Tuesday, February 19, 2013

Rafael Nunez and embodied mathematics

Nunez was co-author with Lakoff of Where Mathematics Comes From. Here is a site with his publications including books, book chapters and articles. Therein one can download the Preface, Introduction, Table of Contents and first four chapters of WMCF. From the Preface about the romance of mathematics, which they then meticulously debunk. Quote:

• Mathematics is abstract and disembodied—yet it is real.
• Mathematics has an objective existence, providing structure to this universe and any possible universe, independent of and transcending the existence of human beings or any beings at all.
• Human mathematics is just a part of abstract, transcendent mathematics.
• Hence, mathematical proof allows us to discover transcendent truths of the universe.
• Mathematics is part of the physical universe and provides rational structure to it. There are Fibonacci series in flowers, logarithmic spirals in snails, fractals in mountain ranges, parabolas in home runs, and pi in the spherical shape of stars and planets and bubbles.
• Mathematics even characterizes logic, and hence structures reason itself—any form of reason by any possible being.
• To learn mathematics is therefore to learn the language of nature, a mode of thought that would have to be shared by any highly intelligent beings anywhere in the universe.
• Because mathematics is disembodied and reason is a form of mathematical logic, reason itself is disembodied. Hence, machines can, in principle, think.

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