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.

    Examples of analytical techniques are drawn from such areas as life sciences, clinical chemistry, air and water pollution, and industrial analyses. New to this edition: Excel spreadsheets on CD-ROM * New chapters on good laboratory practice, as well as genomics and proteomics * A more modern flavor.

    The key feature of this classic title is the section of star charts that are cherished by backyard astronomers everywhere. Each new edition has outsold the previous one because of thorough revisions and additional new material.NightWatch has been acclaimed as the best general interest introduction to astronomy. The fourth edition has improvements over the 3rd edition in every chapter, including:The famous charts, ideal for stargazers using a small telescope or binoculars A complete update of the equipment section, including computerized telescopes An enlarged photography section, including how-to instructions for using the new generation of digital cameras for astronomical photography, both with and without a telescope The tables of future solar and lunar eclipses, planetary conjunctions and planet locations, updated through 2025. This edition includes star charts for use in the southern hemisphere. There are also dozens of new photographs throughout the book that show the latest thrilling discoveries made by current space observatories and probes.

    In this book you will find some shocking details of the great figures of science such as Newton, Galileo, Kepler, Copernicus and Kant, presented with the characteristic humor that only a popularizer of science as Sergio de Regules could bring to this wonderful collection of essays.

    As huge as the Pantheon of Rome and as heavy as the Statue of Liberty, this magnificent instrument is so precisely built that its seventeen-foot mirror was hand-polished to a tolerance of 2/1,000,000 of an inch. The telescope's construction drove some to the brink of madness, made others fearful that mortals might glimpse heaven, and transfixed an entire nation. Ronald Florence weaves into his account of the creation of "the perfect machine" a stirring chronicle of the birth of Big Science and a poignant rendering of an America mired in the depression yet reaching for the stars.

    Anthony Brandt and David Eagleman rifle through the inventions of human society like paleontologists ransacking the fossil record. Exploring examples from Apollo 13 to Pablo Picasso, they seek to answer the question: what lies at the heart of humanity's ability--and drive--to create? If you took a snapshot of any animal species' behavior, from apes to barnacles, and contrasted it with the same species 10,000 years ago, they'd all be carrying on pretty much as usual (and if they aren't, it's likely due to human influence). Humanity, on the other hand, would be nearly unrecognizable. Above all else, our drive to create is what makes us unique among all living things. Yet where does this all creation, innovation, and change come from? Why us? And if we better understand this -cognitive software-, can we harness it more responsibly to improve our lives, schools, businesses and institutions? Brandt and Eagleman examine hundreds of examples of human creativity through dramatic storytelling and stunning images in this beautiful, full-color volume. By drawing out what creative acts have in common and viewing them through the lens of cutting-edge neuroscience, they uncover the essential elements of this critical human ability, and encourage a more creative future for all of us.

    Includes expert coverage of new topics: Turbocodes, Turboequalization, Antenna Arrays, Digital Cellular Systems, and Iterative Detection. Convenient, sequential organization begins with a look at the historyo and classification of channel models and builds from there.

    In late 2017, scientists at a Hawaiian observatory glimpsed an object soaring through our inner solar system, moving so quickly that it could only have come from another star. Avi Loeb, Harvard’s top astronomer, showed it was not an asteroid; it was moving too fast along a strange orbit, and left no trail of gas or debris in its wake. There was only one conceivable explanation: the object was a piece of advanced technology created by a distant alien civilization.   In Extraterrestrial, Loeb takes readers inside the thrilling story of the first interstellar visitor to be spotted in our solar system. He outlines his controversial theory and its profound implications: for science, for religion, and for the future of our species and our planet. A mind-bending journey through the furthest reaches of science, space-time, and the human imagination, Extraterrestrial challenges readers to aim for the stars—and to think critically about what’s out there, no matter how strange it seems.

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

    For the alternate cover edition by Simon & Schuster, see hereClear and concise explanations of the development of theories explaining physical phenomena.

    Climate change is only the most visible of the modifications we've made—up until this point, inadvertently—to the planet. And our current behavior threatens not only our own future but that of countless other creatures. By comparing Earth's story to those of other planets, astrobiologist David Grinspoon shows what a strange and novel development it is for a species to evolve to build machines, and ultimately, global societies with world-shaping influence.Without minimizing the challenges of the next century, Grinspoon suggests that our present moment is not only one of peril, but also great potential, especially when viewed from a 10,000-year perspective. Our species has surmounted the threat of extinction before, thanks to our innate ingenuity and ability to adapt, and there's every reason to believe we can do so again.Our challenge now is to awaken to our role as a force of planetary change, and to grow into this task. We must become graceful planetary engineers, conscious shapers of our environment and caretakers of Earth's biosphere. This is a perspective that begs us to ask not just what future do we want to avoid, but what do we seek to build? What kind of world do we want? Are humans the worst thing or the best thing to ever happen to our planet? Today we stand at a pivotal juncture, and the answer will depend on the choices we make.

    He also looks at philosophical issues in particular sciences, including the problem of classification in biology, and the nature of space and time in physics. The final chapter touches on the conflicts between science and religion, and explores whether science is ultimately a good thing.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 hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    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.

    Inside, he finds the first exact solution to the equations of general relativity, unaware that it contains a monster that could destroy his life's work.The great mathematician Alexander Grothendieck tunnels so deeply into abstraction that he tries to cut all ties with the world, terrified of the horror his discoveries might cause.Erwin Schrödinger and Werner Heisenberg battle over the soul of physics after creating two equivalent yet opposed versions of quantum mechanics. Their fight will tear the very fabric of reality, revealing a world stranger than they could have ever imagined.Using extraordinary, epoch-defining moments from the history of science, Benjamín Labatut plunges us into exhilarating territory between fact and fiction, progress and destruction, genius and madness.

    This is a book about how many of the 'big' philosophical and religious questions that have puzzled mankind for centuries can be answered by recent breakthroughs in science.