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Math and Theology

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By Wendy Alsup

(Disclaimer: The views expressed by guest authors do not necessarily reflect those of GodandMath.com. Guest articles are sought after for the purpose of bringing more diverse viewpoints to the topics of mathematics and theology. The point is to foster discussion. To this end respectful and constructive comments are highly encouraged.)

Mathematics is the language with which God wrote the universe.

– Galileo Galilei

This week a student who loves God but struggled with math wrote me wondering what in the world I meant when I linked math and theology. So this is a word of encouragement to her and others on the value of sticking with it. Regardless of the value of math, not everyone will find it easy. This post is not intended to make anyone feel bad if math is hard for them.

I know as a veteran math teacher that few people are ambivalent on math. Some people love it. But many, many people had their worst experiences in high school or college in or around a math course. I’ve often thought that the main problem with math classes is that they are too often taught by people who never struggled with math. When math has only ever come easy for a math teacher, it’s hard to identify with a 9th grader who tears up at the site of a beginning algebra problem.

The most formative moment in my training to become a math teacher came while taking a horrible course called Numerical Analysis my senior year of college. I remember sitting in my dorm, studying notes for another class. I happened to look up and catch a glimpse through the front doors of my Numerical Analysis classroom across the street. I immediately burst into tears. Just looking at the classroom caused panic. My first or second year teaching Algebra, it dawned on me that some of my students felt the exact same way about my math classroom.

For a long time, I did math because it was easier for me than, say, English. I could never figure out what English teachers wanted from me, but in math, there was a right answer to every problem. However at some point, I needed a better reason for spending my life teaching math than the fact it came relatively easy to me. I loved God. I loved His creation. Over time, I started to see how fundamental math was to uncovering and appreciating the nuances of God’s very complicated creation.

Math is a symbolic representation of a real concept. 2 + 3 = 5. But really, it started out as 2 fish plus 3 fish equals 5 fish or something like that. Non-math people often hate word problems, yet word problems are the culmination of the most useful aspects of math. We take some real problem in life we want to figure out. We assign the various parts of the problem numbers and symbols. Then we drop all the words and manipulate the numbers and symbols. Voila! We reach an answer, and we can attach back to the symbolic answer it’s real world meaning. That’s the power of math.

In Genesis 1, God creates His perfect world and crowns it with the creation of man and woman in His image. He then gives them the great task of subduing the earth, having dominion over it. “My creation has gravity, but you can subdue it. My creation has deep oceans, but you can have dominion over them. It has wind, and you can harness it for power. It has fruit trees. You can harvest the seeds and plant them where you wish.” This simple command from God is the foundation of all that is good and right in science, physics, biology, and so forth. And every Genesis-inspired scientific discovery and advance in technology is dependent on some form of mathematics. Fruit trees are planted in parallel rows, spaced evenly apart. Rockets follow the path of a quadratic equation. Ships displace water based on their volume and shape. We take a real problem, assign it numbers and symbols, manipulate it, and discover an answer that unlocks yet another piece of God’s creation for our use.

My all time favorite intersection of math and theology is chaos theory and fractal geometry. These are newer branches of mathematics that give particular insight into the wonder of the mind of God and His incredible creation. Studies in these fields involve millions of numeric calculations we’d never do by hand and have taken off in the last few decades with advances in computer science. The resulting observations point to the existence of mathematical order behind seemingly random events in the Universe. Chaos Theory actually supports, not weakens, the belief in the great Engineer Who planned the Universe and set it in motion governed by mathematical principles.

Contrary to the connotations implied by its name, chaos theory does not eradicate the possibility of order. It does not serve to propagate notions of chaos. Chaos theory is really a science about finding organization in seemingly complex systems. It serves to find order in disorder.

(Library.advanced.org/12170; A. Davenport, S. Kraynak, B. Timko)

Consider this simple illustration of chaos theory. It’s called the Sierpinski Triangle and is an example of finding order in events that seem to be random. Draw a triangle, and pick a point anywhere outside of the triangle. Then arbitrarily pick one of the corners of the triangle (it’s important that the corner chosen be completely random). Find the middle between the first point and that corner. Then mark that as the next point. Repeat this process again and again. The points you plot seem random, but if you plotted 1000 points, you’d begin to see a pattern. Eventually you’d see that all of the points fall into the pattern shown here.

