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    These dramatic first-person essays detail spectacular serendipities, impossible cures, breathtaking resuscitations, extraordinary awakenings, and recovery from unimaginable disasters. Still other essays give voice to cases in which the physical aspects were less dramatic than the emotional aspects, yet miraculous and transformational for everyone involved. Positive impacts left in the wake of even the gravest of tragedies, profound triumphs of heart and spirit. Preeminent physicians in many specialties, including deans and department heads on the faculties of the top university medical schools in the country describe, in everyday language and with moving testimony, their very personal reactions to these remarkable clinical experiences. Among the extraordinary cases poignantly recounted by the physicians witnessing them: A priest visiting a hospitalized patient went into cardiac arrest on the elevator, which opened up on the cardiac floor, right at the foot of the cardiac specialist, at just the right moment.A tiny premature baby dying from irreversible lung disease despite the most intensive care who recovered almost immediately after being taken from his hospital bed and placed on his mother's chest.President John F. Kennedy's son Patrick, who died shortly after birth, and whose disease eventually led to research that saved generations of babies.A nine-year-old boy who was decapitated in a horrific car accident but survived without neurological damage.A woman who conceived and delivered a healthy baby—despite having had both of her fallopian tubes surgically removed.A young man whose only hope for survival was a heart transplant, but just at the moment he developed a potentially fatal complication making a transplant impossible, his own heart began healing itself.A teenage girl near death after contracting full-blown rabies who became the first patient ever to recover from that disease after an unexpected visit by Timothy Dolan, the man who would go on to become the Archbishop of New York.A Manhattan window-washer who fell 47 stories—and not only became the only person ever to survive a fall from that height, but went on to make a full recovery. Miracles We Have Seen is a book of inspiration and optimism, and a compelling glimpse into the lives of physicians—their humanity and determined devotion to their patients and their patients' families. It reminds us that what we don't know or don't understand isn‘t necessarily cause for fear, and can even be reason for hope

    This essay by Copernicus (1473-1543), revolutionized the way we look at the earth's placement in the universe, and paved the way for many great scientists, including Galileo and Isaac Newton, whose theories stemmed from this model. Featuring a biography of Copernicus and an accessible, enlightening introduction, both written by the renowned physicist Stephen Hawking, On the Revolution of Heavenly Spheres provides a fascinating look at the theories which shaped our modern understanding of astronomy and physics.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers, mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers like Boltzmann’s constant and the Chandrasekhar limit are not as well known, and they do far more than one might imagine: They tell us how this world began and what the future holds. Much more than a gee-whiz collection of facts and figures, Cosmic Numbers illuminates why particular numbers are so important—both to the scientist and to the rest of us.

    Here, for the first time, is the complete history of the quest to understand Earth’s magnetism—from the ancient Greeks’ fascination with lodestone, to the geological discovery that the North Pole has not always been in the North—and to the astonishing modern conclusions that finally revealed the true source.Richly illustrated and skillfully told, North Pole, South Pole unfolds the human story behind the science: that of the inquisitive, persevering, and often dissenting thinkers who unlocked the secrets at our planet’s core.

    This hilarious and informative book is designed for anyone who is sci-curious and wants to know more about the world around them, especially the elements of everyday science that other books ignore.

    Lewellyn Powys called it "the greatest work of prose of the greatest period of English prose-writing," while the celebrated surgeon William Osler declared it the greatest of medical treatises. And Dr. Johnson, Boswell reports, said it was the only book that he rose early in the morning to read with pleasure. In this surprisingly compact and elegant new edition, Burton's spectacular verbal labyrinth is sure to delight, instruct, and divert today's readers as much as it has those of the past four centuries.

    In many parts of the world, that information is still readily available. But in our society, even as technology makes certain kinds of information more accessible than ever, other connections are irrevocably lost.In Glass, Paper, Beans, Leah Cohen traces three simple commodities on their geographic and semantic journey from her rickety table at the Someday Café to their various points of origin. As Cohen draws the reader Oz-like across time and continents, she brings to life three unforgettable characters whose labor provides the glass for her mug, the pulp for her newspaper and the beans for her cup of coffee. In prose as sophisticated as it is simple, she braids the myths, lore, and history of these three simple staples and conjures an unseen world where economics, fetishization, and manufacture meet.An elegant and inspired inquiry into the true nature of things, Glass, Paper, Beans is a classic work on the economy of everyday life.

    - predicted the reappearance of a lost planet, - discovered basic properties of magnetic forces, - invented a surveying tool used by professionals until the invention of lasers. Based on extensive research of original and secondary sources, this historical narrative will inspire young readers and even curious adults with its touching story of personal achievement.

    These noteworthy accounts of the lives of David Hilbert and Richard Courant are closely related: Courant's story is, in many ways, seen as the sequel to the story of Hilbert. Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Contance Reid.

    

    Ian Hacking here presents a philosophical critique of early ideas about probability, induction and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth and seventeenth centuries. The contemporary debate centres round such figures as Pascal, Leibniz and Jacques Bernoulli. What brought about the change in ideas? The author invokes in his explanation a wider intellectual framework involving the growth of science, economics and the theology of the period.

    

    In the wake of discoveries through the telescope and Copernican theory, the notion of an ordered cosmos of "fixed stars" gave way to that of a universe infinite in both time and space—with significant and far-reaching consequences for human thought. Alexandre Koyré interprets this revolution in terms of the change that occurred in our conception of the universe and our place in it and shows the primacy of this change in the development of the modern world.