Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being - Hardcover

Lakoff, George; Nunez, Rafael E.

Hardcover

ISBN 10: 0465037704 ISBN 13: 9780465037704

Publisher: Basic Books, 2000

Synopsis

When you think about it, it seems obvious: The only mathematical ideas that human beings can have are ideas that the human brain allows. We know a lot about what human ideas are like from research in Cognitive Science. Most ideas are unconscious, and that is no less true of the mathematical ones. Abstract ideas, for the most part, arise via conceptual metaphor-a mechanism for projecting embodied (that is, sensory-motor) reasoning to abstract reasoning. This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on. Even the real numbers, the imaginary numbers, trigonometry, and calculus are based on metaphorical ideas coming out of the way we function in the everyday physical world.This book is about mathematical ideas, about what mathematics means-and why. The authors believe that understanding the metaphors implicit in mathematics will make mathematics make more sense. Moreover, understanding mathematical ideas and how they arise from our bodies and brains will make it clear that the brain's mathematics is mathematics, the only mathematics we know or can know.

About this title

Review

If Barbie thinks math class is tough, what could she possibly think about math as a class of metaphorical thought? Cognitive scientists George Lakoff and Rafael Nuñez explore that theme in great depth in Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. This book is not for the faint of heart or those with an aversion to heavy abstraction--Lakoff and Nuñez pull no punches in their analysis of mathematical thinking. Their basic premise, that all of mathematics is derived from the metaphors we use to maneuver in the world around us, is easy enough to grasp, but following the reasoning requires a willingness to approach complex mathematical and linguistic concepts--a combination that is sure to alienate a fair number of readers.

Those willing to brave its rigors will find Where Mathematics Comes From rewarding and profoundly thought-provoking. The heart of the book wrestles with the important concept of infinity and tries to explain how our limited experience in a seemingly finite world can lead to such a crazy idea. The authors know their math and their cognitive theory. While those who want their abstractions to reflect the real world rather than merely the insides of their skulls will have trouble reading while rolling their eyes, most readers will take to the new conception of mathematical thinking as a satisfying, if challenging, solution. --Rob Lightner

From the Back Cover

"Where Mathematics Comes From is an unprecedented attempt to base advanced mathematics on the working of the brain. It may well be the beginning of a whole new direction in the philosophy of mathematics. It is beautifully written and a pleasure to read." -Reuben Hersh, Professor of Mathematics, University of New Mexico; co-author of The Mathematical Experience, author of What is Mathematics Really?

"an unusually provocative naturalistic treatment of the foundations of mathematics based on lived experience and metaphor. It should force mathematicians to think harder about the foundations of their discipline." -Felix Browder, President of the American Mathematical Society; University Professor of Mathematics at Rutgers University

"This fascinating book pioneers the application of modern cognitive science to mathematics, building detailed support to the often-denied truth that mathematics is founded on human thought. By systematically attacking the central romantic mythology of mathematics, this book is certain to provoke heated controversy, but it has great promise, when the dust finally settles, to leave us better able to teach, to communicate and to think mathematics." -Bill Thurston, Professor of Mathematics, University of California, Davis and Fields Medal winner

"This is an important book, which challenges some deep seated beliefs about the nature of mathematics. If Lakoff and Nunez are right, and I believe they are, then what they say has significant implications for mathematics education." -Keith Devlin, author of The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip When you think about it, it seems obvious: The only mathematical ideas that human beings can have are ideas that the human brain allows. We know a lot about what human ideas are like from research in Cognitive Science. Most ideas are unconscious, and that is no less true of mathematical ideas. Abstract ideas, for the most part, arise via conceptual metaphor-a mechanism for projecting embodied (that is, sensory-motor) reasoning to abstract reasoning.

This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on. Even the real numbers are constituted by metaphorical ideas coming out of the way we function in the everyday physical world.

This book is about mathematical ideas, about what mathematics means-and why. It is concerned not just with which theorems are true, but with what theorems mean and why they are true by virtue of what they mean. And it provides an answer to one of the deepest problems of the philosophy of mathematics: how a being with a finite brain and mind can comprehend infinity.

This is the first full-scale serious study of the cognitive science of mathematical ideas. It provides a Theory of Embodied Mathematics. It is the first attempt at a rigorous methodology for Mathematical Idea Analysis-a cognitive analysis of the structure of mathematical ideas, of how those ideas are rooted in everyday bodily experience, what cognitive mechanisms they use, and how they are related to one another.

The authors believe that understanding the ideas implicit in mathematics-especially the metaphorical ideas-will demystify mathematics and allow it to make more sense. Moreover, understanding mathematical ideas and how they arise from our bodies and brains will make it clear that embodied mathematics is all that mathematics is-the only mathematics we know or can know.

Mathematics is not built into the universe.

The portrait of mathematics has a human face.

Edition details

• Publisher: Basic Books
• Publication date: 2000
• ISBN 10: 0465037704
• ISBN 13: 9780465037704
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 512