Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

     Alife-changing twelve-week program, The Artist's Way has touched the lives of millions of people around the world. Now, for the first time, fans will have this elegantly designed and user-friendly volume for use in tandem with the book. The Artist's Way Workbook includes: - more than 110 Artist's Way tasks; - more than 50 Artist's Way check-ins; - a fascinating introduction to the workbook in which Cameron shares new insights into the creative process that she has culled in the decade since The Artist's Way was originally published; - new and original writings on Morning Page Journaling and the Artist's Date-two of the most vital tools set forth by Cameron in The Artist's Way. The Artist's Way Workbook is an indispensable book for anyone following the spiritual path to higher creativity laid out in The Artist's Way.

    As sociologist and network science pioneer Duncan Watts explains in this provocative book, the explanations that we give for the outcomes that we observe in life—explanation that seem obvious once we know the answer—are less useful than they seem.Drawing on the latest scientific research, along with a wealth of historical and contemporary examples, Watts shows how common sense reasoning and history conspire to mislead us into believing that we understand more about the world of human behavior than we do; and in turn, why attempts to predict, manage, or manipulate social and economic systems so often go awry.It seems obvious, for example, that people respond to incentives; yet policy makers and managers alike frequently fail to anticipate how people will respond to the incentives they create. Social trends often seem to have been driven by certain influential people; yet marketers have been unable to identify these “influencers” in advance. And although successful products or companies always seem in retrospect to have succeeded because of their unique qualities, predicting the qualities of the next hit product or hot company is notoriously difficult even for experienced professionals.Only by understanding how and when common sense fails, Watts argues, can we improve how we plan for the future, as well as understand the present—an argument that has important implications in politics, business, and marketing, as well as in science and everyday life.

    But is it for the better? Amid a chorus of doomsayers, Clive Thompson delivers a resounding "yes." The Internet age has produced a radical new style of human intelligence, worthy of both celebration and analysis. We learn more and retain it longer, write and think with global audiences, and even gain an ESP-like awareness of the world around us. Modern technology is making us smarter, better connected, and often deeper—both as individuals and as a society. In Smarter Than You Think Thompson shows that every technological innovation—from the written word to the printing press to the telegraph—has provoked the very same anxieties that plague us today. We panic that life will never be the same, that our attentions are eroding, that culture is being trivialized. But as in the past, we adapt—learning to use the new and retaining what’s good of the old. Thompson introduces us to a cast of extraordinary characters who augment their minds in inventive ways. There's the seventy-six-year old millionaire who digitally records his every waking moment—giving him instant recall of the events and ideas of his life, even going back decades. There's a group of courageous Chinese students who mounted an online movement that shut down a $1.6 billion toxic copper plant. There are experts and there are amateurs, including a global set of gamers who took a puzzle that had baffled HIV scientists for a decade—and solved it collaboratively in only one month. Smarter Than You Think isn't just about pioneers. It's about everyday users of technology and how our digital tools—from Google to Twitter to Facebook and smartphones—are giving us new ways to learn, talk, and share our ideas. Thompson harnesses the latest discoveries in social science to explore how digital technology taps into our long-standing habits of mind—pushing them in powerful new directions. Our thinking will continue to evolve as newer tools enter our lives. Smarter Than You Think embraces and extols this transformation, presenting an exciting vision of the present and the future.

    They employ what psychologists call "lateral thinking: to rethink convention and break "rules" that aren't rules.These are not shortcuts, which produce often dubious short-term gains, but ethical "smartcuts" that eliminate unnecessary effort and yield sustainable momentum. In Smartcuts, Snow shatters common wisdom about success, revealing how conventions like "paying dues" prevent progress, why kids shouldn't learn times tables, and how, paradoxically, it's easier to build a huge business than a small one.From SpaceX to The Cuban Revolution, from Ferrari to Skrillex, Smartcuts is a narrative adventure that busts old myths about success and shows how innovators and icons do the incredible by working smarter—and how perhaps the rest of us can, too.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    This easy to follow, step-by step guide to developing reasoning skills even applies the techniques to tasks such as reading, note-taking, and writing.

    Cahn's advice on the professorial life covers an extensive range of critical issues: how to plan, complete, and defend a dissertation; how to navigate a job interview; how to improve teaching performance; how to prepare and publish research; how to develop a professional network; and how to garner support for tenure. He deals with such hurdles as a difficult dissertation advisor, problematic colleagues, and the pressures of the tenure clock. Whether you are beginning graduate study, hoping to secure an academic position, or striving to build a professorial career, Cahn's insights are invaluable to traversing the thickets of academia.

