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.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Life remains the only way to make life. Are we still missing a vital ingredient in its creation?      Like Richard Dawkins' The Selfish Gene, which provided a new perspective on how evolution works, Life on the Edge alters our understanding of our world's fundamental dynamics. Bringing together first-hand experience at the cutting edge of science with unparalleled gifts of explanation, Jim Al-Khalili and Johnjoe Macfadden reveal that missing ingredient to be quantum mechanics; the phenomena that lie at the heart of this most mysterious of sciences. Drawing on recent ground-breaking experiments around the world, each chapter in Life on the Edge engages by illustrating one of life's puzzles: How do migrating birds know where to go? How do we really smell the scent of a rose? How do our genes copy themselves with such precision? Life on the Edge accessibly reveals how quantum mechanics can answer these probing questions of the universe. Guiding the reader through the rapidly unfolding discoveries of the last few years, Al-Khalili and McFadden communicate the excitement of the explosive new field of quantum biology and its potentially revolutionary applications, while offering insights into the biggest puzzle of all: what is life? As they brilliantly demonstrate in these groundbreaking pages, life exists on the quantum edge.

    The story of how we got from there to here is full of fascinating people, and in this elegant, entertaining book, Paul Strathern introduces us to ancient philosophers, medieval alchemists, and the earliest chemists-and to Dimitri Mendeleyev, the card-playing nineteenth-century Russian who claimed that the answers came to him in a dream. "Chemistry has been a neglected area of science writing, and Mendeleyev, the king of chemistry, is a largely forgotten genius. [This book] goes a long way toward correcting this injustice." (Simon Singh, author of Fermat's Last Theorem, in the Sunday Telegraph)

    In this reader-friendly, unabridged edition of three of his best-selling books, renowned science writer Isaac Asimov demystifies physics, teaching the fundamentals in a manner easily understood by lay people. Including the complete text of Motion, Sound and Heat, Light, Magnetism and Electricity, and The Electron, Proton and Neutron, this volume will guide you through the evolution of physics from its early Greek beginnings up to the modern theories of the creation of time, space and matter. Each volume relates the tale of the human quest through the ages for answers to the fundamental questions of how the universe works. Told in its historical context, this quest for knowledge is a story of high drama and uncommon valor, when men put their very lives on the line for the sake of scientific truth.3 Volumes in One: Motion, Sound & Heat; Light, Magnetism & Electricity; The Electron, Proton & Neutron. 1993 Barnes & Noble reprint of three Isaac Asimov classics. Originally published in 1966.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    In all the current highly publicized debates about creationism and its descendant "intelligent design," there is an element of the controversy that is rarely mentioned—the "evidence," the empirical truth of evolution by natural selection. Even Richard Dawkins and Stephen Jay Gould, while extolling the beauty of evolution and examining case studies, have not focused on the evidence itself. Yet the proof is vast, varied, and magnificent, drawn from many different fields of science. Scientists are observing species splitting into two and are finding more and more fossils capturing change in the past—dinosaurs that have sprouted feathers, fish that have grown limbs. Why Evolution Is True weaves together the many threads of modern work in genetics, paleontology, geology, molecular biology, and anatomy that demonstrate the "indelible stamp" of the processes first proposed by Darwin. In crisp, lucid prose accessible to a wide audience, Why Evolution Is True dispels common misunderstandings and fears about evolution and clearly confirms that this amazing process of change has been firmly established as a scientific truth.

    Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching players bluff in a poker game inspired John von Neumann--father of the modern computer and one of the sharpest minds of the century--to construct game theory, a mathematical study of conflict and deception. Game theory was readily embraced at the RAND Corporation, the archetypical think tank charged with formulating military strategy for the atomic age, and in 1950 two RAND scientists made a momentous discovery.Called the prisoner's dilemma, it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain. Introduced shortly after the Soviet Union acquired the atomic bomb, the prisoner's dilemma quickly became a popular allegory of the nuclear arms race. Intellectuals such as von Neumann and Bertrand Russell joined military and political leaders in rallying to the preventive war movement, which advocated a nuclear first strike against the Soviet Union. Though the Truman administration rejected preventive war the United States entered into an arms race with the Soviets and game theory developed into a controversial tool of public policy--alternately accused of justifying arms races and touted as the only hope of preventing them.A masterful work of science writing, Prisoner's Dilemma weaves together a biography of the brilliant and tragic von Neumann, a history of pivotal phases of the cold war, and an investigation of game theory's far-reaching influence on public policy today. Most important, Prisoner's Dilemma is the incisive story of a revolutionary idea that has been hailed as a landmark of twentieth-century thought.

    He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass.In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener.And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.

    Johnson takes us to those times when the world seemed filled with mysterious forces, when scientists were dazzled by light, by electricity, and by the beating of the hearts they laid bare on the dissecting table. We see Galileo singing to mark time as he measures the pull of gravity, and Newton carefully inserting a needle behind his eye to learn how light causes vibrations in the retina. William Harvey ties a tourniquet around his arm and watches his arteries throb above and his veins bulge below, proving that blood circulates. Luigi Galvani sparks electrical currents in dissected frog legs, wondering at the twitching muscle fibers, and Ivan Pavlov makes his now-famous dogs salivate at ascending chord progressions.For all of them, diligence was rewarded. In an instant, confusion was swept aside and something new about nature leaped into view. In bringing us these stories, Johnson restores some of the romance to science, reminding us of the existential excitement of a single soul staring down the unknown.

    

    For real.If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.