The Mathematics of Holy Saturday
God is infinite and eternal, says the Abrahamic monotheist. God becomes finite and temporal, says the Christian. God becomes nothingness, again says the Christian. God becomes finite and eternal, says the Christian once more. Then, finally, God, the finite and eternal, reunifies with the infinite and eternal.
It’s an interesting tale at the least. But mathematically, it’s beautiful. This essay uses a lot of Christian jargon which I will do my best to make meaningful for reader. If one keeps digging, the marvelous ideas in traditional Christian theology will reward those inclined to philosophizing about mathematics. While I won’t be able to tie up all loose ends within this essay, at the very least, I hope what I have written will spark imaginative thought about the relationship between infinity, finiteness, zero, and God.
Loosely, the traditional 30,000 foot view of the narrative of Christ is:
1) Pre-Incarnation
2) Incarnation
3) Crucifixion
4) Burial
5) Resurrection
6) Ascension
With a bit more explanation:
1) The Christos is the Logos of God and resides in an eternal, heavenly realm.
2) The Christos becomes a frangible human.
3) The Christos is killed on the cross.
4) The Christos, while dead, defeats death through his power.
5) The Christos raises to life again, but now in eternal glory.
6) The Christos ascends as a human, returning to the eternal, heavenly realm.
Central to Christianity is the belief that Jesus the Christos, or saving force-being, is “Lord of the Universe.” What in the world does that mean? Well, it means a lot of things. For one, it means that everything, from sub-atomic quarks to human quirks, are moving through narrative of the Christ. Again, what in the world does that mean? It’s like saying that the story of Jesus is the story of everything: the underlying laws of physics are governed by the laws of the Christos; the patterns of evolutionary biology are guided by the nature of the Christos; the tides of human politics are overseen by the kingship of the Christos. In this framework, the Christos is the leader of everything.
For many, this perspective is markedly different from what they’ve heard in churches. It’s much bigger and encompassing than the “personal Lord and Savior” version of Jesus. Yet, it is one that is central to historical Christianity and is copiously described throughout Judeo-Christian sacred texts. If the story of Jesus were truly the centerpiece of all existence, what might be the implications?
Now we turn to mathematics.
Something essential to Christianity is that humans are not sufficient on their own. Everything a person does is imperfect, no matter how hard he or she tries; nothing they does is guaranteed success. Likewise, no thing is sufficient on its own. As one of my pastors liked to describe it, “Life is messy.” Another way of saying this is, “Entropy has marred everything.” Humankind, and all of finite physicality, therefore needs something else, something that is perfect, to make it perfect.
A natural consequence of this idea is that perfection is like an infinite slope, inaccessible by human efforts alone. Something I found in my eleventh grade AP Calculus class beautifully taught me this perspective. One of the early chapters in my textbook dealt with limits of functions. A section of this chapter introduced the concept of discontinuous but differentiable functions. I turned the page and one image gripped my heart: a vertical asymptote. In that image, I felt my personal perfectionistic tensions erupting through that generalized mathematical pattern. The two sides of the asymptote never touched, but always almost did. An asymptotic function was utterly discontinuous and yet beautiful in balance. Only one value could fill the asymptote, and it did not belong to the function.
Perfection is like an asymptote. No matter how hard we try, a perfect GPA, a perfect career, a perfect body, a perfect wardrobe, or a perfect partner will always be just out of reach, because all things eventually change, fade, or die. We cannot do anything to finally ascend to perfection, for it is infinite----a sad reality for us living creatures. Yet, only in light of this fact can we really feel free from expectations of entitlement----only when we see our efforts cannot give us one-to-one earnings are we able to feel like good things are gifts.
With regard to the asymptotic tension latent in perfectionism, it could seem that we are hopeless—if indeed we are finite and perfection is utterly infinite. But Christians believe that God entered into the world of physicality and suffered the plagues of entropy, change, and death. In the Incarnation of Christ----the birth of Jesus----the infinite becomes finite, suggesting that friendship is possible between infinity and finitude. For those familiar with complex analysis, consider the Riemann Sphere and the extended complex plane.
