Mathematical Theology by Sarah Voss
Although the concept can be traced back to the ancient Greeks, the term "mathematical theology" is relatively new. Fifteen years ago, when I was teaching calculus at a small Midwestern college and my career in ministry was still barely a dream, I struggled to find anything in the literature that would even justify the term.
Today things are different. Today we find the occasional book bearing an explicitly mathematic-theological title,(1) and we find numerous works where the relation between math and theology is indirect and metaphorical, but no less intent.(2) Today mathematical physicists and other scientists often make direct statements relating God to mathematical concepts.(3) Today even the prestigious Scientific American recognizes the term, albeit somewhat less than enthusiastically.(4)
So, what is mathematical theology, anyhow? What good is it? Why should we take any note of it?
The short answers to these questions are simple. Mathematical theology is a study of the Divine which in some way draws on mathematics. It's good because it opens our minds (and maybe our hearts) to new possibilities. And, thirdly, it brings hope.
The longer answers are too involved for this essay, but perhaps I can point you in a direction. In the process, maybe you'll become intrigued by how much mathematics counts in the theological world (pun intended).
First, more on the nature of mathematical theology. When guests enter our home, they are often startled to find a large mannequin sitting on our sofa. "Jonesy" greets our visitors in part because she's unusual and in part because she's wearing a T-shirt that pretty much sums up (humorously, but also seriously) what I mean by "mathematical theology." Unless I draw their attention to it, most people overlook her T-shirt inscription:(5)
and God said
and there was light!
The implication, of course, is that God speaks in mathematics in all creation. This idea is old. The Pythagoreans held much the same view, believing that "Number is all" and that "the harmony of the spheres" depended upon right relationship between those numbers.
Through most of the years since the Pythagoreans, many individuals have held variations on this same theme. Only in the last couple of hundred of years did 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.
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. The other way is through metaphor. Most of the book titles I cited earlier (footnotes 1 & 2), are also metaphors drawn from mathematics and applied to theological and spiritual notions. For example, the universe has been said to work like a mathematical hologram and theology is in some manner like mathematical chaos theory.
It has only been in the last decade or so that our society has 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." Mathematical theology involves both straight calculation and mathaphors, but it leans more heavily on the latter.(6) I'll say more about one such holy mathaphor when we talk about "hope."
What good comes from examining holy mathaphors? Elsewhere,(7) I have explored ten ways in which metaphors drawn from mathematics are impacting us. In short, these analogies are
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changing our metaphors for God. challenging our human role in the universe. helping us accept ambiguity. revamping our understanding of the one and the many. revising our thoughts about free will and determinism. moving us toward pluralistic, multi-world views. pushing the envelope on what consciousness is. altering our expectations for after-life. offering the hope of a more compassionate future. encouraging faith perspectives that are always incomplete and in process. |
While a case can be made for all of these statements (and probably others), the point here is that ideas drawn from mathematics greatly extend our spiritual world-views. 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.
Mathematics, it should be noted, has long been a reservoir for radical change. Consider holography, for instance. Twenty years before the invention of the laser which is essential to producing holographic images, the theory of holography was nonetheless complete and available in the mathematics textbook. Nor is this an isolated example. Over and over we first become aware of valuable new ideas through the language of mathematics.
To some, drawing analogies from math and the hard sciences is a suspect process. Some fear that extrapolating scientific concepts to a non-scientific 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.(8) Yet to prematurely close our minds to the exciting possibilities that mathematical analogies can bring to such non-mathematical disciplines is, in my opinion, a sorry tragedy.
A tragedy, in fact, is what my favorite mathematician's life turned out to be when his mathematical discoveries were labeled "heretical" by his more successful colleagues. The man was Geog Cantor. He 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. A deeply religious man himself, Georg Cantor became a mathematics professor at what he considered a "second-rate" University of Halle; forever after Cantor chafed under the constant and often mean-spirited criticism of his own former teacher and very 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 in the space of his 73 years, Georg Cantor virtually single-handedly contributed to the world what is now known as transfinite set theory. This theory, which introduced the notion of the actual infinite,(9) revolutionized mathematics. Although Cantor did not live to see this revolution happen, he never doubted that it someday would. He had a quasi-religious self-justification for his work, believing his ideas had come to him as a messenger of God. In the hindsight of the century which has passed since his great discoveries, perhaps it is time to wonder if he was right.