You can play it and see the progression from random dots to clear pattern for yourself here.

God and theology tend to make sense when we see the natural order of creation, when things work as they should, governed by known forces of the Universe. It’s the random, unpredictable events in life that cause us to question God. It’s the chaos. I remember the first time I played the chaos game on that unsophisticated German website. I did it one at a time, but that took too long. Then 10 at a time, but I didn’t have the patience for that one either. It was playing 100 at a time that I started to see it. I was stunned, because the spiritual implications were immediately obvious. Order out of chaos. Meaning out of random nonsense.

The Sierpinski Triangle gave me perspective on Romans 8:28:

And we know that God causes all things to work together for good to those who love God, to those who are called according to His purpose.

Ephesians 1 speaks similarly. Before time began, God had a coherent, clear plan for you and I in Christ. But life appears so random at times, so chaotic. Yet, we have been chosen and our destiny set in motion “according to His purpose who works all things after the counsel of His will (Eph. 1:11).”

Hudson Taylor said it this way.

Learn to think of God as the One Great Circumstance in Whom we live and move and have our being—and all other circumstances as necessarily the wisest, kindest, and best because either ordained or permitted by Him.

Forget math. It’s served its purpose in my heart now. It pointed me to God. Now I’m just in awe of His sovereignty …

The lot is cast into the lap, But its every decision is from the LORD.

– Proverbs 16:33

Wendy Alsup is the author of the site Practical Theology for Women. She is also the author of two books: Practical Theology for Women: How Knowing God Makes a Difference in Our Daily Lives and By His Wounds You Are Healed: how the message of Ephesians transforms a woman’s identity. Wendy is a wife and mom who happens to love math and theology. She occasionally speaks at women’s events, and worships at a small presbyterian church in Seattle.

Harold Camping’s Judgement Day “Math”

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Billboard Advertising Judgment Day

(This is a post from May, 2011. Harold Camping has since updated his prediction to October 21, 2011. So I thought I would re-post my thoughts.)

If you haven’t heard about Harold Camping, here is his basic position: the rapture of the church was supposed to occur today, Saturday May 21, 2011. His reason for believing this? Biblical study and mathematical equations.

Needless to say I take great issue with both his position and his methodology. There is something about all of this that upsets me greatly. That something is what I will try to describe here briefly, even though I am finding it hard to come up with the right words.

First, after reading some of the literature, it is clear that Camping has a misguided interpretation of certain biblical passages. These faulty interpretations lead to an awkwardly constructed end-times theology (referred to as eschatology).I could devote an entire (very long) post to this topic but I don’t think this is the main issue I want to address. If you would like to see a response to Mr. Camping’s position, I recommend reading An Open Letter to Harold Camping Regarding the Church and May 21, 2011. Also, since eschatology deals with God’s plan for the future and can sometimes be difficult to fully grasp or understand (and thus open to misinterpretations of almost every variety), it may be helpful to check out a free class on eschatology offered by Dallas Theological Seminary on iTunesU. I credit this class with helping cement in my mind and in my faith both what eschatology is, and is not, from a distinctly Christian perspective (thanks Dr. K)! In brief:

Eschatology is…

  • The study of the culmination of God’s plan for His creation
  • The study of the completion of God’s work of redemption and recreation
  • Hope, NOT fear

At this time the best course of action is not a theological debate with Mr. Camping, but rather offering loving support to his many followers. Many of them are coming to the realization that they have pledged their allegiance to a false hope. My prayer is that their disappointment and disillusionment will be aimed where it belongs: at a false teacher, and not the true promises of Christ and the Christian faith.

Blessed be the God and Father of our Lord Jesus Christ, who according to His great mercy has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, to obtain an inheritance which is imperishable and undefiled and will not fade away, reserved in heaven for you, who are protected by the power of God through faith for a salvation ready to be revealed in the last time. In this you greatly rejoice, even though now for a little while, if necessary, you have been distressed by various trials, so that the proof of your faith, being more precious than gold which is perishable, even though tested by fire, may be found to result in praise and glory and honor at the revelation of Jesus Christ; and though you have not seen Him, you love Him, and though you do not see Him now, but believe in Him, you greatly rejoice with joy inexpressible and full of glory, obtaining as the outcome of your faith the salvation of your souls.

