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.

    In this unique biography, astrophysicist John Gribbon and his wife, Mary, pay tribute to this enormously human scientist.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    It explains all this and much more. It discloses the best time to have a sex change, how to have a virgin birth, when to seduce your sisters or eat your lover. Quirky and brilliant, it takes as its starting point all creatures great and small worried about their bizarre sex lives, and the letters they write to the wise Dr Tatiana, the only agony aunt in all creation with a prodigious knowledge of both natural history and evolutionary biology.

    Line drawings and black-and-white photographs.

    If...we could ask and it could reply, it would give up to us the most intimate secrets of life. -from Chapter II Anticipating not only modern scientific theories of psychology but also those of cosmology, this astonishing book sets out a impressive goal for itself: to reconcile human biology with a theory of consciousness. First published in France in 1907, and translated into English in 1911, this work of wonder was esteemed at the time in scientific circles and in the popular culture alike for its profound explorations of perception and memory and its surprising conclusions about the nature and value of art. Contending that intuition is deeper than intellect and that the real consequence of evolution is a mental freedom to grow, to change, to seek and create novelty, Bergson reinvigorated the theory of evolution by refusing to see it as merely mechanistic. His expansion on Darwin remains one of the most original and important philosophical arguments for a scientific inquiry still under fire today. French philosopher HENRI BERGSON (1859-1941) was born in Paris. Among his works are Matter and Memory (1896), An Introduction to Metaphysics (1903), and The Two Sources of Morality and Religion (1932). He was awarded the Nobel Prize for Literature in 1927.

    Prehistory has never been more exciting: New discoveries are overturning long-held theories left and right. Stone tools in Australia date back 65,000 years—a time when, we once thought, the first Sapiens had barely left Africa. DNA sequencing has unearthed a new hominid group—the Denisovans—and confirmed that crossbreeding with them (and Neanderthals) made Homo sapiens who we are today.A Pocket History of Human Evolution brings us up-to-date on the exploits of all our ancient relatives. Paleoanthropologist Silvana Condemi and science journalist François Savatier consider what accelerated our evolution: Was it tools, our “large” brains, language, empathy, or something else entirely? And why are we the sole surviviors among many early bipedal humans? Their conclusions reveal the various ways ancient humans live on today—from gossip as modern “grooming” to our gendered division of labor—and what the future might hold for our strange and unique species.

    In 1996 Joseph LeDoux's "The Emotional Brain" presented a revelatory examination of the biological bases of our emotions and memories. Now, the world-renowned expert on the brain has produced with a groundbreaking work that tells a more profound story: how the little spaces between the neurons-the brain's synapses--are the channels through which we think, act, imagine, feel, and remember. Synapses encode the essence of personality, enabling each of us to function as a distinctive, integrated individual from moment to moment. Exploring the functioning of memory, the synaptic basis of mental illness and drug addiction, and the mechanism of self-awareness, "Synaptic Self" is a provocative and mind-expanding work that is destined to become a classic.