Pi in the Sky: Counting, Thinking, and Being.

The modern world began when Galileo rolled a polished metal ball down an inclined plane. He measured the distances the ball traveled in successive equal intervals of time and found that they increased as the odd numbers beginning with unity: 1, 3, 5, etc. This observation filled Galileo with wonder and delight. His conclusion: The book of nature is written in the language of mathematics.

Today, our most secure knowledge of the world is mathematical. Indeed, it can be said that nonmathematical knowledge is held suspect by scientists. This dependence upon numbers as the guarantors of truth defines the modern, Western way of knowing. It is the source of our power, our hegemony, and our hubris.

There is no greater mystery than this - the efficacy of mathematics as mediator between mind and nature. What we take to be fundamental laws of nature are expressed in simple mathematical form. Nothing in the world eludes mathematical expression. Why? It is the fundamental epistemological question.

John D. Barrow, a professor of astronomy at the University of Sussex in Britain and an accomplished science writer, takes up the question in his latest book, Pi in the Sky: Counting, Thinking, and Being. Several possible answers suggest themselves: (a) Mathematics is a human invention, like the English language or the game of chess, which has proven particularly useful as a tool for learning about the world; (b) the universe is intrinsically mathematical and we learn mathematical thinking by studying the world; or (c) mathematics exists as a kind of Platonic ideal, outside of nature, and reality, including the human mind, participates in this preexisting order.

Barrow does not choose any one of these alternatives. Indeed, his inability to choose is the point of his book. Although mathematics is the foundation of our scientific image of the world, neither mathematicians nor scientists understand what mathematics is or why it works. At root, our faith in science is religious, says Barrow, and discussions of the nature of mathematics bear striking similarities to traditional theological discourse: "Change |mathematics' to |God' and little else might seem to change."

Pi in the Sky is really two books: a provocative history of mathematics, and a philosophical reflection upon the nature of truth. Of course, the two themes are intertwined, as they should be. Certain readers may be impatient to get to the juicy philosophical questions, and skip the demanding chapters on the anthropology of numbers, but that would be a mistake. It is precisely the way this book approaches philosophy (and theology) by counting on the fingers that gives its conclusions weight.

This reviewer is inclined to believe that any theology relevant to the late-twentieth century must begin with mathematics. This idea may sound shocking, even blasphemous to many theologians. Orthodox theology remains grounded in nonmathematical, pre-Galilean cosmology. The Chain of Being that worked so well as a framework for theological discourse in medieval times has no relevance in modem science, yet theologians cling to the old metaphors with a perverse fervor. For all of their efforts to sound up-to-date, theologians still basically offer us the God of Michelangelo's Sistine Chapel ceiling, a gray-bearded version of ourselves ensconced in some heaven up there in the sky.

What's up there in the sky is pi, says Barrow; that is to say, it is mathematics that provides the mysterious link between the human mind and the cosmos. Physicists investigate the creation (the big bang) with the mathematics of relativity and quantum physics. Biologists study the genetic code as a kind of counting. Neuroscientists and artificial intelligence researchers construct mathematical models of consciousness. They do it because "it works"; the mathematical way of knowing has proven overwhelmingly successful.

The human mind evolved in response to the world in which we live, in the same way as our senses of sight, hearing, and smell. If we are mathematical creatures, it is because the world is in some deeply mysterious sense mathematical. Call it, if you will, the mind of God. The phrase is metaphorical, but so is every other definition of God. This particular metaphor emphasizes the mysterious capacity of the human mind to build mental images of external realities. As a metaphor for God, mathematics is more compatible with the substance and spirit of modem science than is the gray-bearded person of medieval theology.

Consider the following passage which stands as the conclusion of Barrow's book:

Many see the mathematics and the

scientific edifice that is built upon

it as the antithesis of traditional immaterial

conceptions of reality. Yet

at root they are strikingly similar in

the tantalizing nature of their incompleteness.

And this is why we

find the Platonic world [of mathematics]

so strangely attractive - we

have been there before. Our ability

to create and apprehend mathematical

structures in the world is merely

a consequence of our own oneness

with the world. We are the children

as well as the mothers of invention.

If I were a theologian, this is where I would begin constructing my concept of God. Through mathematical thought we have come to know the big bang, the universe of the galaxies, and unfolding infinities of space and time. Through math we have plunged into the heart of matter, and explored mysteries of life and mind. We ourselves are mathematics incarnate - to the cores of our beings. It requires but a simple step to imagine that mathematics allows us a glimpse of the eternal, omnipresent, creative foundation of the world.

I'm not a theologian, but I know a ripping good mystery when I see one. John D. Barrow's book is an excellent approach to the mystery. It is hard to imagine any mystery more likely to provide a bridge across the chasm that has separated science and theology since the time of Galileo. Let the theologians take up where Barrow leaves off.