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 Click for words events ADDING UP MATH "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being" by George Lakoff and Rafael Nunez
Most of us think of mathematics as some sort of inaccessible (and sometimes beautiful) language that's hidden within nature, only to be uncovered and plucked out through hours of rigorous and painful scholarship. Mathematics seems to be a language that transcends everyday reality, something outside and without us. Apparently, nothing could be farther from the truth. In "Where Mathematics Comes From," George Lakoff and Raphael Nunez allay our misplaced xenophobic fear. In the tradition of cognitive science's investigation of the "embodiment of the human mind," Lakoff and Nunez take to task a wealth of common assumptions about mathematical "ideas" and, one by one, turn them all on their heads. For starters, the number line isn't actually a line. And the numbers don't actually fill it. It's not for the joy of bashing the king of sciences that Lakoff and Nunez dismantle common myths. The dissection allows us to see how math actually works, and how, as humans, we can possibly understand the ideas. What's being espoused is mind-based mathematics, i.e., a math based on our innate ability to perform rudimentary arithmetic and subitization as infants, on basic cognitive tools like conceptual metaphors, blends, prototypes, frames, etc., and the concept of an embodied mind. Lakoff and Nunez try to show us that math doesn't just consist of moving obscure symbols around in a predetermined fashion, but that it encompasses concepts and ideas that can't be arrived at by standard ways of discussing math. The authors create a series of "idea analyses," explanations of how arithmetic operations are conceived of in terms of collecting objects. And how our concept of actual infinity is based on a series of finite processes-after all, how else could we conceive of the infinite when we, and all we encounter, are undeniably finite. Mathematics is actually a tool that we've constructed, not the language of the universe. The joy in reading George Lakoff rubs off from his own joy in writing books about sophisticated and non-trivial topics. Keeping it readable for a wide audience -- no matter what the education level-he always takes great pain to achieve clarity. Lakoff's egalitarian approach is appropriate, considering the book takes to task the obfuscatory nature of mathematical symbol-mongering, but also because there's a secondary educational motive to the book: Lakoff and Nunez believe there's a better way to teach math. The proposed way teaches not only that theorems are true, but also why they're true. Which, of course, can only be done if we can generate a new understanding of this device we've created. "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being" 
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