Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    In this direct and non-technical discussion of consciousness, Dr. Gerald M. Edelman draws on a lifetime of scientific inquiry into the workings of the brain to formulate answers to the mind-body questions that intrigue every thinking person.Concise and understandable, the book explains pertinent findings of modern neuroscience and describes how consciousness arises in complex brains. Edelman explores the relation of consciousness to causation, to evolution, to the development of the self, and to the origins of feelings, learning, and memory. His analysis of the brain activities underlying consciousness is based on recent remarkable advances in biochemistry, immunology, medical imaging, neuroscience, and evolutionary biology, yet the implications of his book extend farther—beyond the worlds of science and medicine into virtually every area of human inquiry.

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models—from linear regression to random walks and far beyond—that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.

    How can it be possible that the world we see is not objective reality? And how can our senses be useful if they are not communicating the truth? Hoffman grapples with these questions and more over the course of this eye-opening work.Ever since Homo sapiens has walked the earth, natural selection has favored perception that hides the truth and guides us toward useful action, shaping our senses to keep us alive and reproducing. We observe a speeding car and do not walk in front of it; we see mold growing on bread and do not eat it. These impressions, though, are not objective reality. Just like a file icon on a desktop screen is a useful symbol rather than a genuine representation of what a computer file looks like, the objects we see every day are merely icons, allowing us to navigate the world safely and with ease.The real-world implications for this discovery are huge. From examining why fashion designers create clothes that give the illusion of a more “attractive” body shape to studying how companies use color to elicit specific emotions in consumers, and even dismantling the very notion that spacetime is objective reality, The Case Against Reality dares us to question everything we thought we knew about the world we see.

    In addressing them, philosophers have made certain fundamental assumptions-that we can know our own minds by introspection, that most of our thinking about the world is literal, and that reason is disembodied and universal-that are now called into question by well-established results of cognitive science. It has been shown empirically that: Most thought is unconscious. We have no direct conscious access to the mechanisms of thought and language. Our ideas go by too quickly and at too deep a level for us to observe them in any simple way. Abstract concepts are mostly metaphorical. Much of the subject matter of philosophy, such as the nature of time, morality, causation, the mind, and the self, relies heavily on basic metaphors derived from bodily experience. What is literal in our reasoning about such concepts is minimal and conceptually impoverished. All the richness comes from metaphor. For instance, we have two mutually incompatible metaphors for time, both of which represent it as movement through space: in one it is a flow past us and in the other a spatial dimension we move along. Mind is embodied. Thought requires a body-not in the trivial sense that you need a physical brain to think with, but in the profound sense that the very structure of our thoughts comes from the nature of the body. Nearly all of our unconscious metaphors are based on common bodily experiences. Most of the central themes of the Western philosophical tradition are called into question by these findings. The Cartesian person, with a mind wholly separate from the body, does not exist. The Kantian person, capable of moral action according to the dictates of a universal reason, does not exist. The phenomenological person, capable of knowing his or her mind entirely through introspection alone, does not exist. The utilitarian person, the Chomskian person, the poststructuralist person, the computational person, and the person defined by analytic philosophy all do not exist. Then what does? Lakoff and Johnson show that a philosophy responsible to the science of mind offers radically new and detailed understandings of what a person is. After first describing the philosophical stance that must follow from taking cognitive science seriously, they re-examine the basic concepts of the mind, time, causation, morality, and the self: then they rethink a host of philosophical traditions, from the classical Greeks through Kantian morality through modern analytic philosophy. They reveal the metaphorical structure underlying each mode of thought and show how the metaphysics of each theory flows from its metaphors. Finally, they take on two major issues of twentieth-century philosophy: how we conceive rationality, and how we conceive language.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order. Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.

    Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.     But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.     Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.     An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

    The interviewees, ranging from major philosophers to renowned scientists, talk candidly with Blackmore about some of the key philosophical issues confronting us in a series of conversations that are revealing, insightful, and stimulating. They ruminate on the nature of consciousness (is it something apart from the brain?) and discuss if it is even possible to understand the human mind. Some of these thinkers say no, but most believe that we will pierce the mystery surrounding consciousness, and that neuroscience will provide the key. Blackmore goes beyond the issue of consciousness to ask other intriguing questions: Is there free will? (A question which yields many conflicted replies, with most saying yes and no.) If not, how does this effect the way you live your life; and more broadly, how has your work changed the way you live?Paired with an introduction and extensive glossary that provide helpful background information, these provocative conversations illuminate how some of the greatest minds tackle some of the most difficult questions about human nature.

    The author's objective is to offer an understanding of what leads to these moments, be it the excitement of the artist at the easel or the scientist in the lab, so that knowledge can be used to enrich people's lives. Drawing on 100 interviews with exceptional people, from biologists and physicists to politicians and business leaders, poets and artists, as well as his 30 years of research on the subject, Csikszentmihalyi uses his famous theory to explore the creative process. He discusses such ideas as why creative individuals are often seen as selfish and arrogant, and why the tortured genius is largely a myth. Most important, he clearly explains why creativity needs to be cultivated and is necessary for the future of our country, if not the world.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    They are vehicles, a series of hypothetical, self-operating machines that exhibit increasingly intricate if not always successful or civilized behavior. Each of the vehicles in the series incorporates the essential features of all the earlier models and along the way they come to embody aggression, love, logic, manifestations of foresight, concept formation, creative thinking, personality, and free will. In a section of extensive biological notes, Braitenberg locates many elements of his fantasy in current brain research.

    With this long-awaited revision, the authors continue to present the theory in a concise and straightforward manner, now with an eye out for the practical applications. They have revised this book to make it more accessible to today's students, including the addition of more material on writing proofs, more figures and pictures to convey ideas, side-boxes to highlight other interesting material, and a less formal writing style. Exercises at the end of each chapter, including some new, easier exercises, help readers confirm and enhance their understanding of the material. *NEW! Completely rewritten to be less formal, providing more accessibility to todays students. *NEW! Increased usage of figures and pictures to help convey ideas. *NEW! More detail and intuition provided for definitions and proofs. *NEW! Provides special side-boxes to present supplemental material that may be of interest to readers. *NEW! Includes more exercises, including many at a lower level. *NEW! Presents program-like notation for PDAs and Turing machines. *NEW! Increas