数学从哪里来
Where Mathematics Comes From
George Lakoff · 初版 2000 年
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为什么值得读
- 从认知科学与生物学视角审视数学起源
- 批判纯形式证明并转向更直观的身体隐喻
- 系统解释无穷等基础分析概念的形成机制
“本书探讨的是数学思想，关于数学意味着什么——以及为什么。它关心的不仅是哪些定理为真，还包括定理意味着什么，以及为什么它们凭借其所蕴含的意义而成为真理。此外，它还回答了数学哲学中最深奥的问题之一：拥有有限大脑与心智的存在何以能够理解无限。”——封套文案。
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……事实。它们跟人类做过的其他任何事情一样，都根植于尘世。如果想从认知科学的角度换个有趣的视角看数学，可以去翻翻乔治·莱考夫的《数学从何而来》。
…the truth. They are as earthly as anything else we've been doing as a human race. For an interesting perspective on mathematics from a cognitive-scientific point of view, check out George Lakoff's book "Where Mathematics Comes From."
对这个感兴趣的朋友可能也会喜欢莱考夫的《数学从何而来》，我是看了 Bret Victor 的推荐才去读的：http://www.amazon.com/Where-Mathematics-Come-From-Embodied/d... 绝对是一本让人大开眼界的书。
Anyone interested in this might also like Lakoff's "Where Mathematics Comes From," which I read after seeing a Bret Victor recommendation of it: http://www.amazon.com/Where-Mathematics-Come-From-Embodied/d... Absolutely fascinating book.
乔治·莱考夫针对这个写过一本很棒的书，叫《数学从何而来》。他对目前数学教学动不动就从“第一性原理”和形式证明切入的做法提出了批评，认为应该更多从直觉性的身体/隐喻视角入手。他觉得形式证明在很大程度上就是一种学术上的 gatekeeping……
George Lakoff wrote a great book on this called "Where Mathematics Comes From." He is critical of how mathematics is currently taught from "first principles" and proofs rather than from a more intuitive body/metaphor perspective. He believes proofs are in many ways academic gatekeeping.…
……数学就是这么定义的，它并不依赖于我们的生物学构造和感知机制，因为这些定义本身就是我们下的。我手头正在读、也想推荐的一本书是乔治·莱考夫和拉斐尔·努涅斯合著的《数学从何而来：具身心智如何孕育数学》。数学的起源和含义深受认知科学的影响，因此也脱不开生物学。我之前这么说被踩了……
…that's how mathematics is defined and that it doesn't depend on our biology and perception, because we are making those definitions. A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted,…
在深入研究其他人推荐的各种书之前，建议你先读读乔治·莱考夫和拉斐尔·努涅斯的《数学从何而来》：http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring... 那本书阐述了数学分析基本概念的起源和理解方式：无穷大、……
Before digging into the various books others have suggested, you would do well to read "Where Mathematics Comes From" by George Lakoff and Rafael Nunez: http://www.amazon.com/Where-Mathematics-Comes-Embodied-Bring... That book explains the origins and understanding of the basic items of mathematical analysis: infinity,…
我很喜欢莱考夫和努涅斯在他们的书《数学从何而来》[1] 里讲这部分的章节。相关页面可以在 Google Books[2] 上看到。1- http://en.wikipedia.org/wiki/Where_Mathematics_Comes_From 2- http://books.google.com/books?id=YXv6SEjTNKsC&pg=PA432&#...
I enjoyed Lakoff and Núñez's section on this in their book Where Mathematics Comes From[1]. The relevent pages are available at Google Books[2]. 1- http://en.wikipedia.org/wiki/Where_Mathematics_Comes_From 2- http://books.google.com/books?id=YXv6SEjTNKsC&pg=PA432&#...