob Pope takes significant steps forward in the process of rethinking a vexed yet vital concept, all the while encouraging and equipping readers to continue the process in their own creative or 're-creative' ways. Creativity: Theory, History, Practice is invaluable for anyone with a live interest in exploring what creativity has been, is currently, and yet may be.
A respected physicist presents a survey of related discoveries, from Plato and Pythagoras up to the present, that explore how intertwined ideas about beauty and art are with scientific understandings of the cosmos.
Both recalling his life story and recounting many of the major advances in twentieth-century science, a renowned physicist shares his autobiography through letters. Having penned hundreds of letters to his family over four decades, Freeman Dyson has framed them with the reflections made by a man now in his nineties. While maintaining that “the letters record the daily life of an ordinary scientist doing ordinary work,” Dyson nonetheless has worked with many of the twentieth century’s most renowned physicists, mathematicians, and intellectuals, so that Maker of Patterns presents not only his personal story but chronicles through firsthand accounts an exciting era of twentieth-century science. Though begun in the dark year of 1941 when Hitler’s armies had already conquered much of Europe, Dyson’s letters to his parents, written at Trinity College, Cambridge, often burst with the curiosity of a precocious seventeen-year-old. Pursuing mathematics and physics with a cast of legendary professors, Dyson thrived in Cambridge’s intellectual ferment, working on, for example, the theory of partitions or reading about Kurt Gödel’s hypotheses, while still finding time for billiards and mountain climbing. After graduating and serving with the Royal Air Force’s Bomber Command operational research section, whose job it was “to demolish German cities and kill as many German civilians as possible,” Dyson visited a war-torn Germany, hoping through his experience to create a “tolerably peaceful world.” Juxtaposing descriptions of scientific breakthroughs with concerns for mankind’s future, Dyson’s postwar letters reflect the quandaries faced by an entire scientific generation that was dealing with the aftereffects of nuclear detonations and concentration camp killings. Arriving in America in 1947 to study with Cornell’s Hans Bethe, Dyson continued to send weekly missives to England that were never technical but written with grace and candor, creating a portrait of a generation that was eager, as Einstein once stated, to solve “deep mysteries that Nature intend[ed] to keep for herself.” We meet, among others, scientists like Richard Feynman, who took Dyson across country on Route 66, Robert Oppenheimer, Eugene Wigner, Niels Bohr, James Watson, and a young Stephen Hawking; and we encounter intellectuals and leaders, among them Reinhold Niebuhr, George Kennan, Arthur C. Clarke, as well as Martin Luther King, Jr. The “patterns of comparable beauty in the dance of electrons jumping around atoms” invariably replicate themselves in this autobiography told through letters, one that combines accounts of wanton arms development with the not-inconsiderable demands of raising six children. As we once again attempt to guide society toward a more hopeful future, these letters, with their reenactment of what, at first, seems like a distant past, reveal invaluable truths about human nature.
A New Understanding of the Big Bang and the Emergence of Life
Author: Roy R. Gould
Publisher: Harvard University Press
We know the universe has a history, but does it also have a story of self-creation to tell? Yes, in Roy R. Gould’s account. He offers a compelling narrative of how the universe—with no instruction other than its own laws—evolved into billions of galaxies and gave rise to life, including humans who have been trying for millennia to comprehend it. Far from being a random accident, the universe is hard at work, extracting order from chaos. Making use of the best current science, Gould turns what many assume to be true about the universe on its head. The cosmos expands inward, not outward. Gravity can drive things apart, not merely together. And the universe seems to defy entropy as it becomes more ordered, rather than the other way around. Strangest of all, the universe is exquisitely hospitable to life, despite its being constructed from undistinguished atoms and a few unexceptional rules of behavior. Universe in Creation explores whether the emergence of life, rather than being a mere cosmic afterthought, may be written into the most basic laws of nature. Offering a fresh take on what brought the world—and us—into being, Gould helps us see the universe as the master of its own creation, not tethered to a singular event but burgeoning as new space and energy continuously stream into existence. It is a very old story, as yet unfinished, with plotlines that twist and churn through infinite space and time.
A bestseller--more than 300,000 copies sold, translated into seventeen languages, and featured in the Los Angeles Times, Washington Post, Miami Herald, Harvard Business Review, Fast Company, and Fortune; Shows how discoveries in quantum physics, biology, and chaos theory enable us to deal successfully with change and uncertainty in our organizations and our lives; Includes a new chapter on how the new sciences can help us understand and cope with some of the major social challenges of our times We live in a time of chaos, rich in potential for new possibilities. A new world is being born. We need new ideas, new ways of seeing, and new relationships to help us now. New science--the new discoveries in biology, chaos theory, and quantum physics that are changing our understanding of how the world works--offers this guidance. It describes a world where chaos is natural, where order exists ''for free.'' It displays the intricate webs of cooperation that connect us. It assures us that life seeks order, but uses messes to get there. Leadership and the New Science is the bestselling, most acclaimed, and most influential guide to applying the new science to organizations and management. In it, Wheatley describes how the new science radically alters our understanding of the world, and how it can teach us to live and work well together in these chaotic times. It will teach you how to move with greater certainty and easier grace into the new forms of organizations and communities that are taking shape.
