Taming The Unknown

What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.

A wide-ranging history of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age: How do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz’s calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole’s nineteenth-century logic system; and the early programming language ALGOL, short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. Machine learning, in its increasing dependence on words, erodes the line between technical and everyday language, revealing the urgent stakes underlying this boundary. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.

In 1802 a Frenchman and an Englishman famously encountered each other off the shores of South Australia. The voyages of discovery of Nicolas Baudin and Matthew Flinders opened the way for the increasingly rapid colonisation of 'Terra Australis'.

In this comprehensive study, Kenneth Morgan provides an authoritative account of European exploration and discovery in Australia. The book presents a detailed chronological overview of European interests in the Australian continent, from initial speculations about the 'Great Southern Land' to the major hydrographic expeditions of the 19th century. In particular, he analyses the early crossings of the Dutch in the 17th century, the exploits of English 'buccaneer adventurer' William Dampier, the famous voyages of James Cook and Matthew Flinders, and the little-known French annexation of Australia in 1772. Introducing new findings and drawing on the latest in historiographical research, this book situates developments in navigation, nautical astronomy and cartography within the broader contexts of imperial, colonial, and maritime history.

This groundbreaking book reconceptualizes slavery through the voices of enslaved persons themselves, voices that have remained silent in the narratives of conventional history. Focusing in particular on the Islamic Middle East from the late eighteenth to the early twentieth century, Ehud R. Toledano examines how bonded persons experienced enslavement in Ottoman societies. He draws on court records and a variety of other unexamined primary sources to uncover important new information about the Africans and Circassians who were forcibly removed from their own societies and transplanted to Middle East cultures that were alien to them. Toledano also considers the experiences of these enslaved people within the context of the global history of slavery. The book looks at the bonds of slavery from an original perspective, moving away from the traditional master/slave domination paradigm toward the point of view of the enslaved and their responses to their plight. With keen and original insights, Toledano suggests new ways of thinking about enslavement.

Reveals the mass mobilization tactics that helped free Soviet Jews and reshaped the Jewish American experience from the Johnson era through the Reagan–Bush years What do these things have in common? Ingrid Bergman, Passover matzoh, Banana Republic®, the fitness craze, the Philadelphia Flyers, B-grade spy movies, and ten thousand Bar and Bat Mitzvah sermons? Nothing, except that social movement activists enlisted them all into the most effective human rights campaign of the Cold War. The plight of Jews in the USSR was marked by systemic antisemitism, a problem largely ignored by Western policymakers trying to improve relations with the Soviets. In the face of governmental apathy, activists in the United States hatched a bold plan: unite Jewish Americans to demand that Washington exert pressure on Moscow for change. A Cold War Exodus delves into the gripping narrative of how these men and women, through ingenuity and determination, devised mass mobilization tactics during a three-decade-long campaign to liberate Soviet Jews—an endeavor that would ultimately lead to one of the most significant mass emigrations in Jewish history. Drawing from a wealth of archival sources including the travelogues of thousands of American tourists who smuggled aid to Russian Jews, Shaul Kelner offers a compelling tale of activism and its profound impact, revealing how a seemingly disparate array of elements could be woven together to forge a movement and achieve the seemingly impossible. It is a testament to the power of unity, creativity, and the unwavering dedication of those who believe in the cause of human rights.

Fascinating, accessible study recounts the process of discovery, from atomism of the Greeks to quantum revolutions of the 1920s and the theories and conjectures of today. Topics include components of the atom, quantum mechanics, atomic landscape, atoms in isolation, more. "Lucid and entertaining." — The New York Times Book Review.

Taming the Tiger Within is a handbook of meditations, analogies, and reflections that offer pragmatic techniques for diffusing anger, converting fear, and cultivating love in every arena of life-a wise and exquisite guide for bringing harmony and healing to one's life and relationships. Acclaimed scholar, peace activist, and Buddhist master revered by people of all faiths, Thich Nhat Hanh has inspired millions worldwide with his insight into the human heart and mind. Now he focuses his profound spiritual wisdom on the basic human emotions everyone struggles with on a daily basis.