Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    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.

    It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers.

    As exciting as any action/adventure novel, this is actually the story of incredible individuals and engrossing tales behind the most profound, enduring mathematical theorems.Archimedes famously ran naked through the streets shouting, “Eureka, eureka!” after finding a method for measuring the volume of an irregular-shaped object. René Descartes was not only a great French mathematician, philosopher, physicist, and natural scientist; he was also an expert swordsman who traveled with European armies from town to town, dressed in green taffeta and accompanied by a valet. Georg Cantor grappled with mental illness as he explored the highly counterintuitive, bizarre properties of infinite sets and numbers. Emmy Noether struggled to find employment as she laid the mathematical groundwork for modern theoretical physics. And Alexander Grothendieck taught himself mathematics while interned in Nazi concentration camps, only to disappear into the Pyrenees at the zenith of his career.These are just a few stories recounted in this absorbing narrative. In probing the lives of the preeminent mathematicians in history, a Strange Wilderness will leave you entertained and enlightened, with a newfound appreciation of the tenacity, complexity, and brilliance of the mathematical genius.

    In this short book, Andrew Culp polemically argues that this once-radical canon of joy has lost its resistance to the present. Concepts created to defeat capitalism have been recycled into business mantras that joyously affirm “Power is vertical; potential is horizontal!” Culp recovers the Deleuze’s forgotten negativity. He unsettles the prevailing interpretation through an underground network of references to conspiracy, cruelty, the terror of the outside, and the shame of being human. Ultimately, he rekindles opposition to what is intolerable about this world. Forerunners is a thought-in-process series of breakthrough digital works. Written between fresh ideas and finished books, Forerunners draws on scholarly work initiated in notable blogs, social media, conference plenaries, journal articles, and the synergy of academic exchange. This is gray literature publishing: where intense thinking, change, and speculation take place in scholarship.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.

    The more we discover, the more puzzling the universe appears to be. How and why are the laws of nature what they are? A philosopher and a physicist, world-renowned for their radical ideas in their fields, argue for a revolution. To keep cosmology scientific, we must replace the old view in which the universe is governed by immutable laws by a new one in which laws evolve. Then we can hope to explain them. The revolution that Roberto Mangabeira Unger and Lee Smolin propose relies on three central ideas. There is only one universe at a time. Time is real: everything in the structure and regularities of nature changes sooner or later. Mathematics, which has trouble with time, is not the oracle of nature and the prophet of science; it is simply a tool with great power and immense limitations. The argument is readily accessible to non-scientists as well as to the physicists and cosmologists whom it challenges.

    The essays in this volume are intriguing, challenging, & often baffling to the reader, calling him to abandon all superficial scanning & to enter wholeheartedly into the serious pursuit of thinking. Heidegger is not a 'primitive' or a 'romantic.' He is not one who seeks escape from the burdens & responsibilities of contemporary life into serenity, either through the re-creating of some idyllic past or through the exalting of some simple experience. Finally, Heidegger is not a foe of technology & science. He neither disdains nor rejects them as though they were only destructive of human life. The roots of Heidegger's thinking lie deep in the Western philosophical tradition. Yet that thinking is unique in many of its aspects, in its language, & in its literary expression. In the development of this thought Heidegger has been taught chiefly by the Greeks, by German idealism, by phenomenology, & by the scholastic theological tradition. In him these & other elements have been fused by his genius of sensitivity * intellect into a very individual philosophical expression."--William Lovitt's Introduction

    This lively and lucid book provides an introduction to the essential phenomenological concepts that are crucial for understanding great thinkers such as Husserl, Heidegger, and Merleau-Ponty. Written by a leading expert in the field, Dan Zahavi examines and explains key questions such as:- What is a phenomenological analysis?- What are the methodological foundations of phenomenology?- What does phenomenology have to say about embodiment and intersubjectivity?- How is phenomenology distinguished from, and related to, other fields in philosophy?- How do ideas from classic phenomenology relate to ongoing debates in psychology and qualitative research?With a glossary of key terms and suggestions for further reading, the book considers key philosophical arguments around phenomenology, making this an ideal starting point for anyone seeking a concise and accessible introduction to the rich and complex study of phenomenology.

    According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.

    In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    "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.

    Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.