From the acclaimed author of A Tour of the Calculus and The Advent of the Algorithm, here is a riveting look at mathematics that reveals a hidden world in some of its most fundamental concepts. In his latest foray into mathematics, David Berlinski takes on the simplest questions that can be asked: What is a number? How do addition, subtraction, multiplication, and division actually work? What are geometry and logic? As he delves into these subjects, he discovers and lucidly describes the beauty and complexity behind their seemingly simple exteriors, making clear how and why these mercurial, often slippery concepts are essential to who we are. Filled with illuminating historical anecdotes and asides on some of the most fascinating mathematicians through the ages, One, Two, Three is a captivating exploration of the foundation of mathematics: how it originated, who thought of it, and why it matters.
The Caliph’s Splendor is a revelation: a history of a civilization we barely know that had a profound effect on our own culture. While the West declined following the collapse of the Roman Empire, a new Arab civilization arose to the east, reaching an early peak in Baghdad under the caliph Harun al-Rashid. Harun is the legendary caliph of The Thousand and One Nights, but his actual court was nearly as magnificent as the fictional one. In The Caliph’s Splendor, Benson Bobrick eloquently tells the little-known and remarkable story of Harun’s rise to power and his rivalries with the neighboring Byzantines and the new Frankish kingdom under the leadership of Charlemagne. When Harun came to power, Islam stretched from the Atlantic to India. The Islamic empire was the mightiest on earth and the largest ever seen. Although Islam spread largely through war, its cultural achievements were immense. Harun’s court at Baghdad outshone the independent Islamic emirate in Spain and all the courts of Europe, for that matter. In Baghdad, great works from Greece and Rome were preserved and studied, and new learning enhanced civilization. Over the following centuries Arab and Persian civilizations made a lasting impact on the West in astronomy, geometry, algebra (an Arabic word), medicine, and chemistry, among other fields of science. The alchemy (another Arabic word) of the Middle Ages originated with the Arabs. From engineering to jewelry to fashion to weaponry, Arab influences would shape life in the West, as they did in the fields of law, music, and literature. But for centuries Arabs and Byzantines contended fiercely on land and sea. Bobrick tells how Harun defeated attempts by the Byzantines to advance into Asia at his expense. He contemplated an alliance with the much weaker Charlemagne in order to contain the Byzantines, and in time Arabs and Byzantines reached an accommodation that permitted both to prosper. Harun’s caliphate would weaken from within as his two sons quarreled and formed factions; eventually Arabs would give way to Turks in the Islamic empire. Empires rise, weaken, and fall, but during its golden age, the caliphate of Baghdad made a permanent contribution to civilization, as Benson Bobrick so splendidly reminds us.
Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic -- and the mathematical statements he and others built from it -- have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world.
In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure. Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt. The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.
Alchemy is an idea based on superstition and philosophical global traditions spanning hundreds of years. Alchemists made medicines and pharmaceuticals from the earths materials and purified objects through philosophy, magic, and spirituality. Chemistry is based on the material principles of mixed bodies, and spans all natural or physical sciences in its practices. This book on alchemy and chemistry shows the scientific method at work and proves and disproves the subjects at hand. It explores a branch of modern science or a major scientific milestone, comparing and contrasting it with an older idea that has been proved wrong or fails to meet the strict and studied standards of science.
Written by a noted expert on and popular advocate of intelligent design, this book explores more than 60 of the toughest questions asked by experts and non-experts.
What can the starry skies tell you about yourself and others? More than you might imagine. For over four thousand years, people have watched the skies, correlating the movements of the Sun, the Moon, and the planets with human affairs. Astrology for Dummies shows the reader how to use that accumulated wisdom to identify strengths and weaknesses, discover creative abilities, understand relationships, and make the most of the times in which we live. Using an abundance of real-life examples, author Rae Orion offers an incisive account of each sign and planet, taking the reader far beyond the daily horoscope and illuminating the birth chart in all its individuality and complexity. Astrology for Dummies examines the time-honored ways astrology helps us understand ourselves and others. From how to map and interpret individual horoscopes to building and reading birth charts, Astrology For Dummies provides you with the tools to apply the art of astrology to your everyday life. Explore the long, multi-cultural, occasionally bloody history of astrology Discover useful advice about romance, career, and wellness Find the creative potential to be found in every sign and every birth chart Unravel the mysteries behind Mercury retrograde and other celestial phenomena Delve into the horoscopes of dozens of famous (and infamous) people, both past and present Investigate different ways to align yourself with the cosmos. Astrology hasn’t been around for millennia for nothing. It’s a practical tool, a symbolic language, a way to expand awareness, a means to increase empathy, and an exploration that touches the soul. Whether you want to learn about yourself, understand others, or glimpse the opportunities and challenges that lie ahead, the answers are here — and in the stars!
A beautiful book which for the first time explores the relationship between the cycles of Venus and Mars and their impact on our lives. Using many case histories the author shows how, although synastry is important, possibly of greater importance is the aspect between the two planets within their cycles because that can dictate the timing of key moments in a relationship. She shows how the degree of the original conjunction between the two planets ('the degree of passion'), based on the time of birth can indicate the kind of the people we are attracted to and the course a romance can follow. A really absorbing book which will prompt hours of research