This book represents the second of two reading epiphanies I’ve had this year (the first was The Omnivore’s Dilemma). I pulled this book from the shelf at the library looking for a good follow-up to The Mathematical Experience. That book pulled the carpet out from under my mathematical education, and much of my personal philosophy in the process. It was a vivid illustration of my human longing for certainty, and my willingness to accept ideas without evidence in order to lay claim to that certainty. I clung for most of my life to an idea of mathematics as my bedrock, undeniable and pure, yet I had never closely examined that bedrock. When at last I forced myself to examine it critically, I saw there was no bedrock there at all, and the entire edifice collapsed. The false bedrock was the idea that there are basic objective truths that exist independent of humanity from which all of mathematics can be derived. Yet the more I tried to identify these foundational truths, the more convoluted and twisted they became, until I finally found myself unable to accept their reality. To my great wonder and joy, the authors of this book, with great clarity and care, gathered up the leftover bits and pieces of the edifice and rebuilt it before my eyes on an entirely different foundation: my own human experience. I’m convinced that I’ve witnessed a revolution that will probably not fully take hold of mathematics for another generation. The central principal that mathematics arises naturally from human cognition, and has no mystical existence in the fabric of the universe apart from us, will be unacceptable to many. For me, it is a gift to be able to relate to mathematics in terms I can truly have faith in – my own experiences. The idea goes well beyond mathematics and is changing the way I relate to all of my dearly held conceptual constructions. I feel privileged to have discovered it.
5 responses to “Book: Where Mathematics Comes From / Lakoff and Nuñez”
Neat. I’ll add these two books to my list!
It is now officially on the Amazon wish list. Thanks for the recommendation!
I remember coming out of my fourth day of a course in Special Relativity in tears. The idea that not even time was constant, and that time and space were really just a side effect of our limited perception seriously disturbed me. But, now I think its ok. Any language we create is destined to be limited, because we are limited creatures.
Um… Schrodinger’s Cat is (not) dead!
The recognition of mathematics as language is definitely a huge clue that it arises from human cognition. Still, because it can be such a cross-cultural language, it’s easy to mistakenly endow it with even more power, like pure objective existence.
I’m curious to look again at relativity after realizing how metaphorical the mathematical ideas are. I have a feeling the different concepts of time and space largely a result of the employment of new metaphors, and our discomfort arises from the fact the new metaphors are quite different from our old ones. Especially if we’ve taken our old metaphors for time and space literally, the new ones appear to be a disturbing shift of reality!
I remember that you bought the mathmatics book while in Michigan (I think) or at least you were reading it while visiting here last summer. You got me reading the Omnivore’s Dilemma, which is a real idea-of-reality changer. Maybe I should read this math book too, except, being pretty ignorant of mathmatics, I never did stake my philosophy on mathmatical principles. I’m an agnostic about most of that: I know what I know, maybe, I think, but I recognize there is much I dont know which, if I did, might change how I see everything.
It works with people…our assumptions about even those closest to us. We think we know them, but there are things, possibly many thngs, about them that if we knew, it would completely change our concept of them as people. This is why writers and artists never run out of ideas.
I’ve always thought that much of life could only be expressed through story and metaphor, but I never thought of language, mathmatical or otherwise, as metaphor. Layers of metaphor. Wow.
It was The Mathematical Experience that I bought in Michigan. Both books are largely accessible without much mathematical knowledge, but they do include some passages directed at those who have spent time studying it.
The real highlight for me is that the more I investigate myself, the more I discover how dominated my consciousness is by language that I don’t really understand (meaning I don’t effectively relate it to my own experience). I think this is equally true for any subject from math to religion to my conception of those I love.
The layers of metaphor in language are really striking. On of the authors, George Lakoff, wrote another book called Metaphors we live by, which is on my stack now.