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.

    The 10,000 Year Explosion: How Civilization Accelerated Human Evolution

    Inspired by her own feline's instinct to hunt and supported by her studies abroad, Thomas examines the life actions, as well as the similarities and differences of these majestic creatures. Lions, tigers, pumas and housecats: Her observations shed light on their social lives, thought processes, eating habits, and communication techniques, and reveal how they survive and coexist with each other and with humans.

    Beginning at Stonehenge and ending with the current crisis in String Theory, the story of this eternal question to uncover the mysteries of the universe describes a narrative that includes some of the greatest discoveries of all time and leading personalities, including Aristotle, Copernicus, and Isaac Newton, and the rise to the modern era of Einstein, Eddington, and Hawking.

    Of these, gravity may the most obvious, but it is also the most mysterious. Newton managed to predict the force of gravity but couldn't explain how it worked at a distance. Einstein picked up on the simple premise that gravity and acceleration are interchangeable to devise his mind-bending general relativity, showing how matter warps space and time. Not only did this explain how gravity worked – and how apparently simple gravitation has four separate components – but it predicted everything from black holes to gravity's effect on time. Whether it's the reality of anti-gravity or the unexpected discovery that a ball and a laser beam drop at the same rate, gravity is the force that fascinates.

    As the forerunner of such important books as Annie Dillard's Pilgrim at Tinker Creek, Edward Abbey's Desert Solitaire, and Robert Finch's The Primal Place, this classic work remains as relevant today as it was sixty-five years ago.

    The effects of homeopathy don’t go away under rigorous scientific conditions. The laws of nature aren’t what they used to be. Thirty years on, no one has an explanation for a seemingly intelligent signal received from outer space. The US Department of Energy is re-examining cold fusion because the experimental evidence seems too solid to ignore. The placebo effect is put to work in medicine while doctors can’t agree whether it even exists.In an age when science is supposed to be king, scientists are beset by experimental results they simply can’t explain. But, if the past is anything to go by, these anomalies contain the seeds of future revolutions. While taking readers on an entertaining tour d’horizon of the strangest of scientific findings – involving everything from our lack of free will to Martian methane that offers new evidence of life on the planet – Michael Brooks argues that the things we don’t understand are the key to what we are about to discover.This mind-boggling but entirely accessible survey of the outer limits of human knowledge is based on a short article by Michael Brooks for New Scientist magazine. It became the sixth most circulated story on the internet in 2005, and provoked widespread comment and compliments (Google “13 things that do not make sense” to see).Michael Brooks has now dug deeply into those mysteries, with extraordinary results.

    In the insightful How Music Works, Byrne offers his unique perspective on music - including how music is shaped by time, how recording technologies transform the listening experience, the evolution of the industry, and much more.

    The Dream of Enlightenment tells their story and that of the birth of modern philosophy. What does the advance of science entail for our understanding of ourselves and for our ideas of God? How should a government deal with religious diversity - and what is government actually for? Their questions remain our questions, and it is tempting to think these philosophers speak our language and live in our world; but to understand them properly, we must step back into their shoes. Gottlieb puts readers in the minds of these frequently misinterpreted figures, elucidating the history of their times while engagingly explaining their arguments and assessing their legacy. Gottlieb creates a sweeping account of what they amounted to, and why we are still in their debt.

    From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Here we go again with real life and opinions made to look like one big, preposterous animal not unlike an invention by Dr. Seuss...--Kurt Vonnegut, from Fates Worse Than Death

    It far surpasses any previous explanation of Relativity for laypersons.

    This book gives details of their research and investigations into the use of psychedelic drugs for the study of the human mind, and is also a love story. The second half of the book describes in detail a wealth of phenethlyamines, their physical properties, dosages used, duration of effects observed, and commentary on effects.

    Kelly's photos prove that this perspective--from 250 miles above Earth-- while hard-won, is also almost unspeakably beautiful. A gift for photography helped make Kelly a social media sensation, and here his photos are collected alongside his own commentary, which set the images in their proper contexts, human and cosmic.Kelly captures sunsets, moonrises, the aurora borealis, and the luminous, hazy tapestry of the Milky Way. He presents snapshots of life and work on the International Space Station, from spacewalks to selfies. But above all--or floating amidst all--he takes the earth itself as his celestial muse. Here are hurricanes, wrinkled mountains, New York City shining like a galaxy--glorious photographs that are, in themselves, a passionate argument for the preservation of our planet in the face of climate change and environmental destruction.