Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

    Literally. This book does not aim to make your life carefree, to make your problems disappear, to turn you into a saint free from blemish or blame. In fact, you may end up utterly bewildered by The Mystery Experience at times. But you will also be intrigued. Curious.Questioning. Loving. Loved. Overjoyed. Seduced out of the numbness of banality. And most importantly, awake. Gloriously awake, and full of wonder. Philosopher and author Tim Freke leads us on a journey through the nature of the 'Mystery Experience', via quantum physics, Gnosticism, the essence of Tao, meditation, Walt Whitman, Greek mythology, Buddhism, Dub Punk musician Jah Wobble, and Carl Jung. But what is the 'Mystery Experience'? You can taste it by simply focusing your attention on the mystery. But what is the mystery? The mystery is life. The mystery is the journey. The mystery is you. The mystery is me. The mystery makes you want to say, simply: WOW. No one has the answers, but asking the questions is what makes us come alive. Wherever you're coming from, you will find this journey rewarding. The only real requirement is that you're willing to wonder about life - to be curious and open - to be an explorer. Now prepare to leave base camp, because we're about to set off on a grand adventure.

    Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories.Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores what that implies and why some founders of the theory became the foremost objectors to it. Schr�dinger showed that it absurdly allowed a cat to be in a superposition simultaneously dead and alive. Einstein derided the theory's spooky interactions. With Bell's Theorem, we now know Schr�dinger's superpositions and Einstein's spooky interactions indeed exist.Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation.Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial.Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing.Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves.

    In The Life of the Cosmos, Smolin cuts the Gordian knot of cosmology with a simple, powerful idea: "The underlying structure of our world, " he writes, "is to be found in the logic of evolution." Today's physicists have overturned Newton's view of the universe, yet they continue to cling to an understanding of reality not unlike Newton's own - as a clock, an intricate mechanism, governed by laws which are mathematical and eternally true. Smolin argues that the laws of nature we observe may be in part the result of a process of natural selection which took place before the big bang. Smolin's ideas are based on recent developments in cosmology, quantum theory, relativity and string theory, yet they offer, at the same time, an unprecedented view of how these developments may fit together to form a new theory of cosmology. From this perspective, the lines between the simple and the complex, the fundamental and the emergent, and even between the biological and the physical are redrawn. The result is a framework that illuminates many intractable problems, from the paradoxes of quantum theory and the nature of space and time to the problem of constructing a final theory of physics. As he argues for this new view, Smolin introduces the reader to recent developments in a wide range of fields, from string theory and quantum gravity to evolutionary theory the structure of galaxies. He examines the philosophical roots of controversies in the foundations of physics, and shows how they may be transformed as science moves towardunderstanding the universe as an interrelated, self-constructed entity, within which life and complexity have a natural place, and in which "the occurrence of novelty, indeed the perpetual birth of novelty, can be understood."

    Their pioneering work, presented here in an elegant style, challenges much of the conventional wisdom about consciousness. The Universe of Consciousness has enormous implications for our understanding of language, thought, emotion, and mental illness.

    Acclaimed technologist and inventor Amir Husain explains how we can live amidst the coming age of sentient machines and artificial intelligence—and not only survive, but thrive.Artificial “machine” intelligence is playing an ever-greater role in our society. We are already using cruise control in our cars, automatic checkout at the drugstore, and are unable to live without our smartphones. The discussion around AI is polarized; people think either machines will solve all problems for everyone, or they will lead us down a dark, dystopian path into total human irrelevance. Regardless of what you believe, the idea that we might bring forth intelligent creation can be intrinsically frightening. But what if our greatest role as humans so far is that of creators? Amir Husain, a brilliant inventor and computer scientist, argues that we are on the cusp of writing our next, and greatest, creation myth. It is the dawn of a new form of intellectual diversity, one that we need to embrace in order to advance the state of the art in many critical fields, including security, resource management, finance, and energy. “In The Sentient Machine, Husain prepares us for a brighter future; not with hyperbole about right and wrong, but with serious arguments about risk and potential” (Dr. Greg Hyslop, Chief Technology Officer, The Boeing Company). He addresses broad existential questions surrounding the coming of AI: Why are we valuable? What can we create in this world? How are we intelligent? What constitutes progress for us? And how might we fail to progress? Husain boils down complex computer science and AI concepts into clear, plainspoken language and draws from a wide variety of cultural and historical references to illustrate his points. Ultimately, Husain challenges many of our societal norms and upends assumptions we hold about “the good life.”

