Mathematical Theology
by Sarah Voss
Guests in our home are often startled to find a large mannequin sitting on our sofa. Unless I draw their attention to it, most people overlook the inscription on Jonesy's Tshirt, which pretty much sums up (humorously, but also seriously) what I mean by "mathematical theology":
And God said,
and there was light!
The idea that God speaks mathematically is very old. The ancient Pythagoreans, for example, believed that "Number is all" and that "the harmony of the spheres" depended upon right relationship between those numbers. Only in the last few hundred years has the dissociation between the spiritual realm and the world of mathematics become a requirement for scientific excellence. Fortunately, this false separation is now coming to an end.
A few recent books—like Chaos Theology and Quantum Theology—explicitly bring mathematics to theology. Other recent titles find religious dimensions in mathematical ideas, like The Holographic Universe, The Age of Spiritual Machines, or Sacred Geometry. So, what is mathematical theology? Why should we take any note of it?
Mathematical theology is a study of the divine that in some way draws on mathematics. It opens our minds (and maybe our hearts) to new possibilities, and in so doing it brings hope.
God seems to speak in mathematics in two basic ways. One is through the precision of numerical calculation, logical proof, and all the other blessings associated with mathematics in the "hard" sciences. Science can be thought of as a way of interpreting God's revelation found in nature.
The other way is through metaphor. Only in the last decade or so has our society started to acknowledge the existence of mathematical metaphors. I call such metaphors "mathaphors"; when they apply to the spiritual realm, I call them "holy mathaphors."
Ideas drawn from mathematics can greatly extend our spiritual worldviews. Such mathematical notions are suggestive, not conclusive. But in those suggestions lie the makings of new ways of interacting with each other, of healing, of understanding God. In a world that is often spiritually fractured and hurting, we can look to mathematical theology for the seeds of new hope.
To some, drawing analogies from math and the hard sciences is a suspect process. Some fear that extrapolating scientific concepts to a nonscientific discipline such as religion or philosophy will cloud the truth of our spiritual insights and lead to misunderstanding of the science involved. Truthfully enough, this can happen. Yet to prematurely close our minds to the exciting possibilities that mathematical analogies can bring to such nonmathematical disciplines is, in my opinion, a sorry tragedy.
My favorite mathematician's life turned out to be just that—a tragedy—when his mathematical discoveries were labeled "heretical" by his more successful colleagues. Georg Cantor was born in St. Petersburg on March 3, 1845, to a father who converted to Christianity from Judaism and a mother who was Roman Catholic. Deeply religious himself, Cantor became a mathematics professor at what he considered the secondrate University of Halle; forever after Cantor chafed under the constant and often meanspirited criticism of his former teacher, the influential mathematician Leopold Kronecker. These vicious attacks and the general lack of recognition of his mathematical triumphs contributed to Cantor's eventual nervous breakdown. He died in a mental hospital in Halle in 1918, a broken and bitter man.
Yet Cantor virtually singlehandedly contributed to the world what is now known as transfinite set theory. This theory, which introduced the notion of the "actual infinite," eventually revolutionized mathematics.
Cantor's work involves numerous radical conclusions about infinity and the continuity of numbers. For example, he showed that there are different sizes of infinities. Furthermore, the ones we think should be smaller or larger than others are not necessarily so. The set of counting numbers {1,2,3,4, . . .} would seem to most of us to be larger than the set of even counting numbers {2,4,6,8, . . .}, but Cantor showed that, since they could be put into onetoone correspondence with each other, they have an unexpected equivalency. Thus, in an odd way, a part of a set is actually equal to the whole of it. Another way of saying this is that, in mathematics, the part may have the power of the whole.
This is only one of Cantor's unusual notions. In the Cantorian world there also exists an entity that is infinitely many yet simultaneously infinitely sparse; the infinite both is and is not infinite; incompleteness is intrinsic to the structure of the system.
What happens if something like Cantorian set theory applies to an area other than mathematics? Could it describe a theological or spiritual truth as well?
When confronted by the variety of religious traditions in the world, people tend to ask, "Whose faith is right?" The religious exclusivist says, "Mine is." The inclusivist says that lots of religions appear to be right, but that they are all included in one "real" way to salvation or liberation. The pluralist says, "You can have yours and I'll have mine, and that's just fine."
A Cantorian perspective offers another option: The part may have the power of the whole. When we use Cantorian set theory as a metaphor for thinking about contemporary religious pluralism, we find a wonderful precedent for accepting what might appear to be unacceptable contradictions between religions. In other words, many different religious traditions may independently be "equivalent" to the one whole truth.
Cantorian mathaphors give rise to the idea of a "religion that contains all religions." In spite of its initial sense of grandiosity, this mathaphor suggests that such an allencompassing universalism is still just one more religion, with both its good and flawed aspects.
Cantorian mathaphors also offer new possibilities in our understanding of an "infinite" God. For example, might God in some way be both infinite and bounded? Might God be "actual" rather than (or as well as) "potential" in nature? And what are the implications of such a God for our lives?
These and other questions are ripe for further examination. Mathematical theology gives us new tools for our exploration. If we use them, mathematical theology promises to stretch and challenge us, offering us hope.
The Rev. Dr. Sarah Voss is consulting minister at the First Unitarian Church of Sioux City, Iowa. A former mathematics instructor, she is the author of What Number Is God? and Zero: Reflections about Nothing. An expanded version of this essay will appear in a collection of essays in honor of Sir John Templeton, founder of the philanthropic religionandscience research foundation. Voss's Web site is www.pizine.com.