1 Peter 1:3-9

Second, and I think this is the point I really want to address more, Camping’s key “proofs” (a word which he uses loosely and definitely not in any rigorous mathematical sense) focus on the use of important biblical numbers and his derived equations. You can read the link above to see his methodology in greater detail, particularly the document poorly titled “Another Infallible Proof.” Here is a short summary, thanks to LiveScience:

Here’s the gist of Camping’s calculation: He believes Christ was crucified on April 1, 33 A.D., exactly 722,500 days before May 21, 2011. That number, 722,500, is the square of 5 x 10 x 17. In Camping’s numerological system, 5 represents atonement, 10 means completeness, and seventeen means heaven. “Five times 10 times 17 is telling you a story,” Camping said on his Oakland-based talk show, Family Radio, last year. “It’s the story from the time Christ made payment for your sins until you’re completely saved.”

I used this quote because I believe it refers to Camping’s method as what it is: numerology and not mathematics. Whereas mathematics is very logical, providing a clear sequence of steps to a solution, numerology is a practice that ascribes special meaning to certain numbers and thereby manipulates them freely in a manner that can vary from person to person. The sad thing is I don’t think the average person knows the difference.

Since most people have an aversion to mathematics, even to the point of boasting that it was subject they did poorly in, they accept mathematical statements and “proofs” with blind faith rather than a critical eye. Camping is not the first to predict the apocalypse with the use of numbers and he certainly won’t be the last. But his case should serve as a reminder to us in the Christian/Mathematics community about the importance of our work in educating people both in biblical understanding and mathematical practice.

I don’t know how many of Camping’s followers would have been spared the pain and heartbreak of unfulfilled expectations by a better understanding of mathematics. But knowing that the pain they experience could greatly damage their relationship with Christ and breed skepticism in the truth of the biblical message, if just one more person could be spared that fate, then our work is worthwhile.

Black Swans and God Incarnate

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Image from Black Swan Ministries

Black Swan as a term derives from a Latin expression that characterizes something as being  “a rare bird in the lands, and very like a black swan.” When the phrase was coined, the black swan was presumed not to exist. The importance of the simile lies in its analogy to the fragility of any system of thought. A set of conclusions is potentially undone once any of its fundamental postulates is disproved. In this case, the observation of a single black swan would be the undoing of the phrase’s underlying logic, as well as any reasoning that followed from that underlying logic.

This Latin phrase was a common expression in 16th century London as a statement of impossibility. For a long time Europeans believed that all swans were white. That notion only held true as long as their discovered world contained only white swans. At the time,  all historical records of swans reported that they had white feathers. In that context, a black swan was impossible or at least nonexistent. Then Australia was discovered and along with it, the existence of the black swan. The term metamorphosed to connote that a perceived impossibility might later be disproven.

Upon this event, perceptions of the world and what swans were had to change.

A Black Swan event is any event that occurs outside the realm of expectations. Black Swan events were characterized by Nassim Nicholas Taleb in his book, The Black Swan. Taleb regards almost all major scientific discoveries, historical events, and artistic accomplishments as “black swans”—undirected and unpredicted. Taleb asserts in the New York Times:

What we call here a Black Swan (and capitalize it) is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives

Black Swan seems to be a relatively apt statistical description of the incarnation. When gathering resources for this post I even came across Black Swan Ministries who also recognize this connection. I’d briefly like to address Taleb’s three criteria for categorizing something as a Black Swan (with a slight change in wording on the last point).

Rarity

Obviously the incarnation is an extremely rare event: having occurred once in history. To further discuss this point, I’d like to make mention of The Logic of God Incarnate, a work by Tom Morris.

This work is a response to John Hick’s Myth of God Incarnate. Hick attacks a Chalcedonian Christology which affirms that Jesus is fully divine and fully human: two natures, one person. Hick’s objection falls along these lines: God is omnipotent, omniscient, omnibenevolent, eternal, immutable. Humans are limited in power, limited in knowledge, limited in goodness, temporally constrained, changeable. God is perfect. Humans are imperfect. Therefore it is logically incoherent to say that Jesus is God incarnate – no being could be both perfect and imperfect, both fully divine and fully human.

