Infinity and the Mind

Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 9781400849048
Release Date: 2013-07-14
Genre: Mathematics

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

The End of Theory

Author: Richard Bookstaber
Publisher: Princeton University Press
ISBN: 9781400884964
Release Date: 2017-04-17
Genre: Business & Economics

An in-depth look at how to account for the human complexities at the heart of today's financial system Our economy may have recovered from the Great Recession—but not our economics. In The End of Theory, Richard Bookstaber discusses why the human condition and the radical uncertainty of our world renders the standard economic model—and the theory behind it—useless for dealing with financial crises. What model should replace it? None. At least not any version we've been using for the past two hundred years. Instead, Bookstaber argues for a new approach called agent-based economics, one that takes as a starting point the fact that we are humans, not the optimizing automatons that standard economics assumes we are. Bookstaber's groundbreaking paradigm promises to do a far better job at preventing crises and managing those that break out. As he explains, our varied memories and imaginations color our economic behavior in unexpected hues. Agent-based modeling embraces these nuances by avoiding the mechanistic, unrealistic structure of our current economic approach. Bookstaber tackles issues such as radical uncertainty, when circumstances take place beyond our anticipation, and emergence, when innocent, everyday interactions combine to create sudden chaos. Starting with the realization that future crises cannot be predicted by the past, he proposes an approach that recognizes the human narrative while addressing market realities. Sweeping aside the historic failure of twentieth-century economics, The End of Theory offers a novel and innovative perspective, along with a more realistic and human framework, to help prevent today's financial system from blowing up again.

Is God a Mathematician

Author: Mario Livio
Publisher: Simon and Schuster
ISBN: 1416594434
Release Date: 2011-02-22
Genre: Mathematics

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

To Infinity and Beyond

Author: Eli Maor
Publisher: Princeton University Press
ISBN: 0691025118
Release Date: 1991
Genre: Mathematics

Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

What is a number

Author: Robert Tubbs
Publisher: Johns Hopkins Univ Pr
ISBN: UOM:39076002793821
Release Date: 2008-12-19
Genre: Mathematics

Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of topics-from Pythagoras's exploration of the connection between harmonious sounds and mathematical ratios to the understanding of time in both Western and pre-Columbian thought-Tubbs ties together seemingly disparate ideas to demonstrate the relationship between the sometimes elusive thought of artists and philosophers and the concrete logic of mathematicians. He complements his textual arguments with diagrams and illustrations. This historic and thematic study refutes the received wisdom that mathematical concepts are esoteric and divorced from other intellectual pursuits-revealing them instead as dynamic and intrinsic to almost every human endeavor.


ISBN: STANFORD:36105117254479
Release Date: 1995
Genre: American literature

Books in Print

ISBN: UOM:39015054048460
Release Date: 2004
Genre: American literature

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Author: Απόστολος Κ Δοξιάδης
ISBN: 9600329915
Release Date: 2001
Genre: Goldbach conjecture