    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.

    Today there is just one. Us. Homo sapiens. How did our species succeed in the battle for dominance? Why did our foraging ancestors come together to create cities and kingdoms? How did we come to believe in gods, nations and human rights; to trust money, books and laws; and to be enslaved by bureaucracy, timetables and consumerism? And what will our world be like in the millennia to come? In Sapiens, Dr Yuval Noah Harari spans the whole of human history, from the very first humans to walk the earth to the radical – and sometimes devastating – breakthroughs of the Cognitive, Agricultural and Scientific Revolutions. Drawing on insights from biology, anthropology, paleontology and economics, he explores how the currents of history have shaped our human societies, the animals and plants around us, and even our personalities. Have we become happier as history has unfolded? Can we ever free our behaviour from the heritage of our ancestors? And what, if anything, can we do to influence the course of the centuries to come? Bold, wide-ranging and provocative, Sapiens challenges everything we thought we knew about being human: our thoughts, our actions, our power ... and our future.

    On both economic and psychological grounds, author Matthew B. Crawford questions the educational imperative of turning everyone into a "knowledge worker," based on a misguided separation of thinking from doing. Using his own experience as an electrician and mechanic, Crawford presents a wonderfully articulated call for self-reliance and a moving reflection on how we can live concretely in an ever more abstract world.

    Ratey, MD.Did you know you can beat stress, lift your mood, fight memory loss, sharpen your intellect, and function better than ever simply by elevating your heart rate and breaking a sweat? The evidence is incontrovertible: Aerobic exercise physically remodels our brains for peak performance. In SPARK, John J. Ratey, M.D., embarks upon a fascinating and entertaining journey through the mind-body connection, presenting startling research to prove that exercise is truly our best defense against everything from depression to ADD to addiction to aggression to menopause to Alzheimer's. Filled with amazing case studies (such as the revolutionary fitness program in Naperville, Illinois, which has put this school district of 19,000 kids first in the world of science test scores), SPARK is the first book to explore comprehensively the connection between exercise and the brain. It will change forever the way you think about your morning run---or, for that matter, simply the way you think

    In today's volatile job market, ideas are more important than training, innovation is more important than credentials; traditional schooling may no longer be necessary or even useful. The ability to educate oneself 'to learn how to learn' is crucial. In Secrets of a Buccaneer-Scholar James Bach demonstrates how to nurture one's natural curiosities and passions through the whimsical learning process he calls 'buccaneering' demonstrating that those who understand this fundamental principle will come to dominate this new world.

    This witty and informative guide demystifies the ancient Enneagram system with cartoons, exercises, and personality tests that reveal our motivations and desires and show how to put that knowledge to use in our everyday lives.The 9 Types of People:The Perfectionist: Motivated by the need to live life the right way, improve oneself and others, and avoid anger.The Helper: Motivated by the need to be loved and appreciated and to express your positive feelings towards others.The Achiever: Motivated by the need to be productive, to achieve success, and to avoid failure.The Romantic: Motivated by the need to understand your feelings and to be understood to search for the meaning of life, and to avoid being ordinary.The Observer: Motivated by the need to know everything and understand the universe, to be self-sufficient and left alone, and to avoid not having the answer or looking foolish.The Questioner: Motivated by the need for security, to feel taken care of, or to confront your fears.The Adventurer: Motivated by the need to be happy and plan fun things, to contribute to the world, and to avoid suffering and pain.The Asserter: Motivated by the need to be self-reliant and strong, to make an impact on the world, and to avoid being weak.The Peacemaker: Motivated by the need to keep the peace, merge with others, and avoid conflict.

    If you want to understand this central quality of human nature to its roots, read Why We Love." —Edward O. WilsonIn Why We Love, renowned anthropologist Helen Fisher offers a new map of the phenomenon of love—from its origins in the brain to the thrilling havoc it creates in our bodies and behavior. Working with a team of scientists to scan the brains of people who had just fallen madly in love, Fisher proved what psychologists had until recently only suspected: when you fall in love, specific areas of the brain "light up" with increased blood flow. This sweeping new book uses this data to argue that romantic passion is hardwired into our brains by millions of years of evolution. It is not an emotion; it is a drive as powerful as hunger.Provocative, enlightening, engaging, and persuasive, Why We Love offers radical new answers to age-old questions: what love is, who we love—and how to keep love alive.