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.

    

     Carl Sagan is considered one of the greatest scientific minds of our time. His remarkable ability to explain science in terms easily understandable to the layman in bestselling books such as Cosmos, The Dragons of Eden, and The Demon-Haunted World won him a Pulitzer Prize and placed him firmly next to Isaac Asimov, Stephen Jay Gould, and Oliver Sachs as one of the most important and enduring communicators of science. In December 2006 it will be the tenth anniversary of Sagan's death, and Ann Druyan, his widow and longtime collaborator, will mark the occasion by releasing Sagan's famous "Gifford Lectures in Natural Theology," The Varieties of Scientific Experience: A Personal View of the Search for God. The chance to give the Gifford Lectures is an honor reserved for the most distinguished scientists and philosophers of our civilization. In 1985, on the grand occasion of the centennial of the lectureship, Carl Sagan was invited to give them. He took the opportunity to set down in detail his thoughts on the relationship between religion and science as well as to describe his own personal search to understand the nature of the sacred in the vastness of the cosmos. The Varieties of Scientific Experience, edited, updated and with an introduction by Ann Druyan, is a bit like eavesdropping on a delightfully intimate conversation with the late great astronomer and astrophysicist. In his charmingly down-to-earth voice, Sagan easily discusses his views on topics ranging from manic depression and the possibly chemical nature of transcendance to creationism and so-called intelligent design to the likelihood of intelligent life on other planets to the likelihood of nuclear annihilation of our own to a new concept of science as "informed worship." Exhibiting a breadth of intellect nothing short of astounding, he illuminates his explanations with examples from cosmology, physics, philosophy, literature, psychology, cultural anthropology, mythology, theology, and more. Sagan's humorous, wise, and at times stunningly prophetic observations on some of the greatest mysteries of the cosmos have the invigorating effect of stimulating the intellect, exciting the imagination, and reawakening us to the grandeur of life in the cosmos.

      In the past few years, a handful of scientists have been in a race to explain a disturbing aspect of our universe: only 4 percent of it consists of the matter that makes up you, me, our books, and every planet, star, and galaxy. The rest—96 percent of the universe—is completely unknown.   Richard Panek tells the dramatic story of how scientists reached this conclusion, and what they’re doing to find this "dark" matter and an even more bizarre substance called dark energy. Based on in-depth, on-site reporting and hundreds of interviews—with everyone from Berkeley’s feisty Saul Perlmutter and Johns Hopkins’s meticulous Adam Riess to the quietly revolutionary Vera Rubin—the book offers an intimate portrait of the bitter rivalries and fruitful collaborations, the eureka moments and blind alleys, that have fueled their search, redefined science, and reinvented the universe.

    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.

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.

    Darwin was only too aware of the storm his theory of evolution would provoke but he would surely have raised an incredulous eyebrow at the controversy still raging a century and a half later. Evolution is accepted as scientific fact by all reputable scientists and indeed theologians, yet millions of people continue to question its veracity.In The Greatest Show on Earth Richard Dawkins takes on creationists, including followers of ‘Intelligent Design’ and all those who question the fact of evolution through natural selection. Like a detective arriving on the scene of a crime, he sifts through fascinating layers of scientific facts and disciplines to build a cast-iron case: from the living examples of natural selection in birds and insects; the ‘time clocks’ of trees and radioactive dating that calibrate a timescale for evolution; the fossil record and the traces of our earliest ancestors; to confirmation from molecular biology and genetics. All of this, and much more, bears witness to the truth of evolution.The Greatest Show on Earth comes at a critical time: systematic opposition to the fact of evolution is now flourishing as never before, especially in America. In Britain and elsewhere in the world, teachers witness insidious attempts to undermine the status of science in their classrooms. Richard Dawkins provides unequivocal evidence that boldly and comprehensively rebuts such nonsense. At the same time he shares with us his palpable love of the natural world and the essential role that science plays in its interpretation. Written with elegance, wit and passion, it is hard-hitting, absorbing and totally convincing.

    Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The language of symbols and infinitely large (and small) regions of mathematics should be rendered with clarity for the general reader.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.

    It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now.Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own.

    For more than two centuries, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, we know nothing more about these laws than we knew in the 1970s. Why is physics suddenly in trouble? And what can we do about it?One of the major problems, according to Smolin, is string theory: an ambitious attempt to formulate a “theory of everything” that explains all the particles and forces of nature and how the universe came to be. With its exotic new particles and parallel universes, string theory has captured the public’s imagination and seduced many physicists.But as Smolin reveals, there’s a deep flaw in the theory: no part of it has been tested, and no one knows how to test it. In fact, the theory appears to come in an infinite number of versions, meaning that no experiment will ever be able to prove it false. As a scientific theory, it fails. And because it has soaked up the lion’s share of funding, attracted some of the best minds, and effectively penalized young physicists for pursuing other avenues, it is dragging the rest of physics down with it.With clarity, passion, and authority, Smolin charts the rise and fall of string theory and takes a fascinating look at what will replace it. A group of young theorists has begun to develop exciting ideas that, unlike string theory, are testable. Smolin not only tells us who and what to watch for in the coming years, he offers novel solutions for seeking out and nurturing the best new talent—giving us a chance, at long last, of finding the next Einstein.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.