Yet, infinity becoming finite (or perhaps infinity being projected into some finite topological representation) does not seem intellectually or emotionally satisfying enough to me. For, in the words of the Oxford scholar and famed author C.S. Lewis,
We do not want merely to see beauty... we want something
else which can hardly be put into words--to be united with
the beauty we see, to pass into it, to receive it into ourselves,
to bathe in it, to become part of it.
--"The Weight of Glory"
In other words, we seek not merely to be surrounded with life to the full, but to become alive in the fullest; and if perfection has infinite properties, then we want not merely to be with infinity but to become infinity. We finite creatures want to soak infinity into our bones and be glued to it. All our desires for wellbeing suggest an endless fountain of life from which we can continually drink and be replenished. Whether or not the fabled Fountain of Youth exists is one matter; whether or not we want it is another. So, what would it require for infinity to be unified with finite creatures like ourselves?
Continuing my narration of Christ, in the crucifixion, Jesus’ death can be seen like a zeroing out of his life. Thus, in the death of God in Christ, infinity becomes zero. What would it mean if an infinity could be made equal to zero? What kind of algebra would this entail? This, I imagine, will be an interesting topic even to some who do not consider themselves Christians. As food for thought, I would like to point out some curious mathematical details relating to Holy Saturday. Note that I am taking some degree of creative liberty.
When zero is added to any finite number, is the number changed? What if zero is subtracted? Zero cannot add or take away from anything because it is, by definition, nothing. All things relative to infinity are zero, but all things relative to zero are something----that is, all non-zero, determinate numbers. Thus, zero has a sort of positive redemptive quality: it affirms the "somethingness" of numerical value. Personifying zero would make it appear non-competitive and peaceful with finitude. Stretching this concept a little further, all things that are are something; only nothingness can really be boundless and everywhere, for only nothingness belongs to all things (the empty set, the set of numbers containing nothing, is a subset of every set, for no member outside any set is not also outside the empty set).
It is like nothingness fills all things. Does this not resonate with us physically? Are we not mostly composed of empty space? Is not the vast majority of the known universe a void? Is not everything falling apart, doomed to entropy, change, or death? Does not the non-competitive, peaceful, and inclusive persona I have given to zero hint of a rich, indestructible, and non-finite love? What would it mean if we saw zero as a site of unification and rebirth rather than a fate of annihilation? Mathematically, I have alluded that zero has infinite-like qualities. What would this entail from a Christian point of view?
Today on Holy Saturday, Christians recognize the death of Christ and his burial in the tomb. They believe that, while dead, Jesus rescued those trapped by death, shattering its iron gates, and brought together all things, in heaven and on earth, under a banner of peace. Christians believe that as Jesus died, all things will likewise die. Today, Jesus, the finite manifestation of the infinite and eternal God, was nothingness. “[God] made him who knew no sin to be sin for us so that we might become the righteousness of God in him.” (2 Corinthians 5:21) On Holy Saturday, infinity became zero, and zero, by nature, is united with all things. Thus, through becoming nothingness, the rivalry between infinity and finitude is ended. In the nothingness, we find peace. In the nothingness we find everything.
Neat stuff? Christianity is not alone in recognizing the value of nothingness (or some variation thereof)----it is the basis of contemplative practices in many other religions, including Islam, Buddhism, and Taoism. In practice, communion with nothingness can look like silence, meditation, laughter, patience, rest, fasting and poverty, feasting and wealth, meekness, and love, among other things. For brevity, I will refrain from explaining why I say so. At the very least, I would like to comment that Buddhism’s concept of nothingness possessing an infinite loving quality is remarkably similar to Christianity’s narrative of God’s eternal love bringing peace through Christ’s death, and deserves further inquiry.
Here is my argument in summary: Perfection is an infinite slope we finite beings can never attain. If infinity were to become finite, the tension we experience toward perfection could be lessened. Yet, if infinity became nothingness, then finiteness itself could be unified with infinity, the rivalry between them being abolished, and, hence, the imperfect could be pacified with the perfect. The black hole of Holy Saturday is the foundation upon which all of life can flourish----a ground of non-being potent with re-creative energy----for in it, Christ renders peace, forgiveness, and unity to all things. In the same, all things are awaiting another nothingness: that of an empty tomb.
