Order from a Major Online Bookstore
Ultimate Book Price Comparison Engine
Save Your Time And Money
| AnyBook4Less.com | Order from a Major Online Bookstore |
|
| Home | Store List | FAQ | Contact Us | | ||
| Ultimate Book Price Comparison Engine Save Your Time And Money |
||
 |
Title: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by George Lakoff, Rafael E. Nunez, Rafael Nuñez ISBN: 0-465-03771-2 Publisher: Basic Books Pub. Date: 07 August, 2001 Format: Paperback Volumes: 1 List Price(USD): $23.50 |
Average Customer Rating: 3.65 (17 reviews)
Rating: 5
Summary: Mathematics as a product of the human mind
Comment: While I agree with the previous reviewer that the authors may at times suggest a little too much credit for a work that does have its predecessors, I still consider this a great book.
By attacking the transcendental nature of mathematics, and elaborating the grounding of mathematical thought in the metaphorical mapping of the mind, many important implications arise ranging from the meaning of mathematics, the way mathematics is practiced and proofs are formulated, to the way mathematics should be taught. The authors formulate their intention to link the fields of mathematical thought and cognitive sciences to generate the field of mathematical idea analysis. They stress the point that their work should be considered as an initial step and in no way as the final word. In the analysis of the thought process a number important aspects of mathematical thought get visited. Having recently read Aczel's book about Cantor and Infinity- I now feel I over-rated it at 2 stars- Lakoff and Nunez give a treatment of the concept of infinity based on the basic metaphor of infinity (BMI) that simply ridicules Aczel's. Masterful.
Is this book perfect? It's excellent, but could (and will) be improved.
Little attention is paid to the idea of linearization that is such a central concept in much of mathematics. In attempt to save the best for last, the authors conclude with a detailed analysis of the ideas behind Euler's famous formula: e^ip = -1. They claim that such a treatment would be very helpful to develop a better understanding of the formula, than a more standard approach. It may be that my former Dutch high school education, blessed with a great math teacher, deviates from the current US standard. Yet, I must say that the analysis of Lakoff and Nunez is simply not as clear and thorough as the one I received in my teens. Not only did my high school analysis include all the metaphors but a much clearer link between the e^ip and the sin(t) + i sin(t) functions based on the Taylor expansions. It is especially in this last section that the authors undermine their cause, by making statements that an expression e^p would be devoid of implicit meaning.
While I agree with the author's central dogma of mathematics as one of the human mind's most beautiful and enduring products they sometimes take their argument just a little too far. By a careful analysis and conceptualization of simple ideas mathematics has generated formalized concepts that allowed extrapolation into conclusions that initially appeared non- or even counter-intuitive. I think, that this process has been so crucial in establishing the magic or romance of mathematics.
No matter what the authors may say, wherever in the Universe any group of beings draw the line connecting the series of points that share the same distance, r, to this center, the resulting circle will always have a 2pr circumference. They may conceptualize it completely differently, but will come to the same conclusion.
Rating: 5
Summary: Refreshing approach to the ideas of mathematics
Comment: 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.
Rating: 4
Summary: An interesting view of the nature of mathematics
Comment: For as long as Western mathematics has been around, it has generally been viewed as having an existence independent of human experience, as belonging to a Platonic realm of forms and ideas. To make it embodied in the human psyche, as the authors attempt to do in this book, would be a sacrilege to many mathematicians. Such a move would deny the 'eternal truth' of mathematics some would argue.
But the last few decades have seen the rise of cognitive science, and this field has led to many interesting insights into the operation of mind and has demystified its status in the world. The authors though see cognitive science as being deficient in one respect: it has omitted the study of mathematical ideas from a cognitive perspective. There is no cognitive science of mathematics, they say, and hence they endeavor in the book to correct this deficiency. Such a project is definitely worth the effort, for mathematics has to be interpreted in the light of what is known about the mind, or as the authors put it, "it should study precise nature of clear mathematical intuitions".
The book is very interesting to read, and the justifications for the assertions put forward by the authors are certainly the most optimal if viewed in the context of what is currently known in cognitive science. Further work must be done however, particularly in tying their ideas to the very intensive research in neuroscience that is being done at the present time. The prospect of having a science of mathematical thought is an exciting one. This book is the best that is currently available.
The attitude of the authors is most refreshing, in that they not only show great enthusiasm throughout the book, but they are not nervous about discarding what they view as the "romance" of mathematics. They list several statements illustrating this "beautiful romance", such as the view that mathematics has an objective existence, which transcends the existence of human beings; or that human mathematics is merely a part of abstract, transcendent mathematics, and that reason is a form of mathematics. These romantic beliefs appear to be false, the authors say. Instead, they argue, the nature of mathematical ideas is that they are inherently metaphorical in nature. They give several examples of this in the first few pages of the book, with the rest of the book elaborating in great detail their reasons for asserting this.
This is certainly an exciting time to be involved in mathematics, and assuming more evidence is accumulated that supports the authors opinions on the embodied nature of mathematics, it will be even more interesting to be engaged in mathematical research and in the teaching of mathematics. Mathematical thinking will then viewed as part of us, not some abstract collection of statements existing in some vaguely defined realm. Viewing mathematics as purely embodied may also give much more insight into teaching non-human machines how to do mathematics. This is the most exciting prospect of all.
 |
Title: Metaphors We Live by by George Lakoff, Mark Johnson ISBN: 0226468011 Publisher: University of Chicago Press (Trd) Pub. Date: April, 2003 List Price(USD): $14.00 |
 |
Title: Philosophy in the Flesh : The Embodied Mind and Its Challenge to Western Thought by George Lakoff, Mark Johnson ISBN: 0465056741 Publisher: Basic Books Pub. Date: 01 December, 1999 List Price(USD): $24.95 |
 |
Title: Women, Fire, and Dangerous Things: What Categories Reveal About the Mind by George Lakoff ISBN: 0226468046 Publisher: University of Chicago Press (Trd) Pub. Date: January, 1990 List Price(USD): $17.95 |
 |
Title: Moral Politics : How Liberals and Conservatives Think by George Lakoff ISBN: 0226467716 Publisher: University of Chicago Press (Trd) Pub. Date: May, 2002 List Price(USD): $22.00 |
 |
Title: The Way We Think: Conceptual Blending and the Mind's Hidden Complexities by Gilles Fauconnier, Mark Turner ISBN: 0465087868 Publisher: Basic Books Pub. Date: March, 2003 List Price(USD): $20.00 |
Thank you for visiting www.AnyBook4Less.com and enjoy your savings!
Copyright� 2001-2021 Send your comments
