The Language of Mathematics in Theology

By James.B

ALBUQUERQUE, NEW MEXICO (ANS - December 15, 2016) -- Let me be up front: I hated mathematics during my junior and senior high school years. The lowest grades I received in school were in math, and I often worked hard to get out of my math classes ("Mom, I have a headache" was a common call). But something changed: with the help of a tremendous math teacher in college, and with some hard work, I began to love math. Let me repeat: I love math; but this doesn't mean that I'm good at it. I'm not.

So what was it that provoked me to go from hate to love? The answer is fairly complex. But in its simplest form I began to see that math is something that is indispensible to the bank of common, acquired knowledge, a form of understanding that humans share that is practical and elegant. Math is worthy of wonder, a common language that humanity speaks, and the closest approximation to how the universe works. True, math has practical symmetry and a fastidious nature, but it also holds mystery. And the more I read about math (not necessarily doing it) the more I respect and revere the field.

And I'm well aware of the various philosophies of mathematical thought, particularly as it relates to Platonic (math's existence is independent of us and our language, thought, and practices) and Aristotelian (math is based on the material universe), but I think both schools of thought can agree that math is beautiful.

What many people don't realize is the importance mathematics and it's cousin, geometry, has on theology. From the earliest theological discourse to modern usage through allusion and illustration, math has given theologians the same approximation to God's Person that scientists look for in the universe.

The earliest Christian theologians to use numerical concepts as a theological language were individuals such as Ignatius of Antioch (c.100), Justin Martyr (c. 155), Irenaeus (c. 160), Theophilus of Antioch (c. 185), and Tertullian (c. 200). Collectively, the pre-Nicene thinkers (the Nicene Council occurred in 325 AD) focused on the Trinity -- the three-in-one interrelation and nature of God's being: Father, Son, and Holy Spirit.

Relying heavily on Greek thought (Platonic and to a lesser degree, Aristotelian), these men -- though not formulating exact equations -- used mathematical verbiage to make their points. As an example, Justin "argued that Jesus was not only in name distinct or the Father, as the light is from the sun, but was 'numerically distinct' too" [1]. It seems that in explaining the Trinity the theologians had a fundamental understanding of a tri-unity (later represented by a triangle), requiring a general understanding of numbers and geometric shapes.

Even more than the orthodox believers, non-orthodox Christians used logic and geometry to make their theological points. And according to historical theologian, J.N.D. Kelly, they "scandalized the faithful by their interest in logic and geometry, and the deference they paid to Aristotle and Euclid ..." (Kelly, pg. 116). And though the early Christians didn't always agree with one another and at times used other non-numerical illustrations to discuss the nature of the Trinity (such as the sun, light, etc.), mathematical concepts were used to help bring a specific mathematical understanding to theology.

It wasn't until Augustine of Hippo (c. 380) that a more concentrated exposure to mathematical concepts was introduced. But Augustine's thought comes with a hitch. On one hand he promoted learning, likening mathematical concepts to knowledge about God, as this short passage -- as summarized by Adam Drozdek-- testifies:

"First, infinity is an inborn concept which enables any knowledge. Second, infinity can be found in the purest form in mathematics, and thus mathematics is the best tool of acquiring knowledge about God. Third, God is neither finite nor infinite and his greatness surpasses even the infinite." [2]

But on the other hand, Augustine -- like some of his predecessors -- was leery of the abuses in mathematics due to its use by non-orthodox and heretical groups, stating,

"For this reason, the good Christian should beware not only numerologists, but all those who make impious divinations, above all when they tell truth. Otherwise, they may deceive the soul, and ensnare her in a pact of friendship with demons." [3]

Nikolaus Cusanus 01It appears that Augustine liked mathematics, but did not approve of those who used numbers to concoct false prophecies and the like.

By the time of Anselm of Canterbury (c. 1075), the use of mathematical constructs, largely through logical presentations -- the basis of syllogisms, was in full effect. From Anselm's work we find an argument for God's existence called the ontological argument. Anselm's argument was later given a cleaner mathematical construct by the mathematician and logician, Kurt Gödel (1906-1978), and recently verified to be a confirmable equation by German computer scientists -- [4].

In the high Middle Ages the interdependence of math, reason, and faith was gaining great ground, implemented in various regions across Europe due to the influence of the liberal arts approach to education. The seven liberal arts consisted of the Trivium (grammar, logic, and rhetoric) and the Quadrivium (math, geometry, music, and astronomy). With increased learning came increased integrated knowledge, a means to understand and blend various academic fields together into an omnibus (a compilation). Hence, theology used mathematical language more readily.

From roughly 1200 AD on, math was pivotal for theological discussion. Beginning with Albertus Magnus (c. 1200-1280) through his student, Thomas Aquinas (c. 1225-1274), to Robert Grosseteste (c. 1175-1253) and Roger Bacon (1220-1290), mathematical concepts were used in both science and theology.

