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WHERE MATHEMATICS COMES FROM: HOW THE EMBODIED MIND BRINGS MATHEMATICS INTO BEINGby George Lakoff
Synopses & Reviews
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.
Book News Annotation:
Two cognitive scientists examine the structure of mathematical ideas, what mathematics means, and why. Lakoff (linguistics, U. of California, Berkeley) and N<'u><~n>ez (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.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Renowned linguist George Lakoff pairs with psychologist Rafael Nunez to provide a serious study of the cognitive science of mathematical ideas. Illustrations.
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