How Mathematics Influences Faith

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.

Christianity: Always More Than Thinking, Never Less

joshwilkerson1 Comment

A student stopped me in the hallway the other day and posed what he thought was a nice brainteaser:

A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

After doing the basic algebra:

Bat + Ball = 1.10

Bat = 1 + Ball

Substituting:

1 + Ball + Ball = 1.10

2Ball = .10

Ball = .05

I responded that the ball costs $0.05.

The student seemed disappointed that I had solved the puzzle using math of all things. He objected that I shouldn’t have thought about it but just answered with the first thing that came to my mind (…a little glimpse into the thought process of my students).

This response was expected. What he said next was not. “I guess you are less likely to believe in God.”

Wait…WHAT?!

“It’s true,” he said. “I read it in an article.”

I thought that couldn’t possibly be accurate…but it is. Thank you internet.

Intuitive Thinking May Influence Belief in God

Here are the highlights:

In a series of studies, researchers at Harvard University found that people with a more intuitive thinking style tend to have stronger beliefs in God than those with a more reflective style…”We wanted to explain variations in belief in God in terms of more basic cognitive processes,” researcher Amitai Shenhav said. “Some say we believe in God because our intuitions about how and why things happen lead us to see a divine purpose behind ordinary events that don’t have obvious human causes. This led us to ask whether the strength of an individual’s beliefs is influenced by how much they trust their natural intuitions versus stopping to reflect on those first instincts.”

The research was published online in the Journal of Experimental Psychology: General. The study from the Harvard University Psychology Department was conducted by Shenhav, a doctoral student; post-doctoral fellow David Rand, PhD; and associate professor Joshua Greene, PhD.

In the first part of the study, 882 U.S. adults, with a mean age of 33 and consisting of 64 percent women, completed online surveys about their belief in God before taking a cognitive reflection test. The test had three math problems with incorrect answers that seemed intuitive (like the problem above which has an “intuitive” answer of $0.10)…Participants who had more incorrect answers showed a greater reliance on intuition than reflection in their thinking style.

Participants who gave intuitive answers to all three problems were 1 ½ times as likely to report they were convinced of God’s existence as those who answered all of the questions correctly.

First of all, there is clearly a problem in defining intuitive (or at least measuring intuition) as answering incorrectly to a series of math questions. Intuition, as defined by dicitonary.com: direct perception of truth, fact, etc., independent of any reasoning process (emphasis added). I am uncertain then how answering incorrectly shows a direct perception of truth.

I get the impression that the real claim of this study is that people who respond without thinking tend to accept the idea of religion more than those who analyze information that is presented to them.

This reminded of me of the following comic:

For some people this is the “religious” way of thinking: just believe, don’t analyze. What makes the comic humorous is that this is an obviously flawed approach to mathematics. I contend is an equally flawed approach to faith.

The title of this post is a favorite saying of mine from our former pastor in Dallas, “Christianity is always more than thinking, never less.”

There is great danger in putting religion a step below thinking. I am reminded of a segment on NBC Nightly News, “Show of Faith,” from June 23, 2008. Video Courtesy of NBC. While there have been numerous news segments to survey and comment on the religiosity of Americans, this one stood out to me because of one sentence by Rev. Eugene Rivers (emphasis added):

In some cases, because the American public is not terribly theologically literate, they hold contradictory views because they haven’t thought deeply, or been taught deeply, about their faith tradition.

Not examining one’s religious beliefs tends to lead toward contradictory or false beliefs.

Scripture makes this point itself. The book of Romans clearly explains how we are created with an intuition toward the things of God, but that intuition becomes marred by sin. What we need is a renewal of this intuition, a renewal of our minds, not for the purpose of blind acceptance but for testing and approving the will of God.

For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God or give thanks, but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools, and exchanged the glory of the incorruptible God for an image in the form of corruptible man and of birds and four-footed animals and crawling creatures (Romans 1:18-23).

Do not be conformed to this present world, but be transformed by the renewing of your mind, so that you may test and approve what is the will of God– what is good and well-pleasing and perfect (Romans 12:2).

We are charged then to approach our faith as the Bereans. In the book of Acts, the Bereans are praised for examining the Gospel message:

The brothers sent Paul and Silas off to Berea at once, during the night. When they arrived, they went to the Jewish synagogue. These Jews were more open-minded than those in Thessalonica, for they eagerly received the message, examining the scriptures carefully every day to see if these things were so. Therefore many of them believed, along with quite a few prominent Greek women and men (Acts 17:10-12).

As a math teacher I feel that I am charged with teaching students to think well and reason correctly.

As a theologian I feel that I am charged with teaching believers to think well and reason correctly.

We need thinkers. We need teachers of thinkers.