The Waltz of Reason - by Karl Sigmund (Hardcover)

About the Book

"Over Plato's Academy in ancient Athens, it is said, hung a sign: "Let no one ignorant of geometry enter here." Plato thought no one could do philosophy without also doing mathematics. In The Waltz of Reason, mathematician and philosopher Karl Sigmund shows us why. Charting an epic story spanning millennia and continents, Sigmund shows that philosophy and mathematics are inextricably intertwined, mutual partners in a reeling search for truth. Beginning with-appropriately enough-geometry, Sigmund explores the power and beauty of numbers and logic, and then shows how those ideas laid the ground work for everything from the theory of a fair election, to modern conceptions of governance, cooperation, morality, and even of reason itself. Did you know, for example, that John Locke, author of some of the most important texts in the Western theory of government, was motivated in his work by his study of geometry? Or, that Locke was actually terrible at geometry, a seventeenth-century mathematical laughingstock? He was, a fact that might want us to think again about the logic of his life's work. And Locke wasn't the only one! Sigmund reveals how many of our modern ideas about what is true and what is reasonable are based on similarly shaky grounds. The economists and other thinkers who promulgated game theory, classical economics, and behavioral economics-the basis of so much in modern life-were not necessarily good at either math or philosophy, or both. The result is a remarkable book: accessible, funny, and wise, it tells an engrossing history of ideas that spins as dizzyingly and beautifully as a ballroom full of expert dancers. But it doesn't just celebrate the past. Instead, by making all these great ideas accessible to all, The Waltz of Reason empowers as it entertains, giving each of us the tools to ask, what do we know, how do we know it, and what do we want to do, with all these ideas?"--

Book Synopsis

"A mind-bending jaunt ... that makes clear in fascinating detail how math is more than a sum of its parts" (Publishers Weekly)

"Let no one ignorant of geometry enter here," Plato warned would-be philosophers. Mathematician Karl Sigmund agrees.

In The Waltz of Reason, he shows how mathematics and philosophy together have shaped our understanding of space, chance, logic, cooperation, voting, and the social contract. Sigmund shows how game theory is integral to moral philosophy, how statistics shaped the meaning of reason, and how the search for a logical basis for math leads to deep questions about the nature of truth itself. But this is no dry tome: Sigmund's wit and humor shine as brightly as his erudition.

The Waltz of Reason is an engrossing history of ideas as vibrant as a ballroom full of dancers, one that empowers as it entertains, following the complex and occasionally dizzying steps of the thinkers who have molded our thought and founded our world.

Review Quotes

"[Sigmund] writes clearly and with subtle wit, making The Waltz of Reason highly readable... [and] well worth a dance."--American Scientist

"[D]oes the imaginary number i actually exist, or did we invent it? Could an alien civilization develop an alternate form of mathematics, or would they inevitably develop the same one we have? Sigmund's witty tone inspires readers to delve into those questions and others."--Physics Today

"[L]overs of philosophy and human behavior who are at the very least math-curious will be captivated by the author's investigations of game theory, the social contract, the classic prisoner's dilemma and, of course, the looming question of whether computers are truly intelligent, even potentially conscious."--Los Angeles Times

"Sigmund takes readers on a mind-bending jaunt through game theory, gambling systems, and more. This makes clear in fascinating detail how math is more than a sum of its parts."--Publishers Weekly

"An erudite, witty, tongue-in-cheek and wide-ranging discourse on philosophy and mathematics, a Gödel, Escher, Bach for the 21st century."--Christof Koch, PhD, author of The Feeling of Life Itself

"Lucid, readable, and fascinating. Karl Sigmund acts as our friendly guide to topics as diverse as the meaning of numbers, the limits of computers, and the impossibility of a fair voting system. Highly recommended!"--Ian Stewart, author of What's the Use?

"Mathematics and Philosophy have always been great dance partners throughout human history. Karl Sigmund is the perfect companion to lead readers on this merry dance. His combination of deep mathematical and philosophical knowledge combined with his entertaining prose will have readers waltzing through this wonderful book."--Marcus du Sautoy, author Around the World in Eighty Games

"A delightful historical tour of the interplay of Mathematics and Philosophy."--Brian Skyrms, University of California, Irvine

About the Author

Karl Sigmund is a professor emeritus of mathematics at the University of Vienna. One of the pioneers of evolutionary game theory, he has authored several other books on mathematics and philosophy, including Games of Life and Exact Thinking in Demented Times. He lives in Vienna, Austria.