    In the quantum realm, objects can be in two places at once. It's a place where time travel is not only possible, but necessary. It's a place where cause and effect can happen in reverse and observing something changes its state. From parallel universes to antimatter, quantum mechanics has revealed that when you get right down to it, the laws of nature are insane. The scientist J. B. S. Haldane once said, 'Reality is not only stranger than we imagine . . . it's stranger than we can imagine.' Never is this more true than with quantum mechanics; our best, most recent attempt to make sense of the fundamental laws of nature.Fundamental is a comprehensive beginner's guide to quantum mechanics, explaining not only the weirdness of the subject but the experiments that proved it to be true. Using a humorous and light-hearted approach, Fundamental tells the story of how the most brilliant minds in science grappled with seemingly impossible ideas and gave us everything from microchips to particle accelerators. Fundamental gives clear explanations of all the quantum phenomena known to modern science, without requiring an understanding of complex mathematics; tells the eccentric stories of the scientists who made these shattering discoveries and what they used them for; explains how quantum field theory (a topic not covered in detail by any other popular-science book) gave rise to particle physics and why the Higgs boson isn't the end of the story.

    A complete worldview is presented and defended, covering every subject from knowledge to art, from metaphysics to morality, from theology to politics. Topics include free will, the nature of the universe, the meaning of life, and much more, arguing from scientific evidence that there is only a physical, natural world without gods or spirits, but that we can still live a life of love, meaning, and joy.

    Are we products of our culture, or free agents within it? Are our neural pathways fixed early on by a mixture of nature and nurture, or is the possibility of comprehensive, intentional psychological change always open to us? What role does our brain play in the construction of free will, and how much medical evidence is there for the existence of it? What exactly are we talking about when we talk about 'freedom' anyway?In this cogent and compelling book, Julian Baggini explores the concept of 'free will' from every angle, blending philosophy, neuroscience, sociology and cognitive science. Freedom Regained brings the issues raised by the possibilities - and denials - of free to vivid life, drawing on scientific research and fascinating encounters with expert witnesses, from artists to addicts. It will provide a new understanding of our sense of personal freedom - and change the way the reader will think about their own choices.

    You'll discover how the sun shines, why light is both a wave and a particle, the certainty of the Uncertainty Principle, Schrodinger's Cat, Einstein's spooky action, how to build a quantum computer, and why quantum mechanics drives even its experts completely crazy. 'Jim Al-Khalili has done an admirable job of condensing the ideas of quantum physics from Max Planck to the possibilities of quantum computers into brisk, straightforward English' The Times

    By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

    - A unique exposition of the foundations of the quantum theory of black holes including the impact of string theory, the idea of black hole complementarily and the holographic principlebull; Aims to educate the physicist or student of physics who is not an expert on string theory, on the revolution that has grown out of black hole physics and string theory

    Afterlife is an abridged version of Heaven and Hell, with passages specially chosen to highlight the essence of Swedenborg's work.

    This is a presentation of the essential teaching of this direct path to freedom that focuses on the recognition and realization of the True Self. This book identifies the root cause of suffering as the identification with the mind and the belief that the psychological construct that is considered the "person" is actual. It is shown that this idea we have of who we are is an illusion that has been taken to be real and thus creates all forms of psychological suffering and confusion. The freedom from this illusion is shown to be available to anyone who is willing to recognize and realize the truth of who they are. This is a non-dual approach to psychological treatment that is becoming a new approach that has the potential to bring an end to all psychological disorders.

    His matrix theory is one of the bases of modern quantum mechanics, while his "uncertainty principle" has altered our whole philosophy of science.In this classic, based on lectures delivered at the University of Chicago, Heisenberg presents a complete physical picture of quantum theory. He covers not only his own contributions, but also those of Bohr, Dirac, Bose, de Broglie, Fermi, Einstein, Pauli, Schrodinger, Somerfield, Rupp, ·Wilson, Germer, and others in a text written for the physical scientist who is not a specialist in quantum theory or in modern mathematics.Partial contents: introduction (theory and experiment, fundamental concepts); critique of physical concepts of the corpuscular theory (uncertainty relations and their illustration); critique of the physical concepts of the wave theory (uncertainty relations for waves, discussion of an actual measurement of the electromagnetic field); statistical interpretation of quantum theory (mathematical considerations, interference of probabilities, Bohr's complementarity); discussion of important experiments (C. T. R. Wilson, diffraction , Einstein-Rupp, emission, absorption and dispersion of radiation, interference and conservation laws, Compton effect, radiation fluctuation phenomena, relativistic formulation of the quantum theory).An 80-page appendix on the mathematical apparatus of the quantum theory is provided for the specialist.