More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Although the laws of physics create a powerful impression that time is flowing, in fact there are only timeless `nows'. In The End of Time, the British theoretical physicist Julian Barbour describes the coming revolution in our understanding of the world: a quantum theory of the universe that brings together Einstein's general theory of relativity - which denies the existence of a unique time - and quantum mechanics - which demands one. Barbour believes that only the most radical of ideas can resolve the conflict between these two theories: that there is, quite literally, no time at all. The End of Time is the first full-length account of the crisis in our understanding that has enveloped quantum cosmology. Unifying thinking that has never been brought together before in a book for the general reader, Barbour reveals the true architecture of the universe and demonstrates how physics is coming up sharp against the extraordinary possibility that the sense of time passing emerges from a universe that is timeless. The heart of the book is the author's lucid description of how a world of stillness can appear to be teeming with motion: in this timeless world where all possible instants coexist, complex mathematical rules of quantum mechanics bind together a special selection of these instants in a coherent order that consciousness perceives as the flow of time. Finally, in a lucid and eloquent epilogue, the author speculates on the philosophical implications of his theory: Does free will exist? Is time travel possible? How did the universe begin? Where is heaven? Does the denial of time make life meaningless? Written with exceptional clarity and elegance, this profound and original work presents a dazzlingly powerful argument that all will be able to follow, but no-one with an interest in the workings of the universe will be able to ignore.

    It is also, fortunately, not a matter of luck. There are many things to understand about how children’s minds operate and what they need from those who look after them so they can develop into the best version of themselves.The Good Enough Parent is a compendium of lessons, including ideas on how to say 'no' to a child one adores, how to look beneath the surface of 'bad' behaviour to work out what might really be going on, how to encourage a child to be genuinely kind, how to encourage open self expression, and how to handle the moods and gloom of adolescence.Importantly, this is a book that knows that perfection is not required – and could indeed be unhelpful, because a key job of any parent is to induct a child gently into the imperfect nature of everything. Written in a tone that is encouraging, wry and soaked in years of experience, The Good Enough Parent is an intelligent guide to raising a child who will one day look back on their childhood with just the right mixture of gratitude, humour and love.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    Real rationality, of the sort studied by psychologists, social scientists, and mathematicians. The kind of rationality where you make good decisions, even when it's hard; where you reason well, even in the face of massive uncertainty; where you recognize and make full use of your fuzzy intuitions and emotions, rather than trying to discard them. In "Rationality: From AI to Zombies," Eliezer Yudkowsky explains the science underlying human irrationality with a mix of fables, argumentative essays, and personal vignettes. These eye-opening accounts of how the mind works (and how, all too often, it doesn't!) are then put to the test through some genuinely difficult puzzles: computer scientists' debates about the future of artificial intelligence (AI), physicists' debates about the relationship between the quantum and classical worlds, philosophers' debates about the metaphysics of zombies and the nature of morality, and many more. In the process, "Rationality: From AI to Zombies" delves into the human significance of correct reasoning more deeply than you'll find in any conventional textbook on cognitive science or philosophy of mind. A decision theorist and researcher at the Machine Intelligence Research Institute, Yudkowsky published earlier drafts of his writings to the websites Overcoming Bias and Less Wrong. "Rationality: From AI to Zombies" compiles six volumes of Yudkowsky's essays into a single electronic tome. Collectively, these sequences of linked essays serve as a rich and lively introduction to the science—and the art—of human rationality.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    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

    . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald TribuneOne of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader.He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system.In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations.Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature

    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.

    By spinning 28 mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human.

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

    Burger teaches at Wiliams College; Starbird at The University of Texas at Austin. Here, they “reveal the hidden powers of deep understanding (earth), failure (fire), questions (air), the flow of ideas (water), and the quintessential element of change that brings all four elements together. By mastering and applying these practical and proven strategies, readers develop better thinking habits and learn how to create their own successes.”Brilliant people aren't a special breed--they just use their minds differently. By using the straightforward and thought-provoking techniques in "The 5 Elements of Effective Thinking," you will regularly find imaginative solutions to difficult challenges, and you will discover new ways of looking at your world and yourself--revealing previously hidden opportunities.The book offers real-life stories, explicit action items, and concrete methods that allow you to attain a deeper understanding of any issue, exploit the power of failure as a step toward success, develop a habit of creating probing questions, see the world of ideas as an ever-flowing stream of thought, and embrace the uplifting reality that we are all capable of change. No matter who you are, the practical mind-sets introduced in the book will empower you to realize any goal in a more creative, intelligent, and effective manner. Filled with engaging examples that unlock truths about thinking in every walk of life, "The 5 Elements of Effective Thinking" is written for all who want to reach their fullest potential--including students, parents, teachers, businesspeople, professionals, athletes, artists, leaders, and lifelong learners.Whenever you are stuck, need a new idea, or want to learn and grow, "The 5 Elements of Effective Thinking" will inspire and guide you on your way.

    With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of "Logical Dilemmas: The Life and Work of Kurt G del