Corpus Hypercubus

Courtesy of the Association of Christians in the Mathematical Sciences:

Salvador Dali’s painting Corpus Hypercubus (1954) is a fascinating visual representation of a mathematical metaphor for the theological mystery of crucifixion.

Many people are familiar with how to unfold a cube from three dimensions into two as shown in the figures below. Some of the edges of the cube are separated so that the resulting collection of squares can be unfolded into a planar shape. The resulting diagram is called a “net” for the cube. The net is not unique but one common net resembles a cross.

Dali painted the cross in Corpus Hypercubus as a hypercube unfolded into 3-dimensional space. The hypercube consists of eight three-dimensional cubes for hyperfaces. Each hyperface is attached along a two-dimensional square face to six of the other hyperfaces. Just as one can unfold a cube, one can also unfold a hypercube into the shape depicted in Dali’s painting.

Using the analogy of a (mysterious) higher-dimensional object unfolded into three dimensions, Dali depicts the theological mystery of the crucifixion as an event that originated in a higher plane of existence and then unfolded into the world that we perceive. With this understanding, Corpus Hypercubus communicates the idea that though one can discuss the necessity of the Jesus’ sacrifice for salvation or study theological ramifications of the cross, one can only do so by analogy because human nature simply cannot perceive the scope of God’s plan.

More from the ACMS:

Black Swans and God Incarnate

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.

Death in Vain Forbids Him Rise

Listen to these words: Jesus the Nazarene, a man attested to you by God with miracles and wonders and signs which God performed through Him in your midst, just as you yourselves know– this Man, delivered over by the predetermined plan and foreknowledge of God, you nailed to a cross by the hands of godless men and put Him to death. But God raised Him up again, putting an end to the agony of death, since it was impossible for Him to be held in its power.

– Acts 2:22-24

There is love that came for us
Humbled to a sinner’s cross
You broke my shame and sinfulness
You rose again victorious

You are stronger! You are stronger!
Sin is broken
You have saved me
It is written
Christ is risen
Jesus You are Lord of all!

So let Your name be lifted higher!