Amazon.com
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 Publishers Weekly
This groundbreaking exploration by linguist Lakoff (co-author, with Mark Johnson, of Metaphors We Live By) and psychologist N#$ez (co-editor of Reclaiming Cognition) brings two decades of insights from cognitive science to bear on the nature of human mathematical thought, beginning with the basic, pre-verbal ability to do simple arithmetic on quantities of four or less, and encompassing set theory, multiple forms of infinity and the demystification of more enigmatic mathematical truths. Their purpose is to begin laying the foundations for a truly scientific understanding of human mathematical thought, grounded in processes common to all human cognition. They find that four distinct but related processes metaphorically structure basic arithmetic: object collection, object construction, using a measuring stick and moving along a path. By carefully unfolding these primitive examples and then building upon them, the authors take readers on a dazzling excursion without sacrificing the rigor of their exposition. Lakoff and N#$ez directly challenge the most cherished myths about the nature of mathematical truth, offering instead a fresh, profound, empirically grounded insight into the meaning of mathematical ideas. This revolutionary account is bound to garner major attention in the scientific pressDbut it remains a very challenging read that lends itself mostly to those with a strong interest in either math or cognitive science. (Nov. 15) Copyright 2000 Reed Business Information, Inc.
From Booklist
With this ambitious book, Lakoff and Nunez hope to launch a whole new discipline: a cognitive science of mathematics. And they bid fair to bring it off, showing how all mathematical ideas--from simple counting to calculus--can be traced to the discrete workings of the human brain, and not to some transcendent realm of Platonic ideals. This approach to mathematics holds a number of surprises, as even ordinary arithmetic dissolves into conceptual metaphors grounded in the sensory-motor system. The entire panoply of mathematical symbols and calculations--precise and consistent--thus reflects the evolutionary history of brain neurons. Cognitive science can place even that most daunting of mathematical mysteries--infinity--within the observable human mind, explaining it as an aspect metaphor lodged deep in the unconscious. Similar reasoning can also account for the cultural plasticity of mathematics, which appears in one guise among the Mayans and a quite different one among the Chinese. A pioneering work of singular importance for mathematicians and psychologists alike--and of definite appeal to general readers with interest in those subjects. Bryce Christensen
Copyright © American Library Association. All rights reserved
From Book News, Inc.
Two cognitive scientists examine the structure of mathematical ideas, what mathematics means, and why. Lakoff (linguistics, U. of California, Berkeley) and Nuez (psychology, U. of Freiburg) believe that conceptual metaphor plays a central, defining role in mathematical ideas, from simple arithmetic and algebra to sets, logic, and infinity. They argue that understanding the ideas implicit in mathematics, especially the metaphorical ideas, demystifies mathematics so that it makes more sense.Book News, Inc.®, Portland, OR
-The American Scholar
"Adds body heat to the cold and beautiful abstractions of mathematics."
-Science News
"A groundbreaking book."
-Publishers Weekly
"The authors take readers on a dazzling excursion without sacrificing the rigor of their exposition. Revolutionary."
Book Description
Renowned linguist George Lakoff pairs with psychologist Rafael Nuñez in the first book to provide a serious study of the cognitive science of mathematical ideas. This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.
Book Info
Argues that conceptual metaphor plays a central, defining role in mathematical ideas from within the cognitive unconscious, all forms of math, even real numbers being a product of human experience of the world as filtered through the unconscious mind. DLC: Number concept.
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