"Welcome to the maze. A logical maze, a magical maze. A maze of the mind. The maze is mathematics. The mind is yours. Let's see what happens when we put them together. What is mathematics? What do mathematicians do? What is a mathematician? Someone who does mathematics? Not exactly. That's too easy an answer, and it creates too simple a maze—a circular loop of self-referential logic. No, a mathematician is more than just somebody who does mathematics. Think of it this way: what is a businessperson? Someone who does business? Yes, but not just that. A businessperson is someone who sees an opportunity for doing business where the rest of us see nothing; while we're complaining that there's no restaurant in the area, he or she is organizing a telephone pizza delivery service. Similarly, a mathematician is someone who sees opportunities for doing mathematics that the rest of us miss. I want to open your mind to some of these opportunities."—from The Magical Maze Praise for Ian Stewart's Previous Books About Nature's Numbers: "Stewart achieves what other popular mathematics writers merely strive for: an accurate, informative portrayal of contemporary mathematics without a single equation in sight."—Nature About The Problems of Mathematics: "From one of mathematics' most gifted expositors . . . challenging and interesting. Those with no knowledge of the subject will be able to glimpse its beauty and appeal."—New Scientist About The Collapse of Chaos: "This ambitious book fearlessly asks some big questions, challenging us to look at science a new way."—San Francisco Chronicle About Another Fine Math You've Got Me Into: "Ian Stewart's quirky humor and imaginative storytelling entice readers into a fascinating world of mathematical curiosities."—Ivars Peterson author of The Jungles of Randomness Enter the magical maze of mathematics and explore the surprising passageways of a fantastical world where logic and imagination converge. For mathematics is a maze—a maze in your head—a maze of ideas, a maze of logic. And that maze in your mind is a powerful tool for understanding an even bigger maze—the maze of cause and effect that we call "the universe." That is its special kind of magic. Real magic. Strange magic. Infinitely fascinating magic. In this adventure of a book, acclaimed author Ian Stewart leads you swiftly and humorously through the junctions, byways, and secret passages of the magical maze to reveal its beauty, its surprise, and its power. Along the way, he reveals the infinite possibilities that arise from what he calls "the two-way trade between the natural world and the human mind." On your travels you will encounter number magic—both the stage-act variety and the deeper magic of animals, plants, and the physical world. You will come to understand the amazing pattern-forming abilities of the humble slime mold, the numerology of flowers, and the feeding habits of pigs and panthers. You will discover how to solve puzzles the algorithmic way, the artistic way, and the army way. You will be amazed by the deep connections between the founding of Carthage, soap bubbles, and communications networks. You will discover how to use a toy train set as a computer, and find out why this implies that there are unavoidable limits to mathematics. You will join the controversy over cars and goats, find out the terrible truth about confessions, and win endless bets about birthdays. You will see how a new idea about ferns can lead to a multi-million-dollar computer graphics company, and how Jupiter and Mars can combine forces to hurl cosmic rocks at Earth. And you will never again be able to watch a kitten, a kangaroo, or a Chihuahua without noticing the delightfully rhythmic patterns with which they move their feet. If you've always loved mathematics, you will find endless delights in the twists and turns of The Magical Maze. If you've always hated mathematics, a trip through this marvelous book will do much to change your mind.
How the Ladies of the Harvard Observatory Took the Measure of the Stars
Author: Dava Sobel
New from #1 New York Times bestselling author Dava Sobel, the "inspiring" (People), little-known true story of women's landmark contributions to astronomy "A joy to read.” —The Wall Street Journal Named one of the best books of the year by NPR, The Economist, Smithsonian, Nature, and NPR's Science Friday Nominated for the PEN/E.O. Wilson Literary Science Writing Award In the mid-nineteenth century, the Harvard College Observatory began employing women as calculators, or “human computers,” to interpret the observations their male counterparts made via telescope each night. At the outset this group included the wives, sisters, and daughters of the resident astronomers, but soon the female corps included graduates of the new women's colleges—Vassar, Wellesley, and Smith. As photography transformed the practice of astronomy, the ladies turned from computation to studying the stars captured nightly on glass photographic plates. The “glass universe” of half a million plates that Harvard amassed over the ensuing decades—through the generous support of Mrs. Anna Palmer Draper, the widow of a pioneer in stellar photography—enabled the women to make extraordinary discoveries that attracted worldwide acclaim. They helped discern what stars were made of, divided the stars into meaningful categories for further research, and found a way to measure distances across space by starlight. Their ranks included Williamina Fleming, a Scottish woman originally hired as a maid who went on to identify ten novae and more than three hundred variable stars; Annie Jump Cannon, who designed a stellar classification system that was adopted by astronomers the world over and is still in use; and Dr. Cecilia Helena Payne, who in 1956 became the first ever woman professor of astronomy at Harvard—and Harvard’s first female department chair. Elegantly written and enriched by excerpts from letters, diaries, and memoirs, The Glass Universe is the hidden history of the women whose contributions to the burgeoning field of astronomy forever changed our understanding of the stars and our place in the universe.