According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    Contemporary research in the empirical neurosciences and recent research in the philosophy of mind and the philosophy of science are used to illuminate fundamental questions concerning the relation between abstract cognitive theory and substantive neuroscience.

    The author writes of an encounter they had with a being called 'Tal' who looked human but claimed to be an alien. The author believes that this person was in fact an alien due to the content of their conversation and the events that lead to and followed it. The author requested we divulge no information about the book that could influence the first reading of it. We will reveal, however, that in the conversation, Tal attempts to show the author how a far more advanced life form would observe and function in the universe. Tal does not describe a technological superiority, but an actual perceptual and physical difference that leads to a fundamentally greater understanding of the world. The conversation covers many topics; including time, the perception of extra dimensions, quantum theory, infinity, and consciousness. Tal uses examples from modern scientific theory, ancient religions, alien worlds and even chess. The author wished to publish this book because they felt that this encounter dramatically changed their life.

    In Dataclysm, Christian Rudder uses it to show us who we truly are.   For centuries, we’ve relied on polling or small-scale lab experiments to study human behavior. Today, a new approach is possible. As we live more of our lives online, researchers can finally observe us directly, in vast numbers, and without filters. Data scientists have become the new demographers.   In this daring and original book, Rudder explains how Facebook "likes" can predict, with surprising accuracy, a person’s sexual orientation and even intelligence; how attractive women receive exponentially more interview requests; and why you must have haters to be hot. He charts the rise and fall of America’s most reviled word through Google Search and examines the new dynamics of collaborative rage on Twitter. He shows how people express themselves, both privately and publicly. What is the least Asian thing you can say? Do people bathe more in Vermont or New Jersey? What do black women think about Simon & Garfunkel? (Hint: they don’t think about Simon & Garfunkel.) Rudder also traces human migration over time, showing how groups of people move from certain small towns to the same big cities across the globe. And he grapples with the challenge of maintaining privacy in a world where these explorations are possible.   Visually arresting and full of wit and insight, Dataclysm is a new way of seeing ourselves—a brilliant alchemy, in which math is made human and numbers become the narrative of our time.

    Notions like denumerability, modal scope distinction, Bayesian conditionalization, and logical completeness are usually only elucidated deep within difficultspecialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists.The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outliningthe difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem.Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read withpleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    Of the discovery of an alien race and of a kink in time that means humanity — whatever form it takes — will never again be threatened by acts of God.

    Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds.

    Wade have on violent crime? Freakonomics will literally redefine the way we view the modern world.These may not sound like typical questions for an economist to ask. But Steven D. Levitt is not a typical economist. He is a much heralded scholar who studies the stuff and riddles of everyday life -- from cheating and crime to sports and child rearing -- and whose conclusions regularly turn the conventional wisdom on its head. He usually begins with a mountain of data and a simple, unasked question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: freakonomics.Through forceful storytelling and wry insight, Levitt and co-author Stephen J. Dubner show that economics is, at root, the study of incentives -- how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they set out to explore the hidden side of ... well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Ku Klux Klan.What unites all these stories is a belief that the modern world, despite a surfeit of obfuscation, complication, and downright deceit, is not impenetrable, is not unknowable, and -- if the right questions are asked -- is even more intriguing than we think. All it takes is a new way of looking. Steven Levitt, through devilishly clever and clear-eyed thinking, shows how to see through all the clutter.Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world.(front flap)

    His book is a fresh look at the questions that occur to anyone who thinks deeply about these matters, questions about free will, self-determination, destiny, choice, and who are we anyway. I believe this is a “breakthrough book.” Robert’s style of writing about such ephemeral and difficult subjects as awareness and consciousness is honest, concise, and accurate. His ability to describe his experiences of living in a reality quite different from conventional ways of thinking is brilliantly unusual. On first encountering Robert Saltzman’s work, I am reminded of the same feelings of discovery, delight and excitement that I remember from meeting Alan Watts’ “The Wisdom of Insecurity”, Krishnamurti’s “Freedom from the Known,” and Chögyam Trungpa’s “Cutting Through Spiritual Materialism.” His clarity of mind shines brightly through every sentence in this book. His skill at making clear the most difficult ramifications and subtleties of awakened consciousness is so free of conventional cluttered thinking, so free of habitual phrases, so free of the taint of religious dogma and the conventional ways of speaking of such difficult matters, that this book stands out for me as an entirely fresh and illuminated exposition of awakened consciousness: an awakened understanding of what it is to be human. —Dr. Robert K. Hall

    A collection of free excerpts from Sister Souljah’s books.

    This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book contains all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics.