Euclid in living color   Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th century mathematician Oliver Byrne employed the color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid's Elements. The author makes it clear in his subtitle that this is a didactic measure intended to distinguish his edition from all others: “The Elements of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of learners.” As Surveyor of Her Majesty’s Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works previous to 1847, but never anything like his edition on Euclid. This remarkable example of Victorian printing has been described as one of the oddest and most beautiful books of the 19th century. Each proposition is set in Caslon italic, with a four-line initial, while the rest of the page is a unique riot of red, yellow, and blue. On some pages, letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different color plates for printing. Elsewhere, solid squares, triangles, and circles are printed in bright colors, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse, and Derain.

    Many of the difficulties however, are not in the classroom... In The (Un)official Teacher's Manual, Omar Akbar offers direct, humorous and accessible advice on how to deal with the daily issues faced by a teacher- none of which involve teaching! Includes guidance on: lesson observations, emails, promotions, avoiding meaningless extra work, meetings, parents, maintaining a work-life balance, dealing with workplace bullying, and much more. While Omar pulls no punches on the reality of working in a school, a positive streak is maintained throughout. A must read for any teacher or potential teacher. - - - - - - - - - - - - - - Contents: Introduction: Why This Book Was Written 1. How to Get the Most from Observations, Learning Walks, and Book Scrutinies 2. The Don’ts of the School Email System 3. How to Get Promoted and Other Things to Consider 4. How and When to Say No and Yes 5. The Dos and Don’ts of Meetings 6. How to Get Parents on Your Side 7. Guidance for Trainee Teachers 8. Ensuring a Life-Work Balance 9. Bullying: the Problem and the Solution 10. How to Get the Teaching Job You Want 11. Maintaining Good Relationships 12. Why It’s All Worth It

    It describes how the laws and discoveries of information theory now support controversial revisions to Darwinian evolution, begin to unravel the mysteries of language, memory and dreams, and stimulate provocative ideas in psychology, philosophy, art, music, computers and even the structure of society. Perhaps its most fascinating and unexpected surprise is the suggestion the order and complexity may be as natural as disorder and disorganization. Contrary to the entropy principle, which implies that order is the exception and confusion the rule, information theory asserts that order and sense can indeed prevail against disorder and nonsense. From the simplest forms of organic life to the words used to express our most complex ideas, from our genes to our dreams, from microcomputers to telecommunications, virtually everything around us follows simple rules of information. Life and the material world, like language, remain "grammatical." Grammatical man inhabits a grammatical universe.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    From the Difference Engine to magic squares and from the Fibonacci rabbits to Fermat's Last Theorem, this book features the weird world of numbers, imaginary, real or infinite.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    And human beings are gifted with an almost unlimited potential for learning and creativity. Now you can uncover your own hidden abilities, sharpen your senses, and liberate your unique intelligence—by following the example of the greatest genius of all time, Leonardo da Vinci.Acclaimed author Michael J. Gelb, who has helped thousands of people expand their minds to accomplish more than they ever thought possible, shows you how. Drawing on Da Vinci's notebooks, inventions, and legendary works of art, Gelb introduces Seven Da Vincian Principles—the essential elements of genius—from curiosità, the insatiably curious approach to life to connessione, the appreciation for the interconnectedness of all things. With Da Vinci as your inspiration, you will discover an exhilarating new way of thinking. And step-by-step, through exercises and provocative lessons, you will harness the power—and awesome wonder—of your own genius, mastering such life-changing abilities as: •Problem solving •Creative thinking •Self-expression •Enjoying the world around you •Goal setting and life balance •Harmonizing body and mindDrawing on Da Vinci's notebooks, inventions, and legendary works of art, acclaimed author Michael J. Gelb, introduces seven Da Vincian principles, the essential elements of genius, from curiosita, the insatiably curious approach to life, to connessione, the appreciation for the interconnectedness of all things. With Da Vinci as their inspiration, readers will discover an exhilarating new way of thinking. Step-by-step, through exercises and provocative lessons, anyone can harness the power and awesome wonder of their own genius, mastering such life-changing skills as problem solving, creative thinking, self-expression, goal setting and life balance, and harmonizing body and mind.

    This book reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

    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.

    We are addicted to prediction, desperate for certainty about the future. But the complexity of modern life won’t provide that; experts in forecasting are reluctant to look more than 400 days out. History doesn’t repeat itself and even genetics won’t tell you everything you want to know. Ineradicable uncertainty is now a fact of life. In complex environments, efficiency is a hazard not a help; being robust is the better, safer option. Drawing on a wide array of people and places, Margaret Heffernan looks at long-term projects developed over generations that could never have been planned the way that they have been run. Experiments, led by individuals and nations, discover new possibilities and options. Radical exercises in forging new futures with wildly diverse participants allow everyone to create outcomes together that none could do alone. Existential crises reveal the vital social component in resilience. Death is certain, but how we approach it impacts the future of those we leave behind. And preparedness – doing everything today that you might need for tomorrow – provides the antidote to passivity and prediction. Ranging freely through history and from business to science, government to friendships, this refreshing book challenges us to resist the false promises of technology and efficiency and instead to mine our own creativity and humanity for the capacity to create the futures we want and can believe in.

    Yet they remain among the most mysterious of concepts. Is space an entity? Why does time have a direction? Could the universe exist without space and time? Can we travel to the past? Greene has set himself a daunting task: to explain non-intuitive, mathematical concepts like String Theory, the Heisenberg Uncertainty Principle, and Inflationary Cosmology with analogies drawn from common experience. From Newton’s unchanging realm in which space and time are absolute, to Einstein’s fluid conception of spacetime, to quantum mechanics’ entangled arena where vastly distant objects can instantaneously coordinate their behavior, Greene takes us all, regardless of our scientific backgrounds, on an irresistible and revelatory journey to the new layers of reality that modern physics has discovered lying just beneath the surface of our everyday world.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.