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, with some being larger than others. Furthermore, the ones we think should be smaller or larger than others are not necessarily so. The counting numbers {1,2,3,4,...} would seem to most of us to be a larger set than the set of even counting numbers {2,4,6,8,...}, but Cantor showed that, since they could be put into one-to-one 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 the unusual notions that Cantor presented the world. In the Cantorian world there also exists an entity which 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 is interesting is to take these characteristics of Cantorian set theory and say, "What happens if something like this occurs in an area other than mathematics?" In particular, what happens if something similar to these ideas works in our theological and spiritual realms?(10)
One of the possibilities that arises from this reflection is a new notion of pluralistic religion. Until now, there have been three ways of responding to the fact that we humans have more than one religious understanding. Whose faith is "right"? The religious exclusivist says, "Mine is." The inclusivist says that lots of them appear to be right, but that they are all included in one "real" way to salvation or liberation. The traditional pluralist says, "You can have yours and I'll have mine, and that's just fine."
Now, with a Cantorian perspective, we can consider that the part may have the power of the whole. When we use Cantorian set theory as a metaphor for a new way of thinking about contemporary religious pluralism, we find a wonderful precedent for accepting the "unacceptable" contradictions inevitable in any discussion of "right" faith(s). In other words, many different religious traditions are "equivalent" to the one whole truth.(11)
Cantorian mathahors give rise to the idea of a "religion which contains all religions."(12) In spite of its initial sense of grandiosity, this mathaphor suggests that such an all-encompassing religion 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 one tool for doing the exploration. If we use it, it promises to stretch us, to challenge us, to offer us hope.
A Strange Metaphor(13)
Cantor Religion
The lamps are different, but the Light is the same.
-Jalalu'l-Din Rumi (13th century)
In the room my mind
sit many different lamps.
The lamp of Christianity, an old oil
lantern, recently wired for electricity,
all the latest scientific gadgets;
when I approach,
it springs on automatically.
I trust this lamp:
it was the light in the hallway
when I was small and afraid of the dark.
I use this lamp even now, oh,
not all the time... but
when I have moments free,
in fancy Gothic cathedrals
or tiny country chapels
smelling of warm waxed wood.
The Eastern lamp is hand-crafted copper,
gondola-shaped, wick lit
Aladdin's lamp, it charms
with ancient promise
of untold treasure, I must
but rub it and attend, oh
there, can you see?
The earnest, handsome Buddhist
from Sri Lanka
who resides in the basement of my house,
who laments that the young women
in this country don't care much
for the color of his skin. Me?
I'm old. I love the rich
blue-black glow which lives
in the light of this lamp.
The Jewish lamp, really seven candles
welded together. The one
in the room my mind
is highly stylized. Contemporary.
Unorthodox. You can't make out much
in its soft flame, mostly abstract
markings, maybe it makes a difference
if you read Hebrew. Still, I love
to search the shadows it forms
for things familiar and strange,
as order out of nothing
in only seven days
and bushes that burn
with the Sabbath light
now and forever Amen.
In this land where I was born
are Native lamps; mine
a gray clay
artifact, discovered lying
by a tattooed Erie Indian
whose body was dug from a pit
and whose spirit finds me yet today
when I dig my bare toes
deep into the earth
and listen to the breath
of the wind.
All these and more are the lamps
which rest in the room
my mind, yet the one
I cherish most is the chalice
that ignites my heart,
for I see in its light
the room my mind
with all its magnificent lamps,
among them the chalice
that ignites my heart
which shows the room my mind
Dear God of many iterations,
may all their light shine on
and on and on, like a Cantor set
transcending.