Heisenberg’s principle implied that scientific quantities/concepts do not have absolute, independent meaning, but acquire meaning only in terms of the experiments used to measure them. This proposition, undermining the cherished belief that science could reveal the physical world with limitless detail and precision, placed Heisenberg in direct opposition to the revered Albert Einstein. The eminent scientist Niels Bohr, Heisenberg’s mentor and Einstein’s long-time friend, found himself caught between the two.Uncertainty chronicles the birth and evolution of one of the most significant findings in the history of science, and portrays the clash of ideas and personalities it provoked. Einstein was emotionally as well as intellectually determined to prove the uncertainty principle false. Heisenberg represented a new generation of physicists who believed that quantum theory overthrew the old certainties; confident of his reasoning, Heisenberg dismissed Einstein’s objections. Bohr understood that Heisenberg was correct, but he also recognized the vital necessity of gaining Einstein’s support as the world faced the shocking implications of Heisenberg’s principle.

    It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

    Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton's calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians -- an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work's clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.

    The text is established from original sources, with collations of all known manuscripts, chronology and verbal variants recorded. Works in Latin, Greek and Italian are included with new literal translations.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    The darker comedy of The Clouds satirizes Athenian philosophers - Socrates in particular - and reflects the uncertainties of a generation in which all traditional religious and ethical beliefs were being challenged. The Birds takes place in a flawed utopia, with man's eternal flaws observed from up above. In Lysistrata a band of women use sex's manipulative power in order to try and end a war. In The Frogs, the god Dionysus visits the underworld, consulting the late Aeschylus and Euripides regarding whether or not classical Athens will ever have another great dramatist - and provoking an argument between both.Three of the leading Greek translators of the twentieth century - William Arrowsmith, Richmond Lattimore, and Douglas Parker - have created versions of the comedies that are at once contemporary, historically accurate, and funny. Also included are introductions to each play that describe the historical and literary background of the work.

    Topics include the limits of knowledge, paradox of complexity, Maxwell's demon, Big Bang theory, much more. 1985 edition.

    With this work, he created the history of philosophy as a scientific study. He reveals philosophical theory as neither an accident nor an artificial construct, but as an exemplar of its age, fashioned by its antecedents and contemporary circumstances, and serving as a model for the future. The author himself appears to have regarded this book as a popular introduction to his philosophy as a whole, and it remains the most readable and accessible of all his philosophical writings.Eschewing the methods of original history (written during the period in question) and reflective history (written after the period has passed), Hegel embraces philosophic history, which employs a priori philosophical thought to interpret history as a rational process. Reason rules history, he asserts, through its infinite freedom (being self-sufficient, it depends on nothing beyond its own laws and conclusions) and power (through which it forms its own laws). Hegel argues that all of history is caused and guided by a rational process, and God's seemingly unknowable plan is rendered intelligible through philosophy. The notion that reason rules the world, he concludes, is both necessary to the practice of philosophic history and a conclusion drawn from that practice.

    Like you, the elements have lives: personalities and attitudes, talents and shortcomings, stories rich with meaning. You may think of them as the inscrutable letters of the periodic table but you know them much better than you realise. Welcome to a dazzling tour through history and literature, science and art. Here you'll meet iron that rains from the heavens and noble gases that light the way to vice. You'll learn how lead can tell your future while zinc may one day line your coffin. You'll discover what connects the bones in your body with the Whitehouse in Washington, the glow of a streetlamp with the salt on your dinner table. From ancient civilisations to contemporary culture, from the oxygen of publicity to the phosphorus in your pee, the elements are near and far and all around us. Unlocking their astonishing secrets and colourful pasts, Periodic Tales will take you on a voyage of wonder and discovery, excitement and novelty, beauty and truth. Along the way, you'll find that their stories are our stories, and their lives are inextricable from our own.

    The adjective 'medieval' has become a synonym for brutality and uncivilized behavior. Yet without the work of medieval scholars there could have been no Galileo, no Newton and no Scientific Revolution. In God's Philosophers, James Hannam debunks many of the myths about the Middle Ages, showing that medieval people did not think the earth is flat, nor did Columbus 'prove' that it is a sphere; the Inquisition burnt nobody for their science nor was Copernicus afraid of persecution; no Pope tried to ban human dissection or the number zero. God's Philosophers is a celebration of the forgotten scientific achievements of the Middle Ages - advances which were often made thanks to, rather than in spite of, the influence of Christianity and Islam. Decisive progress was also made in technology: spectacles and the mechanical clock, for instance, were both invented in thirteenth-century Europe. Charting an epic journey through six centuries of history, God's Philosophers brings back to light the discoveries of neglected geniuses like John Buridan, Nicole Oresme and Thomas Bradwardine, as well as putting into context the contributions of more familiar figures like Roger Bacon, William of Ockham and Saint Thomas Aquinas.

    Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

    Why do living things and physical phenomena take the forms they do? Analyzing the mathematical and physical aspects of biological processes, this historic work, first published in 1917, has become renowned as well for the poetry of is descriptions.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.