Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the humanist idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

    QFT is the only physics theory that makes sense and that dispels or resolves the paradoxes of relativity and quantum mechanics that have confused and mystified so many people.

    A young laywoman with almost no education, she became renowned for her intense mystical experiences, inspired preaching, and scathing criticism of corrupt political and ecclesial authorities. She is even recognized today as a Doctor of the Church—the only layperson to ever receive the title—yet comes across to us more as an apostle than an intellectual. Her work is like Aquinas’ Summa set on fire.But for all the fascination with Catherine, the distinguishing feature of her life has received surprisingly little attention: her preoccupation with freedom. Catherine had a keen sense of the “unspeakably crazy” love of God and the liberating power of his mercy. But she also knew the terrible bondage of sin—and the necessity of facing our own inner darkness if we are to overcome it. She had a passion for leading those enslaved by fear and oppression to self-knowledge in God—and ultimately, to true freedom. It is this “fire” that inflames almost every page she writes.In this profound book, the Irish Dominican poet and writer Fr. Paul Murray draws us into the fire of this great mystic’s love for God and humanity, reading her life and teaching not only in light of Dominican spirituality, but also the writings of Renaissance philosopher Giovanni Pico della Mirandola and the modern psychologist Carl Jung. What results is a portrait of a preacher of freedom who speaks to us, even today, with compelling authority.

    Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge.

    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    

    In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. Thinking In Numbers will change the way you think about math and fire your imagination to see the world with fresh eyes.

    Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Astronomy; History / General; Juvenile Nonfiction / Science

    This study guide includes the following sections: Plot Summary, Chapter Summaries & Analysis, Characters, Objects/Places, Themes, Style, Quotes, and Topics for Discussion.

    They come armed with arguments to show that belief in God is absurd and dangerous. In the name of societal progress, they promote purging the world of all religious practice. And they claim that people of faith are mentally ill. Some of the new atheists openly declare their hatred for the Judeo-Christian God.Christian apologists have been quick to respond to the new atheists’ arguments. But there is another dimension to the issue which begs to be addressed--the root causes of atheism. Where do atheists come from? How did such folks as Richard Dawkins, Sam Harris, Daniel Dennett, and Christopher Hitchens become such ardent atheists? If we are to believe them, their flight from faith resulted from a dispassionate review of the evidence. Not enough rational grounds for belief in God, they tell us. But is this the whole story?Could it be that their opposition to religious faith has more to do with passion than reason? What if, in the end, evidence has little to do with how atheists arrive at their anti-faith? That is precisely the claim in this book. Atheism is not at all a consequence of intellectual doubts. These are mere symptoms of the root cause--moral rebellion. For the atheist, the missing ingredient is not evidence but obedience.The psalmist declares, “The fool says in his heart there is no God” (Ps. 14:1), and in the book of Romans, Paul makes it clear that lack of evidence is not the atheist’s problem. The Making of an Atheist confirms these biblical truths and describes the moral and psychological dynamics involved in the abandonment of faith.

