In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.
With his critically acclaimed best-sellers The Mathematical Tourism and Islands of Truth, Ivars Peterson took readers to the frontiers of modern mathematics. His new book provides an up-to-date look at one of science's greatest detective stories: the search for order in the workings of the solar system. In the late 1600s, Sir Isaac Newton provided what astronomers had long sought: a seemingly reliable way of calculating planetary orbits and positions. Newton's laws of motion and his coherent, mathematical view of the universe dominated scientific discourse for centuries. At the same time, observers recorded subtle, unexpected movements of the planets and other bodies, suggesting that the solar system is not as placid and predictable as its venerable clock work image suggests. Today, scientists can go beyond the hand calculations, mathematical tables, and massive observational logs that limited the explorations of Newton, Copernicus, Galileo, Kepler, Tycho Brahe, and others. Using supercomputers to simulate the dynamics of the solar system, modern astronomers are learning more about the motions they observe and uncovering some astonishing examples of chaotic behavior in the heavens. Nonetheless, the long-term stability of the solar system remains a perplexing, unsolved issue, with each step toward its resolution exposing additional uncertainties and deeper mysteries. To show how our view of the solar system has changed from clocklike precision to chaos and complexity, Newton's Clock describes the development of celestial mechanics through the ages - from the star charts of ancient navigators to the seminal discoveries of the 17th century from the crucial work of Poincare to thestartling, sometimes controversial findings and theories made possible by modern mathematics and computer simulations. The result makes for entertaining and provocative reading, equal parts science, history and intellectual adventure.
“If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly
An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.
This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.
A journalist's twenty-year fascination with the Manson murders leads to "gobsmacking" (The Ringer) new revelations about the FBI's involvement in this "kaleidoscopic" (The New York Times) reassessment of an infamous case in American history. Over two grim nights in Los Angeles, the young followers of Charles Manson murdered seven people, including the actress Sharon Tate, then eight months pregnant. With no mercy and seemingly no motive, the Manson Family followed their leader's every order -- their crimes lit a flame of paranoia across the nation, spelling the end of the sixties. Manson became one of history's most infamous criminals, his name forever attached to an era when charlatans mixed with prodigies, free love was as possible as brainwashing, and utopia -- or dystopia -- was just an acid trip away. Twenty years ago, when journalist Tom O'Neill was reporting a magazine piece about the murders, he worried there was nothing new to say. Then he unearthed shocking evidence of a cover-up behind the "official" story, including police carelessness, legal misconduct, and potential surveillance by intelligence agents. When a tense interview with Vincent Bugliosi -- prosecutor of the Manson Family and author of Helter Skelter -- turned a friendly source into a nemesis, O'Neill knew he was onto something. But every discovery brought more questions: Who were Manson's real friends in Hollywood, and how far would they go to hide their ties? Why didn't law enforcement, including Manson's own parole officer, act on their many chances to stop him? And how did Manson -- an illiterate ex-con -- turn a group of peaceful hippies into remorseless killers? O'Neill's quest for the truth led him from reclusive celebrities to seasoned spies, from San Francisco's summer of love to the shadowy sites of the CIA's mind-control experiments, on a trail rife with shady cover-ups and suspicious coincidences. The product of two decades of reporting, hundreds of new interviews, and dozens of never-before-seen documents from the LAPD, the FBI, and the CIA, Chaos mounts an argument that could be, according to Los Angeles Deputy District Attorney Steven Kay, strong enough to overturn the verdicts on the Manson murders. This is a book that overturns our understanding of a pivotal time in American history.
Clock the Chaos Mage. A stranger out of time, hidden in the folds of shadow. He is the guardian of Coney Island's supernatural borderlands, and the only thing standing between our reality and the demons that thirst to destroy it. Clock's Watch. An anthology of heroic dark fantasy and terror. Illustrations by Sean Bova, Jay Campbell and MV.
As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Kae Tempest's powerful narrative poem--set to music on their album of the same title, shortlisted for the Mercury Music Prize--illuminates the lives of a single city street, creating an electric, humming human symphony. Let Them Eat Chaos, Kae Tempest's long poem written for live performance and heard on the album release of the same name, is both a powerful sermon and a moving play for voices. Seven neighbors inhabit the same London street, but are all unknown to each other. The clock freezes in the small hours, and one by one we see directly into their lives: lives that are damaged, disenfranchised, lonely, broken, addicted, and all, apparently, without hope. Then a great storm breaks over London, and brings them out into the night to face each other, giving them one last chance to connect. Tempest argues that our alienation from one another has bred a terrible indifference to our own fate, but counters this with a plea to challenge the forces of greed which have conspired to divide us, and mend the broken home of our own planet while we still have time. Let Them Eat Chaos is a cri de cœur, a call to action, and a powerful poetic statement.
