Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    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.

    This work is the result of those requests. It is full of controversial claims, so be warned. I truly believe that if people follow the handful of principles in this short read, they will improve their health and change their lives.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artifical intelligence, business, epidemiology, social science and economics. Students in these areas will find natural models, simple identification procedures, and precise mathematical definitions of causal concepts that traditional texts have tended to evade or make unduly complicated. This book will be of interest to professionals and students in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable. Professor of Computer Science at the UCLA, Judea Pearl is the winner of the 2008 Benjamin Franklin Award in Computers and Cognitive Science.

    Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

    Dreams aren't really anything like reality. Dreams are, well, they're more dreamy. You can just tell. Things happen in dreams that don't happen in reality. Usually, anyway. An intriguing tale that will instill readers with an abiding sense of philosophical wonder. If you're smitten with Sophie's World, you're sure to be entranced by The Dream Weaver. - Christopher Phillips, author, Socrates Cafe. Jack Bowen's novel is like traveling with Alice to a Wonderland inhabited by the greatest philosophers and scientists who ever lived... A triumph! - Wenda O'Reilly, Ph.D., President, Birdcage Press and author, The Impressionist Art Game. The Dream Weaver is an outstanding how-to-think book... This book is a philosophical odyssey that tackles the mysteries of life, of science, and of the meaning of reality. - Susanne Pari, author, The Fortune Catcher.

    Every one has come true! Now he returns with secret lore of the past and startling glimpses of the future.Here is the extraordinary story of Creation and the fabulous lost worlds of Atlantis and Mu, the past lives of Winston Churchill, Franklin Roosevelt, Jackie Onassis, Richard Nixon, Elizabeth Taylor, Richard Burton, and other celebrities. The World Before forecasts things to come, among them:- A solution to the world's energy problem- A reduction in crime throughout America- The rise of a new national leader--in GermanyThe World Before is a dramatic and exciting book that will capture the imagination of everyone who seeks a deeper understanding of the mysteries of life.

    The mind-body problem cannot be confined to the relation between animal minds and animal bodies. If materialism cannot accommodate consciousness and other mind-related aspects of reality, then we must abandon a purely materialist understanding of nature in general, extending to biology, evolutionary theory, and cosmology. Since minds are features of biological systems that have developed through evolution, the standard materialist version of evolutionary biology is fundamentally incomplete. And the cosmological history that led to the origin of life and the coming into existence of the conditions for evolution cannot be a merely materialist history. An adequate conception of nature would have to explain the appearance in the universe of materially irreducible conscious minds, as such. No such explanation is available, and the physical sciences, including molecular biology, cannot be expected to provide one. The book explores these problems through a general treatment of the obstacles to reductionism, with more specific application to the phenomena of consciousness, cognition, and value. The conclusion is that physics cannot be the theory of everything.

    Austin was one of the leading philosophers of the twentieth century. The William James Lectures presented Austin's conclusions in the field to which he directed his main efforts on a wide variety of philosophical problems. These talks became the classic How to Do Things with Words.For this second edition, the editors have returned to Austin's original lecture notes, amending the printed text where it seemed necessary. Students will find the new text clearer, and, at the same time, more faithful to the actual lectures. An appendix contains literal transcriptions of a number of marginal notes made by Austin but not included in the text. Comparison of the text with these annotations provides new dimensions to the study of Austin's work.

    Nussbaum argues that the thought-content of disgust embodies magical ideas of contamination, and impossible aspirations to purity that are just not in line with human life as we know it. She argues that disgust should never be the basis for criminalizing an act, or play either the aggravating or the mitigating role in criminal law it currently does. She writes that we should be similarly suspicious of what she calls primitive shame, a shame at the very fact of human imperfection, and she is harshly critical of the role that such shame plays in certain punishments.Drawing on an extraordinarily rich variety of philosophical, psychological, and historical references--from Aristotle and Freud to Nazi ideas about purity--and on legal examples as diverse as the trials of Oscar Wilde and the Martha Stewart insider trading case, this is a major work of legal and moral philosophy.

    There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular “Good Math” blog, you’ll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird.Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing.If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark’s book will both entertain and enlighten you.

    It is an area that continues to attract and fascinate many people, even though it is generally thought to be highly complex and abstract. For some it is associated with the mystical or religious. For others it is known through the metaphysical poets who talk of love and spirituality. This Very Short Introduction goes right to the heart of the matter, getting to the basic and most important questions of metaphysical thought in order to understand the theory: What are objects? Do colors and shapes have some form of independent existence? Is the whole just a sum of the parts? What is it for one thing to cause another rather than just being associated with it? What is possible? Does time pass? By using simple questions to initiate thought about the basic issues around substance, properties, changes, causes, possibilities, time, personal identity, nothingness, and consciousness, Stephen Mumford provides a clear and down-to-earth path through this analytical tradition at the core of philosophical thought.

    Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

    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.