While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

Sutton-Smith focuses on play theories rooted in seven distinct "rhetorics"--The ancient discourses of fate, power, communal identity, and frivolity and the modern discourses of progress, the imaginary, and the self. In a sweeping analysis that moves from the question of play in child development to the implications of play for the Western work ethic, he explores the values, historical sources, and interests that have dictated the terms and forms of play put forth in each discourse's "objective" theory

To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

A thought-provoking guide to help you lean in to the discomfort of the unknown to turn creative opportunities into intentional design, from Stanford University's world-renowned d.school. “Navigating Ambiguity reminds us not to run from uncertainty but rather see it as a defining moment of opportunity.”—Yves Béhar, Founder and CEO, fuseproject A design process presents a series of steps, but in real life, it rarely plays out this neatly. Navigating Ambiguity underscores how the creative process isn’t formulaic. This book shows you how to surrender control by being adaptable, curious, and unbiased as well as resourceful, tenacious, and courageous. Designers and educators Andrea Small and Kelly Schmutte use humor and clear steps to help you embrace uncertainty as you approach a creative project. First, they explain how the brain works and why it defaults to certainty. Then they show you how to let go of the need for control and instead employ a flexible strategy that relies on the balance between acting and adapting, and the give-and-take between opposing approaches to make your way to your goal. Beautiful cut-paper artwork illustrations offer ways to rethink creative work without hitting the usual roadblocks. The result is a more open and satisfying journey from assignment or idea to finished product.

From the groundbreaking author of The Second Sex comes a radical argument for ethical responsibility and freedom. In this classic introduction to existentialist thought, French philosopher Simone de Beauvoir’s The Ethics of Ambiguity simultaneously pays homage to and grapples with her French contemporaries, philosophers Jean-Paul Sartre and Maurice Merleau-Ponty, by arguing that the freedoms in existentialism carry with them certain ethical responsibilities. De Beauvoir outlines a series of “ways of being” (the adventurer, the passionate person, the lover, the artist, and the intellectual), each of which overcomes the former’s deficiencies, and therefore can live up to the responsibilities of freedom. Ultimately, de Beauvoir argues that in order to achieve true freedom, one must battle against the choices and activities of those who suppress it. The Ethics of Ambiguity is the book that launched Simone de Beauvoir’s feminist and existential philosophy. It remains a concise yet thorough examination of existence and what it means to be human.

Ever since it was first published in 1930, William Empson’s Seven Types of Ambiguity has been perceived as a milestone in literary criticism—far from being an impediment to communication, ambiguity now seemed an index of poetic richness and expressive power. Little, however, has been written on the broader trajectory of Western thought about ambiguity before Empson; as a result, the nature of his innovation has been poorly understood. A History of Ambiguity remedies this omission. Starting with classical grammar and rhetoric, and moving on to moral theology, law, biblical exegesis, German philosophy, and literary criticism, Anthony Ossa-Richardson explores the many ways in which readers and theorists posited, denied, conceptualised, and argued over the existence of multiple meanings in texts between antiquity and the twentieth century. This process took on a variety of interconnected forms, from the Renaissance delight in the ‘elegance’ of ambiguities in Horace, through the extraordinary Catholic claim that Scripture could contain multiple literal—and not just allegorical—senses, to the theory of dramatic irony developed in the nineteenth century, a theory intertwined with discoveries of the double meanings in Greek tragedy. Such narratives are not merely of antiquarian interest: rather, they provide an insight into the foundations of modern criticism, revealing deep resonances between acts of interpretation in disparate eras and contexts. A History of Ambiguity lays bare the long tradition of efforts to liberate language, and even a poet’s intention, from the strictures of a single meaning.