The Waltz of Reason: The Entanglement of Mathematics and Philosophy

by Karl Sigmund

Overview

"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.

Product Details

ISBN-13:	9781541602694
Publisher:	Basic Books
Publication date:	12/19/2023
Pages:	448
Sales rank:	122,014
Product dimensions:	6.20(w) x 9.10(h) x 1.50(d)

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. 

Editorial Reviews

11/06/2023

Sigmund (Games of Life), a professor emeritus of mathematics at the University of Vienna, explores in this spirited study the ways that math has been used to make sense of the world, from abstract controversies over logic to practical insights into elections and ethics. After overviewing concepts in computation, logic, chance, and causality, the author delves into “practical philosophy: morality and economics, politics and the law.” He identifies the intrinsic flaws of ranked voting systems (according to mathematician Ken Arrow’s impossibility theorem, no such system “can satisfy even the most reasonable” fair voting requirements, “as soon as there is a choice between more than two alternatives”) and the complexities of social cooperation as captured by the famous “prisoner’s dilemma” non-zero-sum game. Elsewhere, Sigmund traces evolving perceptions of math’s practical possibilities: as recently as 1940, some mathematicians were sure that general relativity and number theory refused “all possible applications,” but today “Einstein’s field equations are used in GPS, and number theory in all email platforms.” Wading into rich debates over math’s fundamental nature (Is math like a language? Does it have an existence independent of consciousness, or is it a purely mental construct?), 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. (Dec.)

Publishers Weekly

[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] 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

“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

“A delightful historical tour of the interplay of Mathematics and Philosophy.”—Brian Skyrms, University of California, Irvine

“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

“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?

From the Publisher

2023-09-20
Philosophers and mathematicians don’t have much in common, right? A mathematician disagrees.

Sigmund, professor emeritus of mathematics at the University of Vienna and author of Exact Thinking in Demented Times, makes his case in nearly 400 pages of lucid prose. The author is a fine writer, but this is not Mathematics and Philosophy for Dummies; readers without a background in both may struggle. The first section “traces the evolution of the self-image of mathematics.” Evidence alone supports scientific laws; they can never be proven beyond a doubt. Not so with mathematics, but Sigmund’s explanations of mathematical proofs—dense with equations and diagrams—are not for the faint of heart. Surprisingly, proving that 1 + 1 = 2 is a complex operation. In the second section of the book, the author deals with chance, the continuum, and infinity, which goes beyond common sense and often vexes philosophers with problems such as “how an infinitesimal could be smaller than anything and yet not zero.” Beginning with the Enlightenment, mathematicians began stepping on philosophical toes by examining human behavior and institutions with often intriguing results. These occupy the book’s third and fourth sections and are more accessible. In the digital age, computers are the rage even for deep thinkers, and it’s become so difficult to maintain that computers are not intelligent that experts have moved the goalposts to maintain that they are not conscious. It turns out that humans are “utterly inept” at estimating probabilities, risks, and even fairness. Many Americans have no doubt that our winner-take-all voting system is superior, but it’s proven that all voting systems are unfair. Sigmund also examines irresistible areas such as game theory, probability, decisions, and the social contract, as well as parables such as the Prisoner’s Dilemma.

Sigmund delves into fascinating philosophical areas but delivers an overwhelming amount of information.

Kirkus Reviews