    do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

    Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

    Without delving into either mythological or God-centric discourse, the book attempts to understand and explain various insights from the Gita through, in the author's words, derived theory and application. The Gita Way attempts to shed light on matters of self-realisation, and identifying and following the path to achieve the purpose of life. Within the framework of Vedic philosophy represented by Gita, this book explores:How to discover the swa-bhava, the inherent natural strength of our real-self?Is my profession aligned with my swa-bhava? What is my purpose of life?What is the real meaning of moksha, the liberation? How the realization of individual purpose leads us to attain supreme purpose we are born to achieve? Using the principles of Gita, this book presents innovative findings on theory of prarabdha, the luck or destiny, role of knowledge and karma, continuous improvement, yoga of universal harmony and yoga of devotion. To highlight few, in chapter combined discipline of knowledge and karma, authors introduce most important part of their research—Centring. Centring summarizes power of combined application of yoga of knowledge and karma along with simplified theory of spirit and supreme spirit. Chapter Vision of Universal Form and Yoga of Liberation simplifies the meaning of moksha, the state of liberation by linking it to the attainment of supreme purpose of life. Chapters on Yoga of Devotion and Continuous improvement focus on recipe of staying on the unique path of achieving individual goal. Unlike other books on Bhagavad Gita, the Gita Way is not a chapter wise discourse. Instead it presents deduced concepts in first place supported with relevant reference from the whole Gita. For example, in the first chapter of the Gita Way, you may get a reference of last chapter of Gita relevant to the topic of discussion.Contents:1. INTRODUCTION TO ‘THE GITA WAY’ 11Development of ‘The Gita Way’ 17 2. DEVELOPING A SENSE OF PURPOSE IN LIFE 25Goal 28Finding Unique Strength and Developing It 32Joy of the Self-Hobby vs Profession 35How to Set a Goal? 39Doubt in any form is the Biggest Enemyto Self-realisation 45The Story of Barbarika: Why was Barbarika Sacrificed? 47 3. YOGA OF KNOWLEDGE 51Knowledge of Self 54Elements of Self 56Consciousness of Self-Identity 57Intellect 60Primordial Matter 62Source of Perception and Action, One Mind and Five Senses 63Physical Body and Fitness 63False Goals such as Desire, Aversion and Pleasure 64Required Qualities in Self 64How Does One Achieve ‘Absolute Knowledge’? 67Lack of Knowledge is Ignorance which creates Fear 71 4. KARMA YOGA 74Prescribed Act and Prohibited Act 76Yoga and the Attributes of a Yogi 79How does One Achieve Equipoise? 80Desire-Entrap 84Hierarchy of Control 86Theory of Prarabdha or Destiny 88Butterfly Effect 90Hurdles in the Path of Karma-Yoga 93Vikarma 95Law of Growth 96Ultimate Dispassion: Nishkam Karma 97How to stay on the Path of Karma-Yoga? 99 5. COMBINED DISCIPLINE OF KNOWLEDGE AND KARMA 101Self-Realisation 102Wisdom 104Sacrifice 108Centring and Power of Real-Self 112Power of Real-self 113Centring 116Yoga of Self-Control 119 6. YOGA OF DEVOTION 121 The Cycle of Liberation 123How does devotion come to us? 127Devotion to Tame the Mind 129Relevance of Devotion to the Theory of Prarabdha 130Symptoms of Lack of Devotion 134 7. VISION OF THE UNIVERSAL FORM 136Universal Form of Goal 140Concept of Self 147Redirecting the Purpose of Desire 150 8. CONTINUOUS IMPROVEMENT ON THREE MODES OF NATURE 152Inner Purification by Knowing Sattva, Rajas and Tamas 159Sattva 159Rajas 161Tamas 164The Gita Way of Continuous Improvement 165Elimination of Waste 166 9. YOGA OF LIBERATION 170How is Sattva linked with the Supreme Goal? 173How does one attain sattva? 174Non-violence in thoughts and Action. 175Absence of Pride 175Internal and External Purity 176Steadfastness of Mind 176Control of Body, Mind and Senses 176Sincerity 177Forbearance 177Uprightness of Speech and Mind 177Devout Service to the Preceptor 177 Austerity of Mind 178Sattvika Intellect 178Sattvika Sacrifice 179Leadership by Creating Order Around 180 Yoga of Liberation 182

    Breaking down the symbols themselves, they pose a series of questions: What is energy? What is mass? What has the speed of light got to do with energy and mass? In answering these questions, they take us to the site of one of the largest scientific experiments ever conducted. Lying beneath the city of Geneva, straddling the Franco-Swiss boarder, is a 27 km particle accelerator, known as the Large Hadron Collider. Using this gigantic machine—which can recreate conditions in the early Universe fractions of a second after the Big Bang—Cox and Forshaw will describe the current theory behind the origin of mass.Alongside questions of energy and mass, they will consider the third, and perhaps, most intriguing element of the equation: 'c' - or the speed of light. Why is it that the speed of light is the exchange rate? Answering this question is at the heart of the investigation as the authors demonstrate how, in order to truly understand why E=mc2, we first must understand why we must move forward in time and not backwards and how objects in our 3-dimensional world actually move in 4-dimensional space-time. In other words, how the very fabric of our world is constructed. A collaboration between two of the youngest professors in the UK, Why Does E=mc2? promises to be one of the most exciting and accessible explanations of the theory of relativity in recent years.

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.