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Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being Hardcover – November 2, 2000

3.7 out of 5 stars 40 customer reviews

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Editorial Reviews

Amazon.com 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 --This text refers to the Paperback edition.

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.
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Product Details

  • Hardcover: 512 pages
  • Publisher: Basic Books; 1St Edition edition (November 2, 2000)
  • Language: English
  • ISBN-10: 0465037704
  • ISBN-13: 978-0465037704
  • Product Dimensions: 1.5 x 8 x 10 inches
  • Shipping Weight: 2.2 pounds
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (40 customer reviews)
  • Amazon Best Sellers Rank: #413,016 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
Whenever a person finds out that I'm a math enthusiast, 9 times out of 10 I get an uncomfortable reaction along the lines of "Oh, I HATE math!" In my experience, the mathphobe's biggest gripe is that math is a completely abstract concept, all based on memorization of some strange language, with so much of it having absolutely no comparison to the physical world.
This book strives to show that mathematics, from basic arithmetic to more advanced branches, can in fact all be reduced down to mental metaphors of physical concepts. Early in the book, the authors present the sound scientific evidence that humans have an innate understanding of the concept of quantity, and some degree of manipluation with quantity. This ultimately leads to an understanding of addition, and then subtraction. Those concepts, combined with the understanding of how to group objects in like sets, leads to an understanding of multiplication (add like sets) and division (subtract like sets). The book then introduces a few more fundamental ideas that the human brain can use to make analogies with (motion along a path, rotation, etc.), and recreates more common mathematical concepts in increasing complexity: geometry, trigonometry, logic, set theory, etc. At the end the book the authors even successfullly tackles Euler's equation (e^i*pi = -1), a classic example of something in mathematics that doesn't make any logical sense at first glance.
The book is extremely thorough in the way it presents all this. Most chapters start off by introducing a new cognative metaphor, then including a table showing the mathematical concepts to be presented and to which cognative metaphor each one relates. For a book on mathematics, this is actually a rather long read.
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Format: Hardcover
I give this book 5 stars not because it is definitive and "correct," but because it proposes an exciting new tack in the philosophy of mathematics. This deeply fascinating book would have been a major addition to that philosophy, a most noble subject, were it not that the authors know little about it. For starters, they do not appreciate the extent to which intuitionists and constructivists have anticipated their attack on what they rightly deprecate as the Romance of (Platonic) Mathematics. Intuitionists entirely agree that mathematics is a human construction serving human purposes; mathematics has no existence apart from this fact.

The philosophy of math has attracted some fine and exciting minds since Frege published his Begriffschrifft in 1879. Around 1900: Russell, of course, but also Husserl. Around 1940: Godel, Quine, Fraenkel, Bernays, Church, Curry, Brouwer, Weyl. More recently: Chihara, Boolos, Parsons, Resnick, Maddy, Shapiro, Detlefsen, Hartrey Field, Burgess, Rosen, Putnam. Regrettably, Lakoff and Nunez appear to have assimilated almost none of this literature.

This cognitive business will eventually have to interact with logic and Ed Zalta's formal theory of abstract objects.

Mathematicians reviewing this book in professional journals, as well as a number of Amazon reviewers, have complained of serious failings in L&N's understanding of some mathematical points. Lakoff argues that the errors found in earlier printings of WMCF are now corrected. On verra...

Readers should keep in mind that Lakoff is a linguist who made his reputation by linking linguistics to cognitive science and the analysis of metaphor. Nunez is a product of the Swiss school of mathematics as grist for cognitive psychology, founded by Piaget.
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Format: Hardcover
As a physicist and recreational mathematician, I found this book stimulating and reassuring. The connection of mathematics to human realities in our embodied world gives a new way to understand the conceptual and practical power of mathematics, as well as approach its limitations. I also found it helps to explain my preference for "seat of the pants" approach to some subjects, as contrasted to the proof-driven esthetic of many professional mathematicians. I think this book may encourage new ideas in mathematics education as well. If you're a Platonist, you'll find a lot to scream about, but its a great read for any math nut.
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Format: Hardcover
As a person interested in math, physics, philosophy, and cognition, I was delighted to find a book that helps tie these fields together. I've read many popularizations of math history and theory, and this books goes far beyond any of them.

First of all, this book is NOT a popularization, nor is it a book on math. It is a serious and ambitious effort to apply cognitive processes to the origin of mathematical concepts. What delighted me was that in doing so, the authors helped me improve the depth of my own understanding of those concepts.

I realize that many of the reviewers here and elsewhere have found errors in the presentation of the ideas, but I challenge them to offer a book that better presents those ideas in a conceptual format. Nowhere else have I read a book that describes the problems I had as a young student trying to understand the non-geometric approaches to limits and calculus. Also, their explanation of a program of discretization of continuity is one that closely resembles scientific reductionism and a similar discretization in physics.

To me, finding 19 reviews here is proof enough that the book is important, accessible, and useful. The authors do seem to have a thesis that they expound past exhaustion, dealing with the metaphysics of math, but much more interesting to me is their extremely useful methodology of mapping concepts. This is something I would like to see applied to quantum mechanics, fractal geometry, set theory, and computer programming, and hope that other cognitive scientists will step up to the task.

Although people who are more knowledgeable of the math literature than me may disagree, I think that this book does a scholarly job of collecting more than a few important concepts from several fields into one volume, something that is immensely helpful to persons like me at the bottom of the mathematical curve. ;)
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