Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    The theme of Heisenberg's exposition is that words and concepts familiar in daily life can lose their meaning in the world of relativity and quantum physics. This in turn has profound philosophical implications for the nature of reality and for our total world view.

    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.

    The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

    "A Treatise Concerning the Principles of Human Knowledge" is one of Berkeley's best known works and in it Berkeley expounds upon this idea of subjective idealism, which in other words is the idea that all of reality, as far as humans are concerned, is simply a construct of the way our brains perceive and according to Berkeley no other sense of reality matters beyond that which we perceive.

    

    Mingling acute observation with often wild speculation, it offers a fascinating view of the world as it was understood in the first century AD, whether describing the danger of diving for sponges, the first water-clock, or the use of asses’ milk to remove wrinkles. Pliny himself died while investigating the volcanic eruption that destroyed Pompeii in AD 79, and the natural curiosity that brought about his death is also very much evident in the Natural History — a book that proved highly influential right up until the Renaissance and that his nephew, Pliny the younger, described ‘as full of variety as nature itself’. John F. Healy has made a fascinating and varied selection from the Natural History for this clear, modern translation. In his introduction, he discusses the book and its sources topic by topic. This edition also includes a full index and notes.

    

    His feverish and singular pursuit of this goal has come to define his life. Now an old man, he is looked on with suspicion and shame by his family-until his ambitious young nephew intervenes.Seeking to understand his uncle's mysterious mind, the narrator of this novel unravels his story, a dramatic tale set against a tableau of brilliant historical figures-among them G. H. Hardy, the self-taught Indian genius Srinivasa Ramanujan, and a young Kurt Gödel. Meanwhile, as Petros recounts his own life's work, a bond is formed between uncle and nephew, pulling each one deeper into mathematical obsession, and risking both of their sanity.

    St. Thomas Aquinas has much to teach us--most especially how to confront the classic questions that are still with us after centuries of thought.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    Among those you'll investigate are the accounts of the creation of the world in Hesiod's Theogony and Ovid's Metamorphoses; the gods Zeus, Apollo, Demeter, Persephone, Hermes, Dionysos, and Aphrodite; the Greek heroes, Theseus and Heracles (Hercules in the Roman version); and the most famous of all classical myths, the Trojan War.Professor Vandiver anchors her presentation in some basics. What is a myth? Which societies use myths? What are some of the problems inherent in studying classical mythology? She also discusses the most influential 19th- and 20th-century thinking about myth's nature and function, including the psychological theories of Freud and Jung and the metaphysical approach of Joseph Campbell. You'll also consider the relationship between mythology and culture (such as the implications of the myth of Demeter, Persephone, and Hades for the Greek view of life, death, and marriage), the origins of classical mythology (including the similarities between the Theogony and Mesopotamian creation myths), and the dangers of probing for distant origins (for example, there's little evidence that a prehistoric "mother goddess" lies at the heart of mythology).Taking you from the surprising "truths" about the Minotaur to Ovid's impact on the works of William Shakespeare, these lectures make classical mythology fresh, absorbing, and often surprising.Disclaimer: Please note that this recording may include references to supplemental texts or print references that are not essential to the program and not supplied with your purchase.©2000 The Teaching Company, LLC (P)2000 The Great Courses

    Proceeding from the assumption that human beings desire pleasure (and avoid pain), Bentham's unique perspective, known as utilitarianism, is used to construct a fascinating calculus for determining which action to perform when confronted with situations requiring moral decision-makingthe goal of which is to arrive at the "greatest happiness of the greatest number." Toward this end, he endeavors to delineate the sources and kinds of pleasure and pain and how they can be measured when assessing one's moral options. Bentham supports his arguments with discussions of intentionality, consciousness, motives, and dispositions.Bentham concludes this groundbreaking work with an analysis of punishment: its purpose and the proper role that law and jurisprudence should play in its determination and implementation. Here we find Bentham as social reformer seeking to resolve the tension that inevitably exists when the concerns of the many conflict with individual freedom.The Principles of Morals and Legislation offers readers the rare opportunity to experience one of the great works of moral philosophy, a volume that has influenced the course of ethical theory for over a century.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.