On Hick’s view it is not possible to have the two natures of the divine and human because they comprise incompatible attributes. If his premises are right, then his argument is true. But since the conclusion of his argument is false, there must be something wrong with his premise.

Hick’s argument begins by assuming being perfect is essential to divinity. God could not have failed to be perfect. This is true.

His argument also assumes that imperfection is essential to humanity, but is it? Morris argues this is wrongheaded. The essence of a “thing” is the set of properties which are individually necessary and jointly sufficient for being that thing; if you lack any one of those properties then you are not that thing. Hick assumes that the each of the properties listed under being human are part of the set of properties that are essential to being human and this is what Morris attacks.

Morris makes a difference between nearly universal properties and essential properties. Nearly universal property is one that almost every member of a kind possesses, but isn’t necessary for that thing. Case in point: having white feathers was a nearly universal property of swans, but it wasn’t essential to being a swan. Being limited in power, limited in knowledge, limited in goodness, etc. are nearly universal properties: Christians believe there is one human being in history who was human but lacked the property of being limited in power, limited in knowledge, limited in goodness, etc. Jesus of Nazareth.

Impact

To Christians, this category goes without explanation. But let’s try anyway…

As purposed by God, the eternal Son of God (Isa 9:6; John 1:1-2; 8:58; Col 1:17; Heb 1:10-12; Rev 1:8; 21:6) came into this world that He might manifest God to men, fulfill prophecy, and become the Redeemer of a lost world. To this end He was born of the virgin, and received a human body and a sinless human nature (Luke 1:30-35; John 1:18; 3:16; Heb 4:15). He was completely, 100% deity (John 1:1, 18; 10:30-33; 20:28; Rom 1:3-4; 9:5; 1 Cor 15:45-49; Phil 2:6-8; Titus 2:13; Pet 1:1). He was also completely, 100% human (Matt 13:55; John 1:14, 19:5; 1 Tim 2:5; Heb 2:14).

Jesus Christ was incarnate. The eternal second person of the Godhead entered space and time and became man for us and for our salvation (John 1:1, 14; 2 Cor 8:9; Phil 2:6-8; 1 Tim 3:16). He was miraculously born of a Virgin and the Holy Spirit (Matt 1:18-25; Luke 1:26-38). He led a sinless life (2 Cor 5:21; 1 Pet 2:22; 1 John 3:5) of perfect obedience to the Father (John 6:38; Rom 5:18-19; Phil 2:8). He spent His life preaching, teaching and performing miraculous wonders to evidence His divine mission and to proclaim the new advent of God’s kingdom (Matt 4:23-24; 7:28-29; 9:35-36; John 20:30-31). In the fulfillment of prophecy, He came first to Israel as her Messiah-King, was rejected of that nation (John 1:11; Acts 2:22-24), and gave His life as a ransom for all (1 Tim 2:6).

Jesus Christ was crucified as a substitutionary atonement for sin. On the cross in Christ, God bore the just penalty for the world’s sin, satisfied His justice, and thus made a way for reconciliation (Isa 53:4-12; John 3:15-17; Rom 3:21-26; 5:6-11; Heb 2:14-17). It was necessary for Him to be both true God and true man in order to redeem (1 Tim 2:5). As man, He represent us (Heb 4:15) and as God He saves us (Heb 7:24-25).

Belief in the divinity of Christ is a prerequisite of salvation (Rom 10:9; 2 Peter 1:3) and to deny His humanity is to be labeled the antichrist (2 John 7).

Retrospective Recognition

Gospel writers quote the Old Testament to show how Jesus in his life and ministry fulfilled the Old Testament Scriptures (Mat 21:4-9; Mar 11:7-10; Luk 19:35-38; Joh 12:12-15). Matthew includes nine additional proof texts (1:22-23; 2:15, 17-18, 23; 4:14-16; 8:17; 12:17-21; 13:35; 27:9-10) to drive home his basic theme: Jesus is the fulfillment of the Old Testament predictions of the Messiah.

Jesus himself makes this clear:

Beginning with Moses and with all the prophets, (Jesus) explained to them the things concerning Himself in all the Scriptures (Luke 24:27).

All the Scriptures center about the Lord Jesus Christ in His person and work in His first and second coming, and hence no portion, even of the Old Testament, is properly read, or understood, until it leads to Him.