Books about Ambiguity from Amazon.com

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.

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

Every child knows what it means to play, but the rest of us can merely speculate Is it a kind of adaptation, teaching us skills, inducting us into certain communities? Is it power, pursued in games of prowess? Fate, deployed in games of chance? Daydreaming, enacted in art? Or is it just frivolity? Brian Sutton-Smith, a leading proponent of play theory, considers each possibility as it has been proposed, elaborated, and debated in disciplines from biology, psychology, and education to metaphysics, mathematics, and sociology.

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.

This work reveals more distinctions and disjunctions than affinities, with one striking exception: however different their descriptions and interpretations of play, each rhetoric reveals a quirkiness, redundancy, and flexibility. In light of this, Sutton-Smith suggests that play might provide a model of the variability that allows for "natural" selection. As a form of mental feedback, play might nullify the rigidity that sets in after successful adaption, thus reinforcing animal and human variability. Further, he shows how these discourses, despite their differences, might offer the components for a new social science of play.

In Biomedical Ambiguity, Ian Whitmarsh describes how he followed a team of genetic researchers to Barbados, where he did fieldwork among not only the researchers but also government officials, medical professionals, and the families being tested. Whitmarsh reveals how state officials and medical professionals make the international biomedical research part of state care, bundling together categories of disease populations, biological race, and asthma. He points to state and industry perceptions of mothers as medical caretakers in genetic research that proves to be inextricable from contested practices around nation, race, and family. The reader's attention is drawn to the ambiguity in these practices, as researchers turn the plurality of ethnic identities and illness meanings into a science of asthma and race at the same time that medical practitioners and families make the opaque science significant to patient experience. Whitmarsh shows that the contradictions introduced by this "misunderstanding" paradoxically enable the research to move forward..
Price: $19.90 [Notify me when price goes down.]