Over the past few centuries we've learned that the sun does not revolve around the earth. We've learned that we evolved from smaller (I won't say lesser) creatures over aeons of time. We've learned that our behavior is that of a particular kind of primate, and that even our most sophisticated endeavors all reflect our evolutionary heritage.

But, throughout this process of social disappointment and readjustment, we've always been able to say that at least mathematics is a real and incontrovertible link to the Divine. At least here, in the fortress of our own minds, we can transcend our earthly shell.

Well, no, we can't.

As Lakoff and Nunez show in exhaustive detail in this book, cognitive science has uncovered how the human thought processes underlying mathematical reasoning actually work. These thought processes, it turns out, aren't just different from the classical and Platonic models of human reasoning--they preclude them. Very briefly put, we reason mathematically by using systems of metaphor that are grounded in our use of the human body and in its sensorimotor system. There is no evidence that mathematical reasoning (as opposed to calculation) can be done in any other way and still be what we would recognize as mathematical. Mathematical thinking, it turns out, has no features that are different from other kinds of thought, it simply organizes these mental activities in a particular way.

At the very root of math lies metaphor; and at the root of metaphor lies the human body, which is both the dictionary and grammar of the metaphor-using brain. Mathematics never breaks free of its grounding in human existence; it can't (although, once again, calculation can be performed by machines, but calculation is not mathematical reasoning). The pythagorean religion is dead with our generation.

Of course, there have been rumblings of this sort for over a century. Russel and Godel undermined the self-consistency of math; but they didn't touch the issue of transcendence. The results of the cognitive scientists are of a completely different order, because not only have they shown that we perform math using the metaphor system grounded in our animal bodies; one could continue to argue that some sort of perfect transcendental mathematics exists that we clumsily mimic using our crude brains. In fact, the results of cognitive studies have shown that our actual ways of thinking about math indicate clearly that no such transcendent mathematical realm exists.

To understand that argument, you should read the book. I will say, however, that over the years I've known many people who are literally fanatical in their Pythagorean beliefs. It's very common for professionals and scientists to adhere to a quiet faith in the existence of a realm of mathematical truth that exists outside the universe itself, eternal and inviolable. The level of fanaticism in such people is often so deep that they will never accept the findings of Lakoff and Nunez, no matter how they're explained. In this, our best and brightest descend to the level of the worst religious fanatics that they themselves hold in contempt.

A perfect example is provided by one of the customer reviews of the book on Amazon.com's website. Here's how he starts out:

Firstly, I must admit I have not read the book.

It gets better. He goes on to say, ...The Book, "Where Mathematics Comes From" is flawed in that it attempts to describe the very mathematics that determines who we are and how our metaphorical conceptions evolve. We live in a Universe whose processes are determined by mathematical and physical laws. As such our embodied metaphorically predisposed minds are very much a product of that mathematics. Turner and Nunez have erred on this point. Our metaphors may determine how we perceive mathematics but, more importantly, it is the mathematics that determines how we become predisposed to use metaphor.

I've bolded the key indicator of where this reviewer's reasoning goes completely astray. He or she begins with the assumption that mathematics exists outside the universe, and shapes it from outside via actually existent, physical laws. In fact, scientists today tend to view physical laws as formulations to describe pre-existing phenomena; they are descriptions, not laws. The old way of thinking is that Newton saw the law of gravity as it exists in the mind of God; the modern view is that he used a special language to accurately describe a particular class of observations and potential observations. The reviewer above assumes without evidence that mathematics comes prior to physical reality, and so has no need to read the book. In fact, everything in Where Mathematics Comes From clearly shows that the world works the other way around: the orderly physical world allows us to formulate reliable descriptions of it using the language of mathematics.

So, dear reader, assuming that you care about such things, how adventurous are you, really? Do you believe in the old Pythagorean heaven, a perfect mathematical realm existing parallel but separate to our own? Or are you willing to strike out in a new direction, one more human-centric? I am; it's my commitment to such new directions that led to the name of this website, after all. I want to write SF that reflects a worldview of clearly 21st century pedigree, which is why books like Where Mathematics Comes From inspire me.

What I hope will come from these studies (if I may don my SF-writer hat and look into the future) is a gradual shift in society away from an awed acceptance of the pronouncements of scientists and mathematical thinkers, towards a direct engagement with them as peers. The accuracy and value of mathematics can't be denied, especially not by the findings presented in this book; but the arrogance of an intellectual class that pretends to have a private pipeline to God in the form of mathematical truth can be reduced. Actually, there's scope for a better kind of pride now that we know the transcendent mathematical realm doesn't exist; a mathematician can no longer pretend modesty and claim he or she simply discovered what was there all along. No--you made it. Be proud of your creation, but don't hide behind the Ozma-mask of transcendence; be prepared to own mathematics as your creation.

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