But it was the work of Johannes de Sacrobosco (c. 1221) and Nicholas of Cusa, also referred to as Nicholas of Kues and Nicolaus Cusanus (1401-1464) that mathematics came to a prominent role in theological discourse. In Cusa's work, De Docta Ignorantia (On Learned Ignorance), he used, as science writer, John Freely writes, "mathematics and experiential science in his attempts to determine the limits of human knowledge, particularly the inability of the human mind to conceive the absolute, which to him was the same as mathematical infinity."

From this point forward, math and theology went hand and hand with people such as Johanees Kepler (b. 1571), Blaise Pascal (b. 1623), and Isaac Newton (b. 1642). Math became both a theological and scientific language. And continues today through such individuals such as Oxford mathematicians John Lennox, William Dembski, and others.

As you can see, I'm intrigued by the interrelationship between theology and math. So it comes as no surprise that I keep my ears open for news and events that involve mathematics.

One recent event is the Santa Fe Institutes' (an organization dedicated to research and complex systems) announcement of a mini-conference to determine if the equation P = NP is correct (the equation was first postulated by Kurt Gödel in 1956) [5]. P stands for polynomial time; NP stands for nondeterministic polynomial time [6]. And as odd as it may sound, I've been a fan of P = NP for years, even incorporating the equation in some of my Pop-inspired watercolor paintings (something I'm much more acquainted with than math). And I even dream that maybe, just maybe, someone will be able to solve the equation in my lifetime.

PNPThe conference in Santa Fe, New Mexico lists the abstract as follows: "P versus NP is the question of whether brute-force search algorithms can always be simulated by significantly more efficient algorithms. Given that thousands of computational problems in science, business, mathematics, medicine, engineering, and throughout society are in NP, the P versus NP problem is perhaps the most important problem in all of mathematics and compute science. Even if it turns out that the answer is "no" (as most researchers expect), a proof of this fact is expected to shed a bright light on our understanding of computing and the universe."

These are heavy words. Something that can change the universe is, obviously, full of grand potential. And though I'll never be able to formulate an algorithm that could incorporate such an elaborate complex system, at its core P = NP calls out for symmetry, elegance, even oneness -- if it turns out to be true. Like those before me, I liken the search for mathematical understanding as a quest to discover the thoughts of God -- His simplicity (unified nature, without parts). For me -- as complex P = NP is -- it is simple. Take the repeated number (what I like to call an "icon" number) for either P or NP and divide it by P or NP and you get the number one: P = N/N or (P/P) =1. Of course the "icon" number is metaphysical in that it is unknown, beyond the physical -- an exact image of that which is undetermined, incorporating untold probabilities (hence the need for an algorithm). The "icon" number would need to be the sum total of all numerical qualities -- both external and internal -- extant in the property. But if you were to know the possible number for NP or P, then a divided, repeated "icon" number would reduce it to 1. As you gather, there is lots of theology-speak in my mental processes.

SantaFeInstituteBut all this talk concerning P = NP is just gibberish. I really don't know what the heck I'm talking about. But why I mention all of this mental murmuring is that the mathematical thought I'm working through is a process of mystery, an enigmatic quest to understand and take hold of that which I can't fully comprehend. And as magnificent as mathematics is, it really is human process of trying to apprehend the divine, a confluence of physical and the metaphysical.

Seeking God through His handiwork is a quest worth taking. And because of this, I say, add on, multiply more, and compute until we see God face to face (Coram Deo). And then I'm sure we'll have all eternity to learn bigger, better, and brighter equations that will continue to confound our senses, discovering the intricacies of God's creation in the universe and beyond.

And if you ask me, it's a fascinating way to spend eternity, uncovering the majesty, eloquence, and wonder of God [7].

1) See JND Kelly, Early Christian Doctrines, chapters 4 and 5.

2) http://rationalcatholic.blogspot.com/2012/05/mathematics-handmaiden-of-theology.html 

3) http://cantanima.blogspot.com/2006/03/augustine-and-mathematicians.html 

4) http://www.breakingchristiannews.com/articles/display_art.html?ID=16469 

5) https://www.santafe.edu/ and https://www.santafe.edu/events/geometric-complexity-theory 

6) https://en.wikipedia.org/wiki/P_versus_NP_problem 

7) https://acmsonline.org/home2/wp-content/uploads/2016/05/McIntyreReflections.pdf 

Photo captions: 1) Kurt Godel. 2) Nicholas of Cusa. 3) P = NP. 4) Santa Fe Institute. 5) Brian Nixon.

BrianNixonAbout the writer: Brian Nixon is a writer, musician, artist, and minister. He's a graduate of California State University, Stanislaus (BA), Veritas Evangelical Seminary (MA), and is a Fellow at Oxford Graduate School (D.Phil.). To learn more, click here: http://en.wikipedia.org/wiki/Brian